ACCESIBILITY

BUREAU OF TRANSPORTATION STATISTICS UNITED STATES DEPARTMENT OF TRANSPORTATION

JOURNAL OF TRANSPORTATION AND STATISTICS

Volume 4 Numbers 2/3

September/December 2001

ISSN 1094-8848

SPECIAL ISSUE ON METHODOLOGICAL ISSUES IN ACCESSIBILITY

The views presented in the articles in this journal are those of the authorsand not necessarily the views of the Bureau of Transportation Statistics. Allmaterial contained in this journal is in the public domain and may be usedand reprinted without special permission; citation as to source is required.


MARY LYNN TISCHER Editor-in-ChiefSUSAN LAPHAM Associate EditorJOHN V. WELLS Associate EditorMARSHA FENN Managing EditorLISA PENDRICK Assistant to the Editor-in-ChiefDORINDA EDMONDSON Desktop PublisherCHIP MOORE EditorPEG YOUNG Statistical ConsultantMARTHA COURTNEY EditorLORISA SMITH Editorial AssistantKETREENA HAMILTON Editorial Assistant

KENNETH BUTTON George Mason UniversityTIMOTHY COBURN Abilene Christian UniversityANTONIO ESTEVE U.S. Department of TransportationSTEPHEN FIENBERG Carnegie Mellon UniversityGENEVIEVE GIULIANO University of Southern CaliforniaJOSE GOMEZ-IBANEZ Harvard UniversityDAVID GREENE Oak Ridge National LaboratoryKINGSLEY HAYNES George Mason UniversityDAVID HENSHER University of SydneyPATRICIA HU Oak Ridge National LaboratoryRICHARD JOHN Volpe National Transportation Systems Center, USDOTT.R. LAKSHMANAN Boston UniversityTIMOTHY LOMAX Texas Transportation InstituteGARY MARING U.S. Department of TransportationPETER NIJKAMP Free UniversityKEITH ORD Georgetown UniversityALAN PISARSKI ConsultantJEROME SACKS National Institute of Statistical SciencesTERRY SHELTON U.S. Department of TransportationKUMARES SINHA Purdue UniversityROBERT SKINNER Transportation Research BoardCLIFF SPIEGELMAN Texas A&M UniversityMARTIN WACHS University of California at BerkeleyC. MICHAEL WALTON The University of Texas at Austin

EDITORIAL BOARD



ISSN 1094-8848

JOURNAL OF TRANSPORTATIONAND STATISTICS

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iii


Volume 4 Numbers 2/3September/December 2001

Contents

Papers in This Issue

Introduction to the Special Issue on Methodological Issues in Accessibility Measureswith Possible Policy ImplicationsPiyushimita (Vonu) Thakuriah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Computational Tools for Measuring Space-Time Accessibility Within Dynamic Flow Transportation NetworksYi-Hwa Wu and Harvey J. Miller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Accessibility: Concepts and ApplicationsBritton Harris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Performance of Accessibility Measures in EuropeSiamak Baradaran and Farideh Ramjerdi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Accessibility Improvements and Local Employment: An Empirical AnalysisJoseph Berechman and Robert Paaswell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Evaluating Neighborhood Accessibility: Possibilities and PracticalitiesSusan L. Handy and Kelly J. Clifton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Path-Based AccessibilitySvante Berglund . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Guidelines for Manuscript Submission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93

Index of Reviewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95

Index to Volume 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .97

Introduction to the Special Issue onMethodological Issues in AccessibilityMeasures with Possible Policy Implications

Fundamental to urban and regional transportation analysis is the concept ofaccessibility. Because of the increasing complexity of transportation systemsand their impact on our quality of life, accessibility-based ideas must becomean integral part of transportation planning and evaluation. Although acces-sibility has been studied for a long time and there are various perspectives inits definition and measurement, it is fundamentally concerned with theopportunity that an individual at a given location possesses to participate ina particular activity or set of activities.

The objective of this special issue of the Journal of Transportation andStatistics is to facilitate a discussion on the issues involved in making accessi-bility-based considerations a routine part of transportation planning andevaluation. The measurement of accessibility has a rich, substantive history inthe urban and regional sciences. But, except for assessing the impacts of thetransportation system on special groups and for special purposes, plannersand policymakers have not routinely and continuously evaluated urban sys-tems on the basis of accessibility. However, as transportation planners areincreasingly called on to address a variety of social, economic, and environ-mental considerations beyond historical mobility-based considerations,accessibility measures must be developed and disseminated to practitioners toenhance planning practices and improve policy evaluations. Further, thedevelopment of data and software to estimate these measures will tremen-dously expedite this shift in planning practices.

The papers in this special issue reflect the diverse considerations that must betaken into account in developing means to measure accessibility. Some of thepapers address conceptual issues in defining and measuring accessibility,some target the development of applications tools, while others focus onempirical examples of accessibility measures.

As accessibility-based planning approaches take hold, the need for continuedresearch and development in this area will increase. It is our hope that thepublication of this special issue will raise awareness of the need to main-stream accessibility-based measures in planning and policy analysis andevaluation.

PIYUSHIMITA (VONU) THAKURIAH

Guest Editor

University of Illinois at Chicago

v

ABSTRACT

The space-time prism (STP) and STP-based acces-sibility measures are powerful techniques forassessing the ability of individuals to travel andparticipate in activities at different locations andtimes in a given environment. However, traditionalSTPs and STP-based accessibility measures ignorespatial and temporal variations in travel times in anurban environment. Factors such as traffic conges-tion impose increasingly complex and severe con-straints on individual travel and participation inactivities. This paper reports on the development ofdynamic STP-based accessibility measures andcomputational procedures for assessing individualaccessibility in networks with time-varying flow.We extend static network-based STPs to the casewhere network flow and travel velocities varyacross time due to congestion. These tools can eval-uate the accessibility of travelers under differenttraffic congestion scenarios, alternative networkflow control strategies, and activity scheduling poli-cies (e.g., flextime and telecommuting).

INTRODUCTION

Much travel behavior research focuses on under-standing an individual’s decision processes andanalyzing the elementary factors determining travel

1

Computational Tools for Measuring Space-Time AccessibilityWithin Dynamic Flow Transportation Networks

YI-HWA WU

HARVEY J. MILLERUniversity of Utah

Yi-Hwa Wu, University of Utah, DIGIT Laboratory, 260S. Central Campus Dr. Room 270, Salt Lake City, UT84112-9155. Email: [email protected].

activity. Consequently, most transportation plan-ning tools emphasize travel demand patterns andpredicting travelers’ responses to transportationpolicy and management options. These methodsconcern how or when travel activities will takeplace throughout the transportation system.Accessibility measures are alternative approachesthat emphasize the potential for travel behaviorconditioned by the performance of the transporta-tion system. Accessibility measures assess an indi-vidual’s freedom to participate in activities in agiven travel environment rather than explaining orpredicting actual travel choices. Because they high-light constraints on travel rather than revealedtravel choices that intertwine preferences and con-straints, accessibility measures can be a more sensi-tive assessment technique than analyses of actualtravel behavior (Hägerstrand 1970).

Conventional accessibility measures focus ontradeoffs between the attractiveness of opportuni-ties and the travel cost required to obtain theseopportunities (see, e.g., Geertman and Van Eck1995). These indicators usually measure attractive-ness through surrogates such as the size or varietyof the opportunity (e.g., store size for retail oppor-tunities) and travel cost through physical distance,travel time, or monetary cost. Accessibility is usu-ally measured with respect to key activity locationsfor individuals (e.g., home, workplace) and evalu-ates the transportation services provided to thesekey locations to assess their relative advantages(Burns 1979).

Conventional accessibility measures often neg-lect the fact that the temporal dimension alsoaffects individual accessibility. Limited time “budg-ets” or available time for travel and activity partic-ipation can constrain the participation time foreach activity and therefore reduce individual acces-sibility. Periodic activity schedules, conditioned byrequired spatio-temporal events such as a fixedwork schedule or child maintenance activities, varywidely but systematically by life stage, sex, socio-economic status, and culture. An analysis by Kwan(1998) suggests that space-time measures are moresensitive in capturing interpersonal differences inindividual accessibility than conventional meas-ures. Measures that do not capture temporal con-straints created by individual activity schedules are

a one-size-fits-all depiction of accessibility that isinsensitive to individual differences (Kwan 1998;Miller 1999; Miller and Wu 2000).

Hägerstrand’s (1970) space-time prism (STP) isa powerful conceptual tool that captures both spa-tial separation and temporal constraints that limitindividuals’ freedom to travel and participate inrequired and desired activities. Accessibility meas-ures based on the STP consider the spatial extent oftravel and available activity participation time dic-tated by individual activity schedules. Most of thesemeasures capture these schedules by measuringspatial separation with respect to anchor locations(e.g., home, work) and restricting travel extentbased on the individual’s time budget or free timefor travel and activity participation (Miller 1999;Kwan 1998).

A weakness of STP-based accessibility measures,and accessibility measures in general, is their treat-ment of travel times as static. Consequently, thesemeasures cannot capture the potential impacts oftransportation network congestion on accessibility.Traffic congestion is a major problem and policyissue in many cities (Cervero 1986; Plane 1995).The traditional suburb to central city journey-to-work pattern has been replaced by more complexcommuting patterns involving substantial suburb-to-suburb flows. Service sector working hours tendto be staggered and occupy more of the daily clockthan traditional employment. This results in con-gestion being spread beyond the traditional morn-ing and evening peak periods (Hanson 1995). Theincreasing saturation of urban transportation net-works means that localized incidents (e.g., con-struction or accidents) can propagate widelythrough the network. This suggests the need fornew tools to capture dynamic congestion patternsin urban transportation networks and the potentialfor these tools to affect accessibility.

This paper reports on the development ofdynamic space-time accessibility measures andcomputational procedures for assessing individualaccessibility in networks with time-varying conges-tion. We extend static network-based space-timeaccessibility measures to the case where networkflow and travel velocities vary across time due tocongestion. We also develop a computationaltoolkit that uses simulated dynamic traffic condi-

2 JOURNAL OF TRANSPORTATION AND STATISTICS SEPTEMBER/DECEMBER 2001

tions to calculate travel times based on the shortestpath routes through a network with dynamicflows. Our computational toolkit is coupled with ageographic information system (GIS), facilitatingspatial data management and visualization of theresulting accessibility regimes.

Following this introduction, there are six sec-tions to this paper:

Space-Time Accessibility reviews the conceptualand theoretical basis for the space-time accessi-bility measures.

Dynamic Space-Time Accessibility Constructsdiscusses the algorithm for calculating space-time accessibility within dynamic transportationnetworks.

Dynamic Congestion Modeling provides themethodology used for developing the dynamiccongestion module.

System Design describes the system configura-tion for the toolkit.

Example Calculations shows some preliminaryresults.

The Conclusion provides some summary com-ments and directions for continued systemdevelopment.

SPACE-TIME ACCESSIBILITY

Temporal Constraints and Activity Participation

Since all human activities occur in space and time,these dimensions are inseparable from the intrica-cies of human behavior (Hägerstrand 1970).Empirical research has shown that temporal con-straints can impact significantly the ability of indi-viduals to participate in activities. Time-policyresearch suggests that space-time accessibilityaffects individual travel behavior both in space andtime (Tacken 1997). Adding temporal constraintsthat affect the size of individuals’ choice sets canimprove prediction accuracy of behavioral choicemodels (Landau et al. 1981; 1982). The space-timeconstraint framework provides the fundamentalphysical constraints to define individuals’ potentialaction space (Dijst and Vidakovic 1997). Manyactivity-based travel models (e.g., Recker et al.1986) require time constraints to restrict the

number of possible activity schedules when pre-dicting individual activity programs.

Classical Space-Time Prisms

Hägerstrand’s (1970) time geography is an elegantand powerful framework for measuring constraintsto individual accessibility. Time geography incor-porates the spatial, temporal, and transportationelements that affect accessibility within a geo-graphic environment. In its classical form, theactivity pattern of an individual is a space-timepath in three-dimensional space where a two-dimensional horizontal plane represents geo-graphic locations and a vertical axis representstime. The path traces the spatio-temporal positionof the individual’s travel and activity behavior. Thelimits on this path create an accessibility regimethat is a connected and continuous set of positionsin space-time known as the space-time prism(Lenntorp 1976).

An individual’s activity schedule is usually con-strained by fixed (mandatory) activities. Themandatory activities typically include work, home,or other household maintenance activities (e.g.,driving children to school). The STP is an extensionof the space-time path during temporal intervalswhen the individual is free to participate, in discre-tionary activities. These are activities over which theindividual has relative control with respect to loca-tion and timing; examples include shopping andrecreation. The STP is the set of locations in space-time that are accessible to an individual given thelocations and duration of fixed activities, a timebudget for flexible activity participation, and thetravel velocities allowed by the transportation sys-tem. Instead of tracing the observed movementthroughout space of an individual over an intervalof time, the STP indicates what portions of space arepossible for an individual at each moment in time(Miller 1991). The STP also delimits the feasible setof locations for travel and activity participation in abounded territory of space and a limited interval oftime (Burns 1979; Miller 1991; Kwan 1998).

Figure 1 illustrates an STP. The three-dimen-sional volume bounded by the STP is called thePotential Path Space (PPS). An individual’s timebudget (available time for travel and activityparticipation), spatial constraints (fixed activity

WU & MILLER 3

locations that determine travel origin/destinationwithin the discretionary time period), and theavailable travel velocity in the environment deter-mines the PPS. The prism boundaries demarcatingthe STP result from the available travel velocitywithin the geographic environment. In the classicalSTP, travel velocity is assumed to be constantacross space for analytical simplicity.

The Potential Path Area (PPA) is the projectionof the PPS to planar (two-dimensional) space. ThePPA represents the purely spatial extent or area thatan individual can travel within a specified timebudget. It can be calculated directly without refer-ence to the PPS, with any stationary activity partic-ipation time excluded from the overall time budgetto reflect the reduced amount of time available fortravel (Miller 1991).

Several researchers have developed accessibilitymeasures based on the STP. STP-based measuresview accessibility as an individual’s ability to reachactivity locations given the person’s daily activityprogram and spatio-temporal constraints (Kwan1998). STP-based measures usually include the fol-lowing elements. First is a reference fixed-activityevent in space and time from where and when theaccessibility of an individual to other locations ismeasured. Second is a set of destinations (activitylocations) and their attributes representing the dis-cretionary opportunities available to an individual.Third is a transportation system that enables anindividual to overcome the spatial temporal sepa-ration of activity sites. Therefore, any STP-basedmeasure of accessibility may be defined as basically

a quantification of the opportunities for activityparticipation open to an individual from a givenlocation at a given time of day.

Lenntorp (1976) uses the PPS and the PPA tosimulate all possible activity schedules within anurban environment. Lenntorp’s simulation model(Program Evaluating the Set of Alternative SamplePaths) does not calculate the STP directly. Inputvariables are the general characteristics of the trans-portation system, the spatial distribution and oper-ational hours of activity, and a hypothetical activityschedule as variables. The hypothetical activityschedule provides constraints imposed by the fixedactivities. The fundamental assumption is thatgreater freedom for flexible activity participationimplies greater accessibility. Therefore, the numberof possible flexible activity schedules allowed by thePPS and PPA are a surrogate for accessibility.

Other researchers use mathematical and geo-metric methods to directly measure STP properties.For example, Burns (1979) uses geometric methodsto calculate the volume of the STP under differenttransportation environments (e.g., continuousspace versus different types of uniform networkmeshes, travel timing policies). The STP volume isa surrogate for individual accessibility. Similarmethods can be found in Kitamura et al. (1981)and Kondo and Kitamura (1987).

Forer (1998) develops a 3-D raster model usingtaxels as the basic building block for constructingan STP. Its GIS-based method overlays relevant lay-ers of geographic information (e.g., the transporta-tion network, activity locations) during eachdiscrete time interval comprising a temporal studyhorizon. This allows the analyst to visualize acces-sibility as a space-time “aquarium.” It also createsan accessibility mask for spatio-temporal queryingusing customized 3-D data structures. While effec-tive, a shortcoming is the same as for any rastermodel; that is, large data storage requirements asthe spatial and temporal domains of the problemgrow.

Network-Based Space-Time Prisms

The space-time framework provides a powerfuland elegant perspective for analyzing individuals’accessibility within the environment. Instead ofdirectly modeling travel interaction throughout the


Time

Geographicalspace

Potential path area

Potential path space

t2

t1

T

1/ v

T: Time budgetv: Travel velocity

FIGURE 1 Individual's Space-Time Prism (adapted from Miller 1991)

system, the STP provides a measure to describeindividual possible travel behavior under physicalconstraints. However, it is difficult to operate andapply in its classic form as a real-world accessibil-ity tool. The ideal geometries of the STP, PPS, andPPA result from the unrealistic assumption of aconstant and uniform travel velocity.

In order to improve the realism and applicabilityof the space-time prism approach, Miller (1991)developed an operational method for implement-ing a network-based space-time prism using GISprocedures. This approach uses link-based travelspeed, instead of uniform travel conditions,throughout the transportation system. TheNetwork Time Prism (NTP) is comprised of arcsand nodes in the transportation network ratherthan an unrealistic simple geometric set thatassumes constant travel velocities across space. APotential Path Tree (PPT) is a subtree of the net-work consisting of nodes and arcs reachable givenfixed activity locations and a time budget. Its rootis usually the travel origin, although it can also beanchored at the travel destination. Kwan and Hong(1998) extend this approach by incorporating cog-nitive (information, preference) constraints into thePPT. The study defines the feasible opportunity set(FOS) as the subset of opportunity locations avail-able to an individual, based on both temporal andcognitive constraints.

Miller (1999) develops space-time accessibilitymeasures (STAMs) of users’ benefits based on thePPT. These measures are consistent with behavioralchoice theory and with the rigorous Weibull (1976)framework for spatial interaction-based accessibil-ity measures. Miller (1999) also develops computa-tional methods for calculating these measureswithin the network itself for query and visualiza-tion purposes. Miller and Wu (2000) describes thearchitecture of a GIS toolkit for these measures andprovide examples for a detailed, urban-scale trans-portation network.

Using the urban transportation network to cal-culate space-time measures can provide a morerealistic method for evaluating accessibility relativeto classical time geographic measures. However,the previous approaches reviewed above do notconsider the temporal dynamics of real-worldtransportation networks. As mentioned in the

introduction, the increasing saturation of mostreal-world transportation networks means thatassuming static network conditions is as unrealisticas assuming constant travel velocity across space.Our objective in this paper is to implement thedynamic space-time accessibility measures within arealistic time-varying transportation network.

DYNAMIC SPACE-TIME ACCESSIBILITY CONSTRUCTS

The space-time accessibility measures in theresearch focus on how the constraints within urbanenvironments affect an individual’s choice of activ-ity. The space-time prism provides a direct frame-work for this type of accessibility measure. We usesimulated time-varying flows within a transporta-tion network to compute dynamic versions of thebasic NTP constructs.

In a Dynamic Network Time Prism (DNTP),travel times between locations vary with both spaceand time. Travel between any two locations in anetwork with time-varying flows must be con-strained by the start/stop time intervals for thetravel episode and traced along a finite set of con-nected arcs in space-time. Given a travel origin andstart time, a DNTP is a subset of a space-time net-work that indicates the maximum travel extentunder time constraints dictated by the individual’sactivity schedule, including the timing of the traveland activity episode.

A Dynamic Potential Path Tree (DPPT) is atime-dependent maximum coverage tree from anorigin to any network nodes given dynamic net-work flow conditions and a specified departuretime. The DPPT can be combined with geographicvisualization techniques, such as animation tools,to provide powerful visualizations of changingaccessibility conditions over time within a con-gested transportation network. It could also beused to support spatio-temporal network queriesbased on space-time accessibility and as input tomodels such as activity scheduling simulations.

The DPPT can be used to construct the dynamicopportunity set (DOS) of activity locations for anindividual. The DOS extends the FOS concept fromKwan and Hong (1998) to the case of dynamictemporal constraints imposed by time-varying traf-fic flow and therefore travel velocities. This oppor-

WU & MILLER 5

tunity set is based on the timing of travel from theorigin to the activity location, net any activity par-ticipation time:

where

M = the set of accessible discretionary activitylocations, given the travel origin, time budget, anddynamic network flow.

= the set of total discretionary activitylocations.

Tk = participation time at activity discretionaryactivity location k.

T = the overall time budget for travel and activ-ity participation.

= minimum required time for activity partic-ipation time at location k.

= the minimum travel time from xito xk given a departure at time d.

Equation (1) shows that the subset of feasible activ-ity locations must have greater activity participa-tion time (Tk) than the minimum required time fordiscretionary activity k. The minimum requiredtime for each discretionary activity could be stan-dardized for each activity or derived for individualsfrom activity diary data. The activity participationtime is the time budget minus the minimum traveltime The minimum travel time is con-strained by the start time from travel origin anddynamic network flows. Time budgets vary by indi-vidual; these can be extracted from activity diarydata or by self-reporting (see Miller 1999). Theprocedure calculates the dynamic shortest pathfrom the specified travel origin to all possible dis-cretionary activity points. The shortest path is veryeasily extracted once the DPPT is created.

Equation (1) creates a set of feasible discre-tionary activity locations rather than a subset of thenetwork arcs. This type of DNTP calculation onlydelimits feasible activity locations; it does not con-sider activity attractiveness as part of the accessi-bility measure (as in Miller 1999). However, it canbe used to delimit the activity choice set for furtherdynamic accessibility for input into dynamic ver-sions of the STAMs.

DYNAMIC CONGESTION MODELING

Since we need to construct DNTP measures basedon time-varying flow conditions, we require somemethod for computing these flows. The particulardynamic flow model that provides these estimatesis modular in the sense that any model is acceptableif it can generate realistic dynamic flow and traveltime estimates. However, the method must be com-putationally efficient due to the number of calcula-tions required for the DNTP measures.

Initial work on developing dynamic flow modelsbegan in the late 1970s with Merchant andNemhauser (1978a; 1978b). Several approaches tothe dynamic network flow problem have emerged,including: 1) simulation-based approaches; 2) opti-mal control theory; 3) variational inequality; 4)dynamic systems approaches; and 5) mathematicaloptimization. Although several dynamic networkflow models are available (see Friesz et al. 1996;Ran and Boyce 1996; Chen 1999), most of thesemethods (particularly continuous-time formula-tions) are not computationally efficient to thedegree required for the DNTP calculations of inter-est in this paper.

Equilibrium analysis is a relatively efficientapproach to modeling transportation networkflows. The equilibrium approach captures the rela-tionship between users’ travel decisions and net-work performance assuming shortest path travel.However, as Ben-Akiva (1985) argues, traditionalstatic network equilibrium models fail to capturefundamental properties of traffic congestion.Janson greatly improved the applicability ofdynamic network flow modeling to real-world net-work problems by developing a tractable discrete-time dynamic user optimal (DUO) approach(Janson 1991a; 1991b). Furthermore, the JansonDUO model can be solved for realistic, urban-scalenetworks with reasonable computational times(Robles and Janson 1995; Boyce et al. 1997) mak-ing it suitable for constructing DNTP. Because of itstractability, we use the Janson DUO model in ourDNTP procedures, although we can swap this forother dynamic flow models in future system devel-opment if breakthroughs allow more sophisticatedmodels to be solved efficiently.

The DUO is a direct extension of Wardrop’s useroptimal equilibrium conditions. The DUO condi-

( )t x xid

i k, .

( )t x xid

i k,

t km

Ω


( ) M k T t x x tid

i k km= ∈ = − ≥Ω | , ( )Tk 1

tion requires that, at network equilibrium, no trav-eler who departed or arrived during the same timeinterval can reduce his or her travel costs by unilat-erally changing routes. An alternative but equiva-lent statement is that all routes used between anorigin-destination (O-D) pair have the same mini-mal cost, and no unused route has a lower cost fortravelers that departed or arrived during the sametime interval. The DUO is based on either depar-ture or arrival times, not both. Since travel timesare variable, we cannot constrain both departureand arrival times within the equilibrium condi-tions. Therefore, the DUO conditions assumeeither a known (fixed) departure or arrival timeinterval for flows and require equivalent minimaltravel costs for all flows that depart or arrive dur-ing each interval. The DUO principle means thatpositive flow on a route for users who departed(arrived) during a given time interval implies that itmust have a travel cost equal to the minimum costfor the users between the particular origin-destina-tion pair. Second, any route with a cost greater thanthe minimum for users who departed during agiven time interval implies that the flow level forthose users is zero.

The DUO model assumes a known temporalO-D matrix, with each time slice corresponding toa discrete time interval over the study time horizon.Based on this exogenous data, the DUO minimiza-tion problem, when solved, determines thedynamic flow patterns that satisfies the DUO prin-ciple while meeting the O-D flow constraintsimposed by the matrices. The DUO problem is

Subject to

whereN = set of all nodesZ = set of all origin-destination zones (trip

begin/end nodes)L = set of all links (directed arcs)Ln = set of all links incident from node nP = set of all routes between all zone pairsPrs = set of all routes from zone r to zone sKp = set of all links on route pKpn = set of all links on route p prior to node n

= duration of each time interval (same forall t)

T = set of all time intervals in the full analysisperiod

= amount of traffic flow between all zonepairs assigned to link k in time interval t

= amount of traffic flow departing in timeinterval d assigned to route p

= travel impedance (travel time) on linkk in time interval t

= amount of traffic flow from zone r to zones departing in time interval d via any route

= 0-1 variable indicating whether tripsdeparting in time interval d and assigned to route puse link k in time interval t (0 = no, 1 = yes)

= travel time of route p from its origin tonode n for trips departing in time interval d

The dynamic constraints (equations 7–10)ensure temporal flow consistency. The temporalroute-link incidence variable maintains corre-spondence between links and routes across timeintervals for trips departing within a particular time

α pkdt

α pkdt

α pkdt

qrsd

( )f xkt

kt

ν pd

x kt

∆t

WU & MILLER 7

( )MIN f w dwk L t T

ktx k

t

∈ ∈∑ ∑ ∫ ( )2

0

x k L t Tkt

p P d Tpd

pkdt= ∈ ∈

∈ ∈∑ ∑ ν α for all , ( )3

q r Z s Z d Trsd

p Ppd

rs

= ∈ ∈ ∈∈∑ ν for all , , ( )4

ν pd p P d T≥ ∈ ∈0 5for all , ( )

α pkdt

pp P k K d T t T∈ ∈ ∈ ∈ ∈01 6, , , , ( )for all

α pkdt

t Tpp P k K d T t T= ∈ ∈ ∈ ∈

∈∑ 1 7for all , , , ( )

( )b f

p P n N d T t T

pnd

t T k Kkt

pkdt

pn

=

∈ ∈ ∈ ∈∈ ∈∑ ∑ x k

t α

for all , , , (8)

[ ]b pnd

pkdt− ≤

∈ ∈ ∈ ∈ ∈

t t

p P n N k L d T t Tn

∆ α 0

9for all , , , , ( )

( )[ ]b pnd

pkdt− − ≥

∈ ∈ ∈ ∈ ∈

t t

p P n N k L d T t Tn

1 0

10

∆ α

for all , , , , ( )

interval. This is a temporal extension of the staticroute-link incidence variable in the static version ofthis problem (equations 2–5 without the timedimension). However, a major difference is that thetemporal route-link incidence is an endogenousdecision variable solved within the dynamic equi-librium problem. In the DUO, the link compositionof routes for trips that departed within a given timeperiod cannot be predetermined since the timeinterval of link use is affected by travel time, whichin turn is affected by traffic flow loadings (Janson1991a).

The endogenous nature of route-link incidencein the DUO requires the problem to have nonlineardynamic flow constraints to ensure flow consis-tency. First, we require trips to only use each linkon a given route only once within each time inter-val (equations 6–7). Second, we require each routeto be consistent with respect to the required traveltimes to reach each link on the route. To ensurethis, we measure the total travel time on a routefrom the origin to a given node for trips departingwithin a given time interval (equation 8). Then, weforce trips to use the links on a route in a tempo-rally consistent manner. Trips can only use a linkduring the interval that it reaches the from-node ofthe link according to the cumulative travel time tothat from-node. If cumulative travel time to thefrom-node is greater than or less than the cumula-tive clock time then the temporal route-link inci-dence variable is forced to zero and the routecannot use that link (equations 8–10).

We can solve the DUO problem efficiently usinga heuristic procedure that assigns link flows basedon current flow levels, future travel demands, andflows assigned in previous intervals. An alternative,exact algorithm decomposes the main DUO prob-lem into two subproblems, namely, a static UOassignment subproblem and a linear program thatupdates the temporal incidence variables andenforces conditions for temporally continuousflows. For detailed discussion of these solution pro-cedures, see Wu et al. (2001).

SYSTEM DESIGN

Our current software system integrates three majormodules for performing dynamic accessibility meas-ures. Commercial GIS software (Arc/Info® version

7) provides the data management and visualizationfunctions. We implement a dynamic traffic modulebased on Janson’s (1991a) formulation for provid-ing dynamic flow simulation. An accessibility meas-ure module uses the dynamic network flowconditions as space-time constraints to calculate theDNTP. Both modules are stand-alone systems writ-ten in C. Although both modules run as sepa-rate programs, the programs directly read and writeArc/Info® INFO files, allowing the GIS software tomanage the input data and visualize model results.Figure 2 shows the basic system architecture.

Both transportation network and activity loca-tions data are processed into Arc/Info® coverages.The dynamic traffic module reads the networkstructure from coverages and writes new INFOfiles with dynamic flow information, one file foreach time interval modeled. These can be visualizedand queried within the cartographic context of thenetwork coverage using Arc/Info®. The accessibil-ity measure module retrieves dynamic flow infor-mation from these new INFO files and calculatesthe DNTP. The results transfer back into Arc/Info®

and create new coverages. Two discrete space ver-sions of DNTP can be visualized and queriedwithin Arc/Info®. Point entities represent anopportunity set of locations that are choices forindividual activity participation. Arc entities repre-


VisualizationSpatio-temporal

datamanagement

GIS

Arc/Info

DUO modelDynamic Network

Time Prism (DNTP)

Dynamicnetworkmodule

Dynamicaccessibility

measure module

FIGURE 2 System Architecture

sent the subset of space (defined by transportroutes) that is feasible to travel. These can be useddirectly to access accessibility regimes given a con-gested network.

The current prototype performs data transfersbetween the three modules. The user interface isstill in progress. We expect to more fully integratethe three modules using Arc/Info® version 8, whichprovides more powerful interface functionalitythan earlier versions.

EXAMPLES OF CALCULATIONS

We now provide examples of calculations of theDPPT for a realistic problem. The network in thisexample represents northeast Salt Lake City, Utah.It contains 7,812 directed links, 2,328 nodes, and

331 O-D zones. The discrete time interval for theDUO model is three minutes. A 2-hour study timehorizon results in 40 consecutive time slices ofdynamic congestion patterns. A daily O-D matrixwas derived from a travel survey conducted by theUniversity of Utah during spring 1994. We con-structed a local daily peak profile curve to mimicthe aggregate peak hour commute patterns in thestudy area. Therefore, traffic patterns during thefirst and last few intervals are less congested thanthe middle intervals within the modeled time hori-zon. We use the standard Bureau of Public Roadsperformance functions to calculate traffic flow ineach time interval.

Figure 3 shows an example of a dynamic con-gestion pattern for the university area of the Salt

WU & MILLER 9

Very congested

Normal traffic

N

S

W EScale 1:40,000

Miles

0 0.25 0.5 1

0 0.25 0.5 1

Kilometers

FIGURE 3 Dynamic Congestion Pattern in Salt Lake City, Interval 1 (Top) and Interval 20 (Bottom)

Lake City network (northeast corner of study area)in different time intervals estimated from the DUOmodel. For display purposes, we offset the two arcscorresponding to two-way travel within each streetsegment. We classify the congestion level in eacharc into two categories, namely, “very congested”for flow of 80% of capacity or greater and “normaltraffic” for flow levels less than 80% of capacity.The upper half of figure 3 shows the traffic condi-tions during time interval 1 or the first three min-utes of the time horizon. The lower half of figure 3shows the peak traffic conditions in interval 20,which is 57 to 60 minutes into the study horizon. Acomparison of the two graphics shows the tempo-ral flow complexity captured by the DUO model.

Figures 4–8 provide examples of DPPT calcula-tions for the Salt Lake City transportation networkfrom the GIS-DNTP software system. Figures 4and 5 represent the DPPT for a single origin (theUniversity of Utah) and single departure interval(time interval 15, or 42 to 45 minutes into the

modeled time horizon). Figure 4 shows the accessi-ble portion of the transportation network given afive-minute time budget for travel. Figure 5 showsthe accessible portion of the network given a 15-minute time budget for travel. As is the case withthe NTP, the accessible portion of the network isgreater if the available time budget is larger. Aftercalculating the DPPT, the system assigns therequired travel time to each node. We can then usethis information to query activity locations georef-erenced at network nodes to calculate the DOS(equation 1).

Figures 6–8 show DPPTs given the same originand time budget (10 minutes) but based on differ-ent departure time intervals. Figure 6 provides theDPPT based on departing at time interval 1 (threeminutes into the modeled time horizon), figure 7shows the DPPT based on departing in time inter-val 15 (42 to 45 minutes into the horizon), and fig-ure 8 shows the DPPT based on departing duringtime interval 20 (60 to 63 minutes into the hori-


FIGURE 4 Dynamic Potential Path Tree in Salt Lake City, Given 5 Minutes Travel Time

Time interval 15

Origin

Scale 1:80,000Miles

0 0.5 1 2

0 0.5 1 2

Kilometers

N

S

W E


zon). Since the traffic conditions are dynamic, thereachable portion of the network varies dependingon the departure interval. In figure 6, the DPPT hasa relatively large spatial extent due to the low traf-fic flows and higher travel velocities during the ini-tial portion of the modeled time horizon. As trafficflow builds during the middle time periods, the spa-tial extent of the DPPT becomes more curtailed(figure 7), particularly towards the central portionof the city (downtown is the area in the middlenorth of the map, just west of the DPPT extent). Bythe later time intervals, traffic has started to easeand the DPPT spreads outward (figure 8). Notethat the DPPT extends substantially toward thesouth in time interval 20 since traffic flows easefirst in these more peripheral locations of the city.

CONCLUSION

This paper introduces realistic conditions of time-varying flow and congestion within the transporta-

tion network for dynamic space-time accessibilitymeasures. This allows the accessibility measures toconsider the locations and time-varying travelvelocities dictated by the network. These computa-tional procedures are tractable with respect to stor-age space and time requirements, meaning they canbe applied to urban-scale accessibility analyseswith detailed networks. The GIS environment sup-ports visualization, querying, and additional analy-sis of accessibility within the transportationnetwork structure.

The dynamic space-time accessibility measuresin this research only consider the space-time con-straints within the urban environment. The DPPTwe construct is from a specified origin given avail-able travel time and departure time interval.Moreover, DPPT in this research is a path tree thatdepicts travel from a given origin node that termi-nates at network nodes. In other words, the resultsare the subset of original network arcs. In our con-tinuing research, we are developing a Dynamic

WU & MILLER 11

Time

Time interval 15

Scale 1:80,000Miles

0 0.5 1 2

0 0.5 1 2

Kilometers

N

S

W E Origin


Potential Network Area (DPNA) that extends the

potential tree into a potential area. This means that

the travel path can terminate at any location in the

network, even at a location within an arc. This will

be a dynamic version of the extended shortest path

tree developed by Okabe and Kitamura (1996).

In this current stage, we did not include activity

schedules in the calculation of DNPT. A more sensi-

tive dynamic accessibility tool would calculate the

potential path area based on archoring mandatory

activity locations (e.g., home and work locations).

Moreover, the attractiveness of discretionary activity

locations and participation time for activities have

also been ignored in this current research. The objec-

tive of further research is to capture the interactions

between transportation system performance, the

locations of mandatory and discretionary activities,

and the individual’s activity schedule using the

STAMs developed by Miller (1999).

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ABSTRACT

The character of accessibility as measuring the situa-tion of a location in a region rather than its intrinsicqualities is emphasized throughout this paper. Abrief characterization lays the basis for a sketch ofdata requirements, a specification of operationaldefinitions, and a review of earlier findings. The ideaof accessibility under competition is developed withseveral formulations, which are then comparedthrough a synthetic example. Concluding commentssuggest some guidelines and future directions.

INTRODUCTION

This paper will not attempt to serve as a generalreview of the literature on accessibility or of generalpractice in measuring and using it. Rather, it is anattempt to crystallize my own experience and think-ing on the subject and to present a somewhat nor-mative view of how the term accessibility should bedefined and used. The ideas presented here are anextension of my much earlier “Notes onAccessibility” (Harris 1966). This note enjoyed lim-ited circulation, but was never published in a jour-nal. Here I also present a view of spatial competitionapproached through accessibility measures.

The following first three sections of the paperdiscuss the general nature of accessibility, the datarequirements for its calculation, and possible exact

15

Accessibility: Concepts and Applications

BRITTON HARRISProfessor EmeritusUniversity of Pennsylvania

Britton Harris, 114 West Rittenhouse Street, Philadelphia,PA 19144-2714. Email: [email protected].

definitions. Conclusions from earlier work aregiven. Then these definitions are expanded to dealwith spatial competition, and a synthetic exampleis presented with some procedural suggestions. Aconcluding section discusses applications of thesemeasures in a more general context.

THE NATURE OF ACCESSIBILITY

The Oxford English Dictionary defines access, anoun, as amongst other things: “the habit or powerof getting near or into contact with. . . .” Clearlythere is a mechanism governing ease of access. Indealing with locational matters, I focus on theinfluence of separation or distance in reducingaccess, which is thus universally applicable and ofgraded difficulty. Other impediments to accessmight require additional treatment.

Access is between entities, and most usuallybetween actors, but we may conveniently in manycases replace entities with locations, usually assum-ing that these contain aggregates of entities andactors. The appropriateness of this aggregationmust be constantly reviewed.

Accessibility is a measure of ease of access,which must be further defined. Generally, access issymmetrical: if A has access to B, then B has accessto A; however, its measurement may be asymmetri-cal. Most common measures, scoring separation inspace, define inaccessibility, or the opposite of easeof access. For the common-sense definition ofaccessibility I will focus on declining functions ofseparation and discuss them more fully in the sec-ond following section.

Access is not in general one-sided; we should notsay that a given community has “good access”without specifying “access to what.” For a pair ofentities or locations we may define a measure ofaccess, depending on their separation, but such asingle quantity does not have much analytic power.A set of single measurements with one end fixed,such as the distance from the central business dis-trict (CBD), permits us to compare localities withrespect to their centrality or their removal fromsome single center of interest. If we convert dis-tance to some actual costs of access, we get a meas-ure that may vary over time and may then providea changed ranking of localities by centrality. If weaggregate the access measures to the CBD over the

region, we can compare its centrality with that ofother single facilities such as an airport, sports sta-dium, parks, or outlying recreational areas forwhich we might make similar aggregations.

These approaches help us understand the natureof accessibility, but they do not capture its essence.Most metropolitan locational decisions considerthe variation across localities not only of immedi-ate local conditions, or of the accessibility to singlefacilities, but also of situational variables related tothe entire region. Thus there are many suburbancommunities with virtually identical local condi-tions, but with differing proximity to employmentopportunities of different types and to other signif-icant facilities. Useful and meaningful accessibilitymeasurements provide a way to secure a synopticview of locational qualities that result from non-local influences.

This view depends on three factors that our cal-culations will have to bring together. We imagine abeholder taking a view of the region from one loca-tion after another. First, we select a target beingviewed as it is distributed over all locations in theregion. Second, we identify those variations in costof access between the viewing point and other loca-tions that will influence choices. And third, wedecide how a view will evaluate these costs asdiminishing the importance of less accessible tar-gets. I will propose that accessibility be measured,zone-by-zone, by a weighted average of access fromeach zone in the region to some target of opportu-nity in all other zones.

There are thus three essential elements needed toimplement this conception: a distribution of one ormore targets, a measurement of separation betweenzones, and a definition of the functional form ofthis weighted moving average that can reflect vari-ations in attitudes toward interaction. In the nexttwo sections I discuss the data required to supportthese ideas and the formal statement of a functionalrelationship.

DATA REQUIREMENTS

As to data, measuring and computing accessibilitiesrequires: first, a system of subareas that subdividea larger defined region (preferably exhaustively);second, one or more sets of measurements of thepairwise separation of the subareas; and third,


areally distributed data sets of people, activities,and entities of interest. I will limit the possiblechoices in this discussion, but many changes andextensions are possible.

Conventional analysis focuses principally onmetropolitan regions, divided into traffic analysiszones, census tracts, or aggregations of these. Validmeasurements of separation include airline dis-tance, route distances, travel time, cost, lack ofsafety or convenience, amenity, and weighted com-binations of these. These measurements may varyby mode and time of day, and according to personalchoice procedures for routes. (Measuring thesequantities between the centroids of subareas intro-duces virtually unavoidable error. A special andimportant case is within-area travel; its nominalzero cost is often replaced by an estimated average.)

Data needed by subarea may include at least oneof the following: jobs, establishments, workers attheir residences, households, dwellings, vacantland, or facilities serving shopping or recreation, aswell as those serving public health and safety. Thesecategories can, and often should, be subdividedinto more narrowly defined strata, including thosedefined by race, income, gender, family size, andthe like.

Much of the foregoing information is readilyavailable in transportation studies, but in boththese and land-use studies very few items of dataare deployed in any significant detail, even whenmost or all of it is stored in a geographic informa-tion system (GIS). Most land-use studies make lim-ited use of large matrices of zone-to-zone time andcost. Transportation analysis pays little attention todetails of housing types and probably too littleattention to detailed aspects of ridership. Yet withincreasing frequency these two types of studies arebecoming more interdependent, and demands ofequity are side-by-side with those of pollution con-trol in calling for more detailed analyses.

Given the very large computational load in bothtransportation analysis and accessibility computa-tions, it is desirable to focus on relatively few vari-ables for these particular activities. More work willbe needed to determine what accessibility compu-tations capture all the variables that differentiallyaffect locational choices. Analysis of those choices,in turn, may influence the way in which trans-

portation demand analysis interprets travel behav-ior. After a reasonable period of further study, thescope and detail of accessibility calculations maypossibly be reduced without impairing its potentialpower.

FORMALIZING THE CONCEPTS

The idea of accessibility as a weighted moving aver-age of access to targets or “opportunities” may beillustrated in a very simple way, which incidentallydefines a technique that can easily be adapted to theuse of GIS.

Suppose that we are talking about the accessibil-ity of various locations to retail trade customers.Imagine that we have a circular disc with a radiusof one mile. We place the center of that disc on themap centroid of a zone of concern. We tally up allthe customers in locations on the map within thecircle. This tally represents the total accessibility tocustomers of that location. If we divide by the totalof all customers in a relevant region, we have anaverage accessibility which is defined by the pro-portion of all customers who are within one mile ofthe center under study. If we were to use a largercircle, we would have a different average, the firstperhaps applicable to food shopping and the sec-ond to apparel. (The graphic illustration of a circlecan have as a radius only a map distance, but cal-culations could be based on actual time or cost.)

What we have described is a simple weightedaverage: every customer, in or out of the circle, is aweight; the accessibilities of customers within thecircle are all 1 and those outside are all 0. Theweighted sum is simply the count of those cus-tomers within the circle, and the sum of the weightsis all customers. This generalizes to a series of con-centric rings, to which the center has decliningaccessibilities, measured by their inverse radii andweighted by their populations. It can also beextended to deal with, say, purchasing powerinstead of customers. In each case, the result, whenthe weighted sum has been divided by the total tar-get, which is the sum of the weights, including thesewith 0 access, is a kind of proportionate accessibil-ity to the total “market.”

We can now move the disc in any direction, cen-tering it on another zone centroid, and we get anew average. The reader may object, and rightly,

HARRIS 17

that there is a likelihood of error when we deal withareas and their centroids, rather than with the “pre-cise” location of individuals or houses. With mil-lions of houses in large cities, the aggregation byarea is a practical necessity that may be mitigatedbut not eliminated.

I now seek a more flexible measure of accessbetween pairs of locations, which as I have suggestedought to be a declining function of their separation.Unlike the GIS approach just discussed, this functionshould be continuous. Accessibility has a close con-nection with the earlier gravity models, which withtheir implicit connection to Newtonian gravitationused first an inverse square of distance and later ageneral negative power of distance. Distance itselfwas generalized to a composite cost, which mightbecome route distance, time, or monetary cost, orsome combination of such variables as impedeaccess. This definition of access has been modified inlater practice to a negative exponential function,which I will use. The two definitions are equivalent,because if we use the logarithm of composite cost inthe exponential function, it reduces to the negativepower function. (The negative power function has asingularity when the cost equals 0, while the negativeexponential varies from 0 to 1.) More complicatedfunctions may be employed.

Once we have chosen a measure of accessbetween pairs of points, it remains to define themeasure of accessibility as a weighted sum or aver-age of these measures. For any future behavioralanalysis that we may attempt, the appropriateweights would be the targets of behavioral inter-est—such as jobs or shops for resident workers orshoppers, or workers or customers for businessestablishments. Behavioral considerations such aswillingness to travel or completeness of informationinfluence the choice of parameters for any decliningfunction of distance, but the analysis of behavioritself goes beyond the measurement of accessibility.

I will now examine in some more detail the rela-tion of accessibility to some other behavioral con-cepts used in land-use and transport analysis, at thesame time providing a more precise definition ofaccessibility itself.

Let’s first set out a useful example of a definitionof accessibility, designated by Wilson as “HansenAccessibility,” from Hansen’s seminal paper on

“How Accessibility Shapes Land Use” (1959).Hansen accessibility for a given subarea i, to allother subareas j, each containing a sub-populationWkj of some total population of opportunities Wk,is given by:

Where the impedance function f is now usuallyspecified, with C a generalized cost and b a non-negative parameter, by:

fij = exp(–bCij) (2)

When b is small there is little impediment to access,so that accessibility is high, and vice versa.

The foregoing may be modified in a simple waythat facilitates both computations and interpreta-tion. We define the population or target of interestin each subarea as a proportion of the total popu-lation. Hence using lower case variables:

wkj = Wkj/Wk (3)

and

The a’s now represent an average accessibility andcorrespond inversely to a kind of average cost,which can be readily calculated as an average costincurred in accessing activity k from location iunder the current value of b:

cik = –ln(aik)/b (6)

This average approaches 0 as b becomes very large,and becomes larger as b approaches 0. This resultcorresponds with the fact that b represents a meas-ure of unwillingness to travel.

It should be clear that using a normalized popu-lation involves only a change of scale in the acces-sibilities and does not, in a behavioral analysis,


A W fik kjj

ij= ∑ ( )1

( )41w kjj

=∑

( )5a w fik kj ijj

= ∑

affect most comparisons between locations of theresults from computing the values of a with thesame b, k, and set of costs.

It is also important to note the relation betweenHansen accessibility as in either definition above,and the logit or multinomial logit model of discretechoice theory. Discrete choice is based on a conceptof utility, either as a weighted sum of the logarithmof variables contributing to utility or as the productof the exponentiated variables. These are equiva-lent as measurements of utility, but the exponentialform leads to more appropriate definitions of theprobability of choice. (This form has some similar-ity with the Cobb-Douglas production function.)Since C is a measure of disutility, it carries a nega-tive coefficient (-b) that would be reweighted if aspecific accessibility variable were used in a behav-ioral analysis.

With a view to further exploration, this defini-tion of accessibility can be related to the singlyconstrained gravity model, as discussed by Wilson(2000) in a limited context. This model derives thenumber of trips T between subareas i and j by allo-cating the number of originating trips at i, Oi, inproportion to the number of destinations at j, Dj,and in inverse proportion to the impedance or costseparating the two zones. In order to ensure thatthe correct number of trips is distributed from eachorigin, a proportionality factor (call it G) isintroduced:

Tij = GiOiDjfij (7)

with

so that

Pj | i = Djfij/Ai (9)

Thus the proportion of trips leaving i for j is exactlyj’s share of the total Hansen accessibility of i.

EARLIER SUBSTANTIVE CONCLUSIONS

Up to this point I have summarized, with some elab-oration, the basic ideas of my earlier Note. There are

two empirical findings of which we may also takeaccount. First, I found that for fixed k and C, theresults of measuring Hansen accessibilities over dif-ferent b-values were closely related. Accessibilitiescalculated with intermediate values could beexpressed with great accuracy as linear combina-tions of more extreme values. This finding meritsfurther theoretical and empirical investigation.

The second finding was based on a brief explo-ration of accessibility in Hartford, Connecticut, atthe census tract level, using five classes of employ-ment, two modes of travel, and two values of b,corresponding to short and long trips. These 20measures of accessibility for over 100 tracts weresubject to principal component analysis. The firstcomponent defined a general accessibility thataccounted for over 80 percent of the variance.Three other much smaller components accountedfor nearly all the rest of the variance. They meas-ured the difference between auto and transit acces-sibility, accessibility for short and long trips, andaccessibility to manufacturing employment versesall other employment. This analysis is carried outfor populations in an urban area and is shown intables 1 and 2.

These two findings suggest that, although inprinciple scores or hundreds of measures of Hansenaccessibility can be defined, the intrinsic structure ofurban activity distributions and their transportationconnections limits the dimensionality of its signifi-cant variation, perhaps to as few as 5 or 10 com-posite measures. This possibility could be explorednot only in its own right in connection with loca-tional modeling, but as a powerful means of defin-ing and comparing different urban structures.

ACCESSIBILITY UNDER COMPETITION

Anticipating the behavioral applications of thesemeasures, I now discuss a subtle but crucial modi-fication. In many instances, accessibility is notmeasured correctly if we fail to take into accountthe competition from other subareas for access tothe target population. For instance, when consider-ing locating a new shopping center, a developer willmeasure the accessibility to customers—yet if alocation has high accessibility to customers, but iswell served by other nearby centers, it will not beattractive. In some sense, the most attractive

HARRIS 19

G D f Ai j ij ij

= =∑1 1 8/ / ( )


TABLE 1 Mapped Hypothetical Distributions of Strata and Totals of Number of Workers (In thousands; components may not sum to totals because of rounding.)

At place of residence At place of work________________________________________ ________________________________________

Low income13 11 9 8 6 5 3 4 4 3 4 4 6 412 10 9 7 5 4 2 5 4 5 4 7 7 516 14 13 11 7 3 2 18 7 8 6 5 6 424 12 24 27 20 8 4 32 18 14 14 14 7 424 8 39 4 31 4 3 22 14 22 72 22 14 9

Middle income18 16 14 13 11 9 7 3 3 4 5 14 5 47 16 22 20 18 16 14 5 5 4 8 19 22 57 7 11 14 18 14 11 22 4 4 5 6 6 57 4 4 6 7 7 7 32 27 11 14 11 5 67 11 11 11 11 14 11 27 14 16 54 11 8 4

High income4 5 6 7 8 12 12 0 0 0 2 14 5 12 4 5 6 7 9 12 0 0 0 5 18 14 71 2 3 3 5 5 6 5 2 2 3 8 7 51 1 1 1 2 5 7 2 2 5 5 9 5 25 12 9 5 2 12 12 2 2 5 46 9 5 3

Total34 32 30 27 25 25 22 6 8 7 11 31 16 1021 30 35 33 31 30 29 11 9 9 16 44 43 1724 24 26 29 30 23 19 44 14 14 15 19 19 1532 17 28 35 29 20 18 67 47 30 33 34 17 1235 30 59 19 44 30 26 51 30 42 172 42 28 16

Correlations among the eight distributions displayed above1.000 –.364 –.499 .706 .281 .198 –.166 .149–.364 1.000 .255 .291 –.287 –.262 .051 –.207–.499 .255 1.000 .035 –.206 –.190 .053 –.144.706 .291 .035 1.000 .058 –.014 –.136 –.018.281 –.287 –.206 .058 1.000 .886 .720 .959.198 –.262 –.190 –.014 .886 1.000 .705 .948

–.166 .051 .053 –.136 .720 .705 1.000 .849.149 –.207 –.144 –.018 .959 .948 .849 1.000

Principal components analysis of correlations: five eigenvalues and eigenvectors

Trace and cumulative proportions:3.675456 1.951240 1.358312 .711515 .201458.459432 .703337 .873126 .962065 .987247

Principal components or loadings:.140507 –.680508 .073444 .114835 –.180187

–.166218 .215088 .639869 –.582576 .221978–.135377 .397800 .375140 .779367 .051789.001011 –.472908 .635321 .143169 –.052576.502884 –.017996 .045421 .059499 .149829.494478 .034554 .018589 .025862 .559322.414416 .314258 .180428 –.123674 –.757517.514936 .092106 .076467 .001820 .060758

HARRIS 21

TABLE 2 Illustrative Set of Simple Accessibilities: b = 1.0

Accessibilities to 4 residence and 4 workplace distributions over 35 zones

.088 .103 .054 .087 .045 .045 .016 .039

.103 .132 .081 .110 .056 .057 .029 .051

.100 .143 .105 .118 .057 .068 .053 .060

.088 .141 .127 .117 .058 .082 .102 .077

.071 .130 .149 .110 .058 .103 .166 .097

.052 .110 .166 .098 .055 .084 .133 .082

.033 .079 .143 .073 .041 .055 .082 .055

.117 .100 .058 .098 .079 .082 .030 .071

.139 .150 .088 .134 .092 .094 .048 .084

.138 .181 .116 .151 .095 .099 .080 .093

.124 .187 .141 .152 .091 .117 .145 .112

.099 .178 .166 .144 .091 .141 .223 .138

.069 .154 .182 .126 .080 .130 .199 .124

.042 .113 .163 .095 .056 .075 .127 .078

.144 .089 .054 .104 .135 .145 .057 .124

.173 .123 .082 .135 .142 .139 .077 .128

.180 .153 .104 .154 .144 .133 .113 .134

.167 .172 .123 .160 .139 .137 .162 .143

.132 .176 .146 .152 .123 .134 .204 .144

.087 .154 .158 .128 .098 .112 .182 .120

.049 .111 .140 .092 .065 .074 .125 .081

.161 .075 .058 .106 .178 .187 .058 .158

.184 .096 .084 .129 .189 .200 .092 .174

.217 .114 .096 .152 .200 .178 .151 .181

.213 .130 .104 .158 .208 .179 .207 .196

.172 .135 .120 .147 .175 .147 .212 .171

.106 .124 .141 .120 .120 .104 .158 .121

.057 .094 .131 .087 .072 .069 .100 .076

.137 .059 .067 .092 .144 .157 .050 .130

.152 .083 .109 .116 .169 .164 .086 .150

.207 .095 .110 .143 .211 .178 .160 .188

.160 .103 .096 .124 .288 .225 .311 .267

.165 .106 .096 .128 .193 .140 .202 .173

.091 .104 .135 .105 .126 .091 .131 .113

.049 .078 .124 .076 .074 .054 .079 .067

Corresponding simple correlations:1.000 .059 –.530 .718 .831 .792 .184 .747.059 1.000 .438 .709 –.193 –.074 .341 –.028

–.530 .438 1.000 .073 –.356 –.243 .534 –.118.718 .709 .073 1.000 .490 .553 .486 .575.831 –.193 –.356 .490 1.000 .912 .482 .954.792 –.074 –.243 .553 .912 1.000 .491 .947.184 .341 .534 .486 .482 .491 1.000 .687.747 –.028 –.118 .575 .954 .947 .687 1.000

Principal components analysis of correlations: five eigenvalues and eigenvectors

Trace and cumulative proportions:4.415775 2.160169 1.140605 .155717 .102185.551972 .821993 .964569 .984033 .996806

Components or loadings:.418009 –.176421 –.344916 .122811 .441656.056761 .562616 –.492121 –.215538 –.396866

–.100144 .580724 .376128 .596376 .312132.351189 .317475 –.446917 .154137 .243516.446447 –.178123 .158879 –.147357 .243650.446582 –.099333 .131797 .472199 –.645353.281951 .415457 .441514 –.558792 .049976.458735 –.010425 .245144 –.045879 –.111209

locations will have the greatest difference betweenaccessibility to customers and accessibility to othershopping locations. The reverse case in thisinstance is not so clear. A residential area accessibleto shops will not be so adversely affected by thecloseness of other residences unless this leads toegregious overcrowding in the shops. Other casesare more symmetrical. The value of accessibility tojobs from home is diminished by the accessibility ofthe same jobs to other residents. Conversely thevalue to an employer of accessibility to workers isdiminished insofar as the nearest workers haveaccess to many other jobs.

In the event that a market and source of supplyare in perfect spatial balance, the accessibilities toeach should be similar in every location, and no sitewould offer opportunities for greater competitiveadvantage than other sites to either suppliers ordemanders. (It is not clear that this concept of bal-ance would apply under all definitions of imped-ance or cost, or to all levels of unwillingness totravel, as indicated by the level of the parameter b.)I distinguish three basic approaches for opera-tionalizing this concept, all giving somewhat simi-lar results.

First, we may directly compare the accessibili-ties, forming either their difference or their ratio. Aparticular new location is more advantageous tothe supplier or the market, depending on which hasthe lower accessibility from this location. Thebehavior of locators following this rule wouldmodify the relative accessibility in this location soas move the two sides of the market toward spatialbalance. Considering only the accessibilities apply-ing to these two activities, an area favorable for thelocation of one is unfavorable for the other. Wemay thus define two new accessibility variables.(From this point, we will usually assume that allaccessibilities and target populations are normal-ized, without using the lower case representation.)The first of these new variables is the accessibilityto population 1, discounted by the proximity ofpopulation 2, while the second is the inverse of this:

Ai3 = Ai1/Ai2 (10a)

Ai4 = Ai2/Ai1 (10b)

The second approach is one developed by Shen(1998). He calculates the accessibility of each oftwo activities, which we again designate as 1 and 2,from every subarea. He then recalculates the acces-sibility on the basis of one of the two new variablesdefined by

W3j = W1j/Aj2 (11a)

W4j = W2j/Aj1 (11b)

Call activity 1 employment and activity 2 work-ers at home. Then activity 3 will be employmentdiscounted for access to workers at home, withactivity 4 being workers at home, discounted bytheir proximity to employment. If we are to treatthe two possible new accessibilities as a weightedaverage access, then the new activity variables mustbe normalized to sum to 1, but it is perhaps prefer-able to use an unnormalized variable in this case.The result would be a new measure that wouldvary around unity as does the first approach. Thisgeneral approach may be extended to other pairs ofvariables, so long as the universes’ activity totalsare equal, which is true if both are normalized.

As a third approach, we can use the two balanc-ing factors of a doubly constrained gravity model,as defined by Wilson (1970). In this model, tripsbetween (say) home locations and work locationsare to be distributed in proportion to the number ofworkers at each type of location, and in inverseproportion to the impedance between locations.However, ensuring that the totals at each locationare exactly satisfied by the sums of trips requirestwo sets of balancing factors. We define these usinga modification of the standard notation with H andB replacing A and B, and with trips, origins, desti-nations, and impedance factors as above:

Tij = HiOiBjDjfij (12a)

The balancing factors H and B are vectorsunique to a multiplicative factor and are not read-


( )/ 121 bH B D fi j j ijj

= ∑

( )/ 121 cB H O fj i i iji

= ∑

ily comparable in raw form; I adjust them so thattheir geometric means are equal. The reciprocals ofthe balancing factors are modified accessibilities ofthe types discussed in the two previous possibleprocedures, in which two distributions interact.Indeed, as pointed out by a referee, the previousmethod as proposed by Qing is equivalent to thefirst iteration of one way of determining H and B.In practice, such modified accessibilities fall onboth sides of unity, and their interpretation as aver-age costs requires a special approach. In every case,they may be taken to be costs, either positive ornegative, that modify the measured average cost ofseparation. This economic interpretation is clari-fied below, and may be extended by analogy to thesecond procedure above.

We may define two new variables, U and V, asfollows:

Ui = ln(Hi)/b (13a)

Vj = ln(Bj)/b (13b)

These variables, when used in the calculation of T,show how U and V modify the costs, C, and illus-trate the relation between the doubly constrainedgravity model and the transportation problem oflinear programming, or the Hitchcock Problem:

Tij = OiDjexp[–b(Cij–Ui–Vj)] (14)

We may interpret U and V as offsets to interac-tion costs, in the metric of C; these are analogous tothe dual variables required to clear the marketunder the behavioral assumptions of this model.Trips from one origin are distributed over many des-tinations, unlike the case in linear programming,where the number of different active origin-destina-tion pairs is strictly limited. If U or V is negative thisindicates a locational disadvantage and if positivean advantage. With some stretch of the imagina-tion, we may regard the H’s and B’s as inverseHansen accessibilities, so that, for example, a lowbalancing factor corresponds to high competitiveaccessibility, which leads to a high positive offset.

In computing the doubly constrained gravitymodel, I find it useful to normalize both O and D,each to sum to unity. (An adjustment akin to nor-

malization is necessary whenever the two popula-tions are originally unequal in size.) Then as a resultT, which does not enter directly into their defini-tion, would in fact be normalized so that its doublesummation over i and j is also unity. The computa-tion of the doubly constrained model is degenerateif any of the O’s and D’s are nonpositive.

TESTING RELATIONS OF ACCESSIBILITYAND COMPETITION

The previous formulations of accessibility and theeffects of competition were examined in a series ofcomputations based on a simple hypothetical met-ropolitan area. I assumed an array of 35 squarezones, 5 rows by 7 columns, with the central busi-ness district in the center of the lowest row ofzones. Most data reported below are presented as ifmapped in this array. Costs or impedances werecomputed as the Euclidean distances between zonecentroids; no effects of congestion or mode choicewere examined. The unit of distance or impedancein the computations is the separation of two adja-cent zones. This seems to correspond with an actualdistance of about three miles. I arbitrarily assignedthree classes of workers—400,000 low income,400,000 middle income, and 200,000 highincome—to places of employment and residence,according to a pattern that was intended to besomewhat realistic. Calculations were all done withnormalized employment, so that accessibility meas-ures correspond directly with average impedancesor costs. Values of b in the 0.25 to 3.0 range wereemployed, and results for selected values arereported in detail.

The following was the general scheme of theaccessibility calculations. There are eight popula-tions located in the model metropolis: home andworkplace for each of three classes and for theirtotals. These populations were examined in pairsfor each given b-value; there are 28 pairs, a few areof more substantive interest than the rest, but mostshowed similar behavior. For each pair of popula-tions eight measures were calculated: simple acces-sibility and each of the three competitivemeasures—all of these four with respect to eachmember of the pair, three of them in competitionthat was felt through the other member. The corre-sponding average impedances were calculated for

HARRIS 23

each accessibility measure. These calculations werethe basis for a simple statistical analysis. The totaloutput of these computations involved 5 b-values,28 pairs of populations, and 8 types of accessibilityin 2 forms, always for 35 zones: or a total of 78,400“observations” or numbers. There was limitedredundancy but a great deal of collinearity.

From the design of this experiment, it is not pos-sible to examine the relationship of measures acrossmodes of travel or types of impedance measures. Iwill ignore the relationships of accessibilities to agiven population under different b-values, whichtend to be linearly dependent. Similarly, I do notexamine the relationships between accessibilities todifferent populations under various b-values,where a principal component analysis would showa somewhat less striking collinearity, but a strongdominant component with a variety of modifyingfactors based on different locational patterns (seeHarris 1966). My principal focus is on the rela-tionships among the three measures of accessibilityunder spatial competition and the stability or insta-bility of these relations across pairs of populations.The results of this investigation lead to tentativerecommendations as to the practical treatment ofspatial competition in the broader context of amore extensive spatial analysis.

The process of analysis and the results are illus-trated in the following tables:

Table 1: Eight arrays, similar to maps, showingthe hypothetical distribution of workers by placeof residence and place of work. Pairwise corre-lations between these distributions of workersby places of residence and work are displayed,with a principal component analysis.

Table 2: Area accessibilities to each of eight pop-ulations, with b = 1.0, correlations betweenpairs of these measures, and the principal com-ponents of the correlations.

Table 3: Area values of four different accessibil-ity measures, with b = 1.0. Three measuresreflect spatial competition, and all are providedfor each of a single pair of activities—totalworkers at home and at workplaces. Also shownare the pairwise correlations of these eightmeasures.

Table 4: Selected pairwise correlations betweenaccessibility measures for each of 28 pairs of

locational patterns and 3 b-values to analyze themutual substitutability among them.

The basic analysis is supported principally bydata in table 4, but the features of the analysis willbe outlined by considering all the tablesconsecutively.

Table 1. The presentation of the distributions intable 1 is intended to convey a sense of the resi-dential and employment composition of the city.It is roughly intended to resemble the Chicagoarea, but with the lakefront to the south, and issimilar to Toronto or an upside-down Cleveland.The zones would be numbered consecutivelyfrom left to right across the rows, with 1 in theupper left and 35 in the lower right. The centralbusiness district is in zone 32, in the middle ofthe bottom row. The correlations between thesedistributions show that residential types are lesshighly correlated (perhaps more segregated)than employment types, while residence andworkplace by class is associated positively forlow- and middle-income workers, but not forhigh-income workers.

Table 2. Simple accessibilities are presented foreight classes of locators, with b = 1.0. In general,these accessibilities are positively correlated butnot highly so. Other b-values, not shown, dis-play similar patterns: but as b increases, the pro-portion of the target easily reached falls, whilethe implied average trip length rises. (Values of bof 0.5, 1.0, and 3.0 correspond roughly to tripswith average lengths of 3, 2, and 1 grid units.)

Table 3. This table is designed to show how thebasic data for the analysis were derived. For eachof a pair of classes of locators we calculate sim-ple accessibility and three accessibilities reflect-ing competition with the other member of thepair. These eight measures are correlated pair-wise. The upper left and lower right 4 X 4 sub-matrices reflect the relations among measuresfor the two paired locator classes, and areabstracted for all pairs and b-values in table 4.The upper right submatrix shows the relationsbetween pairs of measures for the pair of locatorclasses.

Table 4. The main table consists of three sub-parts, each for a different b-value. Each subtable


HARRIS 25

TABLE 3 Illustrative Computation of Competitive Accessibilities and Average Costs

b = 1.0 Comparison between total of residences and total of jobs, over 35 zones;includes accessibilities and derived average costs.

Accessibilities

Accessibility to employment Accessibility to residents_______________________________________ _______________________________________Simple Ratio Discounted Gravity Simple Ratio Discounted Gravity.045 .515 .371 .087 .088 1.942 1.332 .657.056 .541 .448 .112 .103 1.847 1.414 .663.057 .565 .472 .131 .100 1.770 1.309 .557.058 .653 .549 .164 .088 1.532 1.129 .419.058 .805 .672 .209 .071 1.242 .926 .291.055 1.057 .829 .262 .052 .946 .719 .189.041 1.232 .766 .244 .033 .811 .511 .115.079 .675 .567 .159 .117 1.481 1.292 .614.092 .658 .643 .192 .139 1.520 1.449 .659.095 .683 .681 .220 .138 1.463 1.377 .575.091 .740 .738 .255 .124 1.351 1.215 .449.091 .922 .899 .317 .099 1.084 .999 .319.080 1.147 1.012 .359 .069 .872 .768 .209.056 1.333 .903 .320 .042 .750 .527 .124.135 .941 .893 .287 .144 1.063 1.160 .526.142 .817 .897 .312 .173 1.224 1.348 .586.144 .799 .914 .348 .180 1.251 1.348 .543.139 .831 .955 .389 .167 1.204 1.242 .450.123 .931 1.003 .416 .132 1.074 1.030 .329.098 1.129 1.028 .423 .087 .886 .760 .211.065 1.318 .880 .357 .049 .759 .502 .123.178 1.107 1.127 .407 .161 .904 1.064 .458.189 1.031 1.146 .446 .184 .970 1.175 .486.200 .919 1.181 .510 .217 1.088 1.308 .506.208 .978 1.297 .602 .213 1.022 1.266 .445.175 1.019 1.251 .592 .172 .981 1.099 .344.120 1.128 1.107 .518 .106 .886 .795 .218.072 1.258 .870 .397 .057 .795 .524 .125.144 1.051 .944 .363 .137 .951 .890 .364.169 1.106 1.040 .434 .152 .904 .910 .361.211 1.020 1.241 .578 .207 .980 1.125 .419.288 1.803 1.809 .904 .160 .555 .890 .306.193 1.168 1.334 .678 .165 .856 .957 .292.126 1.394 1.160 .584 .091 .718 .616 .169.074 1.527 .940 .460 .049 .655 .412 .097

Correlations among eight accessibility measures, four in each of two groups 1.000 .351 .856 .823 .832 –.393 .224 .139.351 1.000 .731 .736 –.192 –.937 –.797 –.789.856 .731 1.000 .974 .476 –.769 –.257 –.363.823 .736 .974 1.000 .437 –.737 –.287 –.390.832 –.192 .476 .437 1.000 .080 .669 .576

–.393 –.937 –.769 –.737 .080 1.000 .768 .804.224 –.797 –.257 –.287 .669 .768 1.000 .964.139 –.789 –.363 –.390 .576 .804 .964 1.000

continues

contains 28 lines, for the possible pairs of 8 loca-tor classes. Each line contains six r-values foreach of the upper left and lower right submatri-ces. This arrangement, although unconven-tional, permits more ready comparison forpatterns across pairs of locators and between b-values. Several observations on these compar-isons follow.

1. The correlations presented are for differentmeasures for each member of the pair. Thecorrelations between accessibility measuresfor different members of the pair were notexamined in detail here and no data are pre-

sented. Correlations between the same twosimple accessibility measures for differentlocators are frequently positive, but adventi-tious in size, as shown in table 2. Correla-tions between the same competitive measuresfor paired populations are almost invariablynegative. (See the upper right submatrix intable 3.)

2. In general simple accessibility (variable 1) isweakly correlated with the competitiveaccessibilities (variables 2, 3, and 4). Thisindicates that competitive accessibilities aredistinctively different from the conventional


TABLE 3 Illustrative Computation of Competitive Accessibilities and Average Costs (continued)

Derived average costs

Accessibility to employment Accessibility to residents_______________________________________ _______________________________________Simple Ratio Discounted Gravity Simple Ratio Discounted Gravity3.090 .664 .992 2.440 2.427 –.664 –.287 .4202.886 .613 .803 2.187 2.272 –.613 –.347 .4112.870 .571 .751 2.031 2.299 –.571 –.269 .5852.852 .427 .599 1.810 2.426 –.427 –.122 .8692.856 .217 .398 1.564 2.639 –.217 .077 1.2342.897 –.056 .188 1.341 2.952 .056 .329 1.6643.205 –.209 .267 1.412 3.414 .209 .671 2.1652.539 .392 .567 1.842 2.146 –.392 –.256 .4872.390 .419 .442 1.652 1.971 –.419 –.371 .4182.358 .381 .384 1.513 1.978 –.381 –.320 .5542.392 .301 .303 1.366 2.091 –.301 –.195 .8002.397 .081 .107 1.149 2.316 –.081 .001 1.1432.530 –.137 –.012 1.025 2.667 .137 .264 1.5662.885 –.287 .102 1.139 3.172 .287 .641 2.0872.000 .061 .113 1.249 1.939 –.061 –.149 .6421.955 .203 .109 1.165 1.753 –.203 –.299 .5341.937 .224 .090 1.056 1.712 –.224 –.299 .6101.973 .185 .046 .945 1.787 –.185 –.216 .7982.099 .071 –.003 .876 2.027 –.071 –.029 1.1132.326 –.121 –.027 .860 2.447 .121 .275 1.5552.737 –.276 .128 1.031 3.013 .276 .689 2.1001.725 –.101 –.120 .900 1.826 .101 –.062 .7811.664 –.031 –.136 .808 1.694 .031 –.161 .7221.610 .084 –.167 .673 1.526 –.084 –.269 .6821.570 .022 –.260 .507 1.548 –.022 –.236 .8091.742 –.019 –.224 .524 1.760 .019 –.094 1.0682.121 –.120 –.102 .658 2.242 .120 .230 1.5242.634 –.230 .139 .923 2.864 .230 .647 2.0791.937 –.050 .058 1.014 1.987 .050 .116 1.0111.780 –.101 –.040 .834 1.881 .101 .094 1.0201.556 –.020 –.216 .549 1.576 .020 –.117 .8691.244 –.589 –.593 .101 1.833 .589 .116 1.1841.645 –.155 –.288 .389 1.800 .155 .043 1.2322.069 –.332 –.149 .538 2.401 .332 .484 1.7802.602 –.424 .062 .776 3.025 .424 .887 2.330

HARRIS 27

TABLE 4 Correlations Between Pairs of Accessibility Measures, Within Viewpoints, Across Zones

Each line identifies paired distributions and pairwise correlations of measures by viewpoints

Column 0: paired activities; cols. 1 to 6, and 7 to 12: r's for paired measures as noted

b = 0.5Accessibilities to 2nd member of pair Accessibilities to 1st member of pair

competitively modified by 1st competitively modified by 2nd

0 1–2 1–3 1–4 2–3 2–4 3–4 1–2 1–3 1–4 2–3 2–4 3–4___________________________________________ _____________________________________1 2 .207 .884 .831 .618 .681 .994 .742 .981 .964 .852 .880 .9971 3 .629 .935 .914 .856 .879 .998 .768 .963 .926 .905 .940 .9931 4 –.352 .780 .696 .297 .406 .990 .811 .993 .979 .866 .901 .9961 5 .282 .976 .969 .430 .468 .998 .122 .954 .948 .400 .420 .9971 6 –.223 .924 .926 .074 .079 .998 .504 .982 .979 .628 .643 .9971 7 .557 .945 .928 .774 .804 .998 .425 .884 .870 .783 .801 .9981 8 –.018 .924 .906 .301 .353 .996 .429 .962 .951 .640 .670 .9962 3 .519 .976 .957 .667 .727 .992 .219 .878 .813 .646 .730 .9912 4 .057 .959 .944 .327 .372 .998 .456 .992 .984 .551 .600 .9982 5 .803 .987 .980 .877 .892 .999 .356 .925 .901 .680 .716 .9952 6 .689 .968 .947 .829 .855 .997 .378 .957 .927 .622 .670 .9892 7 .797 .991 .991 .848 .860 .998 –.024 .737 .722 .619 .638 .9992 8 .699 .974 .964 .819 .840 .999 .349 .945 .933 .623 .654 .9943 4 .279 .862 .773 .718 .810 .988 .666 .980 .954 .796 .850 .9943 5 .790 .964 .933 .914 .943 .995 .600 .937 .918 .835 .857 .9963 6 .694 .933 .880 .899 .941 .992 .621 .960 .932 .808 .847 .9953 7 .787 .977 .975 .895 .899 .999 –.341 .947 .943 –.116 –.051 .9933 8 .671 .935 .886 .879 .924 .993 .554 .959 .936 .760 .798 .9954 5 .835 .996 .991 .872 .889 .998 –.182 .815 .771 .409 .466 .9964 6 .718 .993 .978 .785 .821 .994 –.153 .917 .874 .228 .296 .9924 7 .832 .997 .991 .869 .889 .998 –.173 .710 .669 .556 .598 .9984 8 .748 .996 .990 .794 .817 .998 –.164 .905 .883 .254 .295 .9985 6 –.437 .913 .937 –.094 –.136 .997 .677 .994 .997 .689 .713 .9985 7 .497 .915 .896 .786 .816 .998 .359 .887 .865 .720 .755 .9985 8 –.408 .918 .924 –.039 –.050 .998 .632 .995 .993 .643 .692 .9976 7 .659 .969 .945 .803 .849 .996 .222 .856 .818 .682 .733 .9966 8 .270 .976 .978 .384 .420 .998 –.007 .980 .983 .098 .161 .9937 8 .065 .848 .804 .559 .630 .995 .606 .962 .942 .778 .823 .997



0 1–2 1–3 1–4 2–3 2–4 3–4 1–2 1–3 1–4 2–3 2–4 3–4___________________________________________ _____________________________________1 2 .256 .638 .457 .884 .931 .969 .812 .942 .822 .956 .971 .9601 3 .730 .887 .833 .951 .966 .991 .828 .926 .739 .968 .934 .9241 4 –.459 .043 –.118 .844 .906 .978 .892 .977 .884 .959 .969 .9551 5 .351 .856 .822 .730 .736 .974 .083 .671 .577 .768 .804 .9641 6 .000 .582 .482 .717 .770 .982 .390 .825 .793 .804 .801 .9741 7 .552 .822 .706 .898 .946 .977 .246 .539 .555 .922 .867 .9621 8 .090 .642 .514 .749 .804 .962 .319 .739 .654 .845 .862 .9672 3 .600 .877 .851 .888 .854 .946 .333 .666 .385 .901 .942 .9292 4 .080 .693 .534 .760 .863 .971 .632 .949 .883 .828 .899 .9742 5 .888 .967 .932 .968 .979 .990 .492 .798 .686 .907 .916 .9452 6 .823 .931 .848 .958 .966 .980 .453 .796 .739 .880 .794 .8742 7 .876 .966 .944 .955 .954 .988 .037 .278 .257 .939 .942 .9992 8 .827 .938 .898 .955 .965 .990 .427 .744 .745 .898 .877 .9503 4 .352 .638 .320 .921 .936 .924 .790 .946 .879 .938 .952 .9773 5 .868 .937 .800 .976 .943 .947 .710 .871 .830 .949 .929 .9673 6 .803 .889 .736 .972 .941 .951 .650 .879 .860 .915 .857 .9523 7 .862 .931 .883 .980 .976 .986 –.327 –.022 .359 .891 .684 .876

continues

concept and potentially influential in loca-tional analysis.

3. The latter three variables as a group are allclosely correlated, sometimes very highly so.To an extent, this suggests that any of thesethree may be taken as a substitute or proxyfor the other two.

4. There are important systematic variationsamong the pairwise correlations of thesethree variables. The second of them, as pro-

posed by Shen (1998), plays an intermediaterole in their relationships. For low b-values,implying a high willingness to travel, the cor-relation between the first and second com-petitive formulations is lower than thatbetween the second and third, which may behigh. The same variation becomes moremarked as the correlation between the twopopulations becomes weaker, as indicated intable 1. When the b-values are very high, the


TABLE 4 Correlations Between Pairs of Accessibility Measures, Within Viewpoints, Across Zones (continued)

4 5 .921 .989 .970 .965 .967 .989 –.210 .249 .069 .872 .900 .9514 6 .865 .980 .907 .941 .931 .957 –.194 .405 .207 .772 .736 .8824 7 .921 .993 .967 .959 .969 .985 –.235 .075 .037 .925 .920 .9934 8 .883 .986 .960 .943 .937 .978 –.189 .339 .215 .826 .854 .9715 6 –.256 .459 .403 .674 .737 .994 .608 .961 .972 .748 .763 .9885 7 .510 .736 .631 .937 .968 .981 .223 .585 .569 .874 .846 .9865 8 –.276 .491 .358 .657 .756 .970 .550 .967 .937 .671 .735 .9786 7 .692 .904 .759 .904 .945 .960 .159 .595 .566 .854 .863 .9946 8 .316 .902 .860 .545 .710 .968 –.012 .875 .835 .319 .506 .9087 8 –.036 .465 .413 .815 .838 .992 .637 .870 .737 .901 .954 .969



0 1–2 1–3 1–4 2–3 2–4 3–4 1–2 1–3 1–4 2–3 2–4 3–4___________________________________________ _____________________________________1 2 .469 .485 –.086 .998 .462 .466 .893 .917 .303 .997 .362 .3741 3 .805 .818 .442 .999 .603 .608 .787 .814 .354 .998 .484 .4931 4 –.354 –.332 –.252 .997 .517 .530 .907 .929 .366 .995 .411 .4211 5 .726 .763 .136 .996 .470 .461 .229 .263 –.015 .997 .657 .6641 6 .621 .650 –.083 .996 .467 .453 .416 .451 .013 .996 .669 .6711 7 .824 .848 .061 .998 .478 .459 .018 .021 .239 .999 .541 .5541 8 .696 .728 –.114 .997 .439 .416 .327 .353 .004 .998 .669 .6682 3 .838 .879 .536 .995 .652 .649 .224 .318 .201 .991 .377 .4052 4 .333 .422 .258 .991 .467 .511 .862 .899 .416 .996 .568 .5742 5 .921 .938 .461 .998 .502 .515 .795 .816 –.037 .998 .195 .1852 6 .886 .900 .386 .998 .451 .462 .667 .688 .035 .998 .149 .1322 7 .947 .958 .856 .998 .903 .913 .332 .337 .214 .999 .871 .8742 8 .897 .914 .722 .998 .688 .707 .659 .675 .239 .999 .583 .5673 4 .278 .318 –.046 .997 .607 .616 .927 .941 .508 .999 .633 .6293 5 .764 .792 .363 .997 .542 .565 .734 .749 .425 .999 .542 .5433 6 .743 .766 .478 .997 .571 .592 .716 .741 .449 .998 .583 .5823 7 .845 .876 .838 .995 .810 .845 –.117 –.128 –.068 .999 .918 .9163 8 .731 .759 .342 .997 .565 .585 .651 .675 .432 .998 .595 .5904 5 .961 .974 .815 .998 .784 .791 .011 .024 –.249 .998 .276 .2734 6 .957 .971 .503 .998 .407 .416 .096 .108 –.276 .998 .389 .3774 7 .981 .987 .900 .999 .917 .920 .095 .092 .037 .999 .830 .8344 8 .964 .977 .898 .998 .915 .920 .096 .106 –.007 .999 .855 .8555 6 .125 .175 .032 .996 .816 .803 .297 .403 .810 .986 .507 .5935 7 .461 .479 .142 .998 .475 .481 –.157 –.155 .308 .999 .072 .0825 8 .020 .078 –.041 .994 .820 .827 .247 .374 .484 .980 .280 .3636 7 .541 .603 .088 .991 .532 .529 –.184 –.170 .468 .999 .160 .1866 8 .147 .377 .137 .934 .701 .763 .135 .333 .361 .956 .561 .5867 8 –.242 –.235 .266 .999 .113 .132 .534 .587 .138 .992 .544 .546

correlation between the first and secondcompetitive models is tight, and the correla-tion between the second and third may beweaker.

Thus the most interesting finding to emerge hereis the fact that the first measure of competitiveaccessibility, despite its lack of attention to explicitstructure, may be adequate in many analyses. Thiswould prove to be a significant advantage, becauseit makes it possible to bypass the very large numberof pairs of populations whose competitive interac-tion might be considered important in location.Using either the Shen method or the doubly con-strained gravity model requires calculating a newset of measures for relevant pairs of activities, andin the second of these cases, many iterations may berequired. Identifying the most important pairs oflocators, computing numerous competitive accessi-bilities, and using them in a large-scale analysispresent formidable difficulties.

If an analysis is made using methods based onthe theory of discrete choice in a multinomial logitmodel, the variable influencing utility might be theratio of two other variables. In the actual fitting, alog-linear model is used. Thus the ratio of compet-itive accessibilities does not appear, and the influ-ence of the difference of the logarithms of simpleaccessibilities is merged across pairs. Ten differentaccessibilities generate 45 different pairs, but all 55variables can be represented by the logarithms ofthe 10 original accessibilities.

Stated differently, variables that might not beexpected to influence some particular behavior willin fact influence it because of indirect effects. If it isdesired to separate direct and indirect effects, atleast in part, then a more explicit form of spatialcompetition must be introduced. This is only thebeginning of a far more intricate process, owing tothe collinearity of many important influential vari-ables in spatial analysis.

CONCLUDING SUGGESTIONS

The analysis of location involves far more than theexamination of sites and their immediate vicini-ties—contrary to the suggestion of much planningpractice and of the customary applications of GIS.The specification of location within an urbanregion can be accomplished with the designation of

rings and sectors. However, this is vacuous to any-one (like a computer) who cannot immediatelyassociate these designations with the contents ofthese segments, and with their connections with therest of the region, and is consequently invariantover time and circumstance. The character of thesesubregions may be specified by variables like densityand population composition, but these are againlocal and are in fact the result of the connectionswithin the region interacting with local conditions.

Accessibility is a set of measures of varied formand content that makes it possible to overcomelocal myopia. For this, it must be defined clearlyand used carefully. Accessibility is a quality ofplaces that varies from place to place independentof any local conditions except connections with therest of the region. It is not an intrinsic attribute orproperty of actors or classes of people and activi-ties. For example, the accessibility of an area to jobsdoes not depend on the fact that some or most ofits residents are discriminated against in employ-ment. This dependency is defined by the class ofjobs being examined. Thus accessibility’s funda-mental source is the distribution of properly speci-fied activities over the region, but it also depends onthe costs of the means of interaction betweenplaces, on the assumed willingness or actual capac-ity to employ those means, and on the separationfrom the place of measurement from the targetactivity to be accessed.

Important issues of equity and discriminationcan be addressed purely through considerations ofaccessibility. For example, we might want to studythe ability of low-income families to access low-and middle-income employment. Every zone has ameasurable accessibility to these targets. We couldform an average accessibility, weighted by the low-income population of each zone. Then what? Thesame measurement for high-income families’ accessto high-income jobs might show a lower averageaccessibility, because members of these familiestravel further to their jobs. A more sophisticatedanalysis is needed, showing the relative importanceof accessibility in residential choice and the role ofdiscrimination or the lack of transport alternatives(following Shen) in making these choices.

There is a danger in confounding the effects ofaccessibility and related variables. For example,

HARRIS 29

density is closely correlated with accessibility, yetoften one cannot be used as a proxy for the other.When accessibility runs ahead of this expected rela-tionship, growth may be anticipated, and viceversa. Thus in a more complex model, with manylocational decisions, these two variables may playdifferent roles, and these roles may seem to shiftover time as other variables change. This is onlyone example of the complexities of collinearity inurban analysis.

Special attention must be paid to the relationshipbetween accessibility and actual place of work inresidential location choice. Some working-classneighborhoods are concentrated like companytowns around employment opportunities, and gen-eralized accessibility plays little part in the loca-tional choices of its residents. Conversely, manyupper-income residential areas are far fromemployment in the CBD, with low accessibility.There is, however, a large population that seems tomake location choices on the basis not only ofhousing prices and neighborhood variables, but ona mixture of accessibility and closeness to an actualjob. Aggregated and cross-sectional studies are notadequate to sort out these decision processes, andsuitable detailed longitudinal studies are required,with analyses that include accessibility.

All of these examples suggest the importance of anew and more flexible and imaginative use of acces-sibility measures, to which this paper has attemptedto make one of many possible contributions.

ACKNOWLEDGMENT

Part of this research was supported through a con-tract from the U.S. Department of Housing andUrban Development (HUD) with the University ofPennsylvania. The author appreciates the help ofHUD and wishes to thank the referees for manyhelpful suggestions.

REFERENCES

Hansen, W. 1959. How Accessibility Shapes Land Use.Journal of the American Institute of Planners 25:73–6.

Harris, B. 1966. Notes on Accessibility, mimeo, Institute forEnvironmental Studies, University of Pennsylvania,Philadelphia.

Shen, Q. 1998. Location Characteristics of Inner CityNeighborhoods and Employment Accessibility for Low-Wage Workers. Environment and Planning B 18:345, 365.

Wilson, A.G. 1970. Entropy in Urban and RegionalModeling. London, England: Pion.

____. 2000. Complex Spatial Systems. White Plains, NY:Longman Publishing Group.


ABSTRACT

Although there is no universally acknowledged def-inition of accessibility, various indicators with dif-ferent theoretical backgrounds and complexitieshave been proposed and implemented in empiricalinvestigations. Consequently, results from thesemodels are widespread and reflect more or less themodeler’s aim and point of view. Given the impor-tance of accessibility measures as tools in planning,the aim of this paper is to elicit an understanding ofthe mechanism behind their diversity. In this paper,accessibility measures are classified according totheir underpinning theories, complexity in con-structions, and demand on data. The classificationscomprise travel-cost, gravity, constraints-based,utility-based, and composite approaches. Whilesimpler models are less demanding on data, theyfail to address the subject in a theoretically rigorousmanner. The paper also summarizes issues that areimportant in modeling accessibility. We comparethe performance of some conferred accessibilitymeasures in a European context and examine theeffects of functional forms of the deterrence vari-able and agglomeration effect.

INTRODUCTION

Trade and flows of commodities and informationare recognized as important factors behind

31

Performance of Accessibility Measures in Europe

SIAMAK BARADARAN

FARIDEH RAMJERDIRoyal Institute of Technology

Siamak Baradaran, Royal Institute of Technology, Depart-ment of Infrastructure and Planning, Division of Transportand Location Analysis, Fiskartorpsvagen 15-A, SE-100 44Stockholm, Sweden. Email: [email protected].

economic growth and increased welfare. It is in thiscontext that various researchers have related acces-sibility between supply and demand of goods andservices to economic growth (see Lundqvist 1978;Bruinsma and Rietveld 1998). As a result, accessi-bility indices are among the most prevailing meas-ures used by planners and politicians to bolstertheir everyday propositions. Attempts to fosteraccessibility from national governments, policy-makers, and planners have mostly been limited tolocal or nationwide improvement of the trans-portation infrastructure. Less attention andresources have been offered to border regions andinternational accessibility because of geographicaland political borders between countries.

After introduction of the European EconomicCommunity (EEC) in the 1960s, more and morecountries entered the common market. Fur-thermore, the Maastricht Treaty of 19911 intensi-fied economic activities between member states andtransformed Europe into a huge market. Inspiredby the principles of equity and efficiency, whichrequire that all member countries benefit from thenew common market, incentives to improve theEuropean transportation infrastructure and acces-sibility have grown (Vickerman 1995). Clear evi-dence of this is development of the Trans-EuropeanNetwork (TEN) projects. It is hoped that construc-tion of new highways and high-speed railroads willovercome disparities between the EEC memberstates, but an evaluation of the present level ofaccessibility indicators in Europe is needed to gaugethe impact of these measures.

Gould (1969, 64) states “accessibility . . . is aslippery notion . . . one of those common termswhich everyone uses until faced with the problemof defining and measuring it.” Although there is nouniversally acknowledged definition of accessibil-ity, various indicators with different theoreticalbackgrounds and complexity have been proposedand implemented in empirical investigations (see,e.g., Ingram 1971; Morris et al. 1978; Handy andNiemeier 1997). Recognizing the value of accessi-bility measures as planning tools, it is important tounderstand the mechanism behind their diversity.This paper first presents a summary of different

accessibility indicators and clarifies their underpin-ning theories and corresponding properties. It thenaddresses issues important in measuring accessibil-ity. The following section discusses some conferredmeasures applied to major European cities.Similarities and differences between these measuresare then evaluated in the Analysis of Results sec-tion. Finally, some conclusions are presented.

A REVIEW OF ACCESSIBILITYINDICATORS

The two most fundamental questions concerningaccessibility measures are for whom and for what,and the most straightforward description of acces-sibility is the state of connectivity. A location isassumed to be accessible if it is connected to otherlocations via a link to a road or railroad network(see, e.g., Bruinsma and Rietveld 1998) or to an air-port or harbor. Accessibility described as connec-tivity does not need to have a binary form (that thelocation is connected or not). The extent of accessi-bility can also be calculated as the number of dif-ferent links and modes to which the specificlocation has access. Despite the simplicity of theoutline of such indicators, the obscurity of accessi-bility as a measure of connectivity is apparent.

Different accessibility indicators can be em-ployed to describe and summarize characteristics ofthe physical infrastructure (e.g., accessibility to cer-tain links, the network, or specific mode or modes).These conventional indicators, often referred to asobjective or process indicators, reveal the level ofservice of the infrastructure network from the sup-pliers’ perspective, regardless of their utilization.On the other hand, the importance of recognizingperceived accessibility by individuals as the realdeterminant of behavior is emphasized by manyresearchers, and it is argued that proof of access liesin the use of services. The inherent conflict betweenthe choice of process indicators (objective indica-tors) and outcome indicators (perceived measuresthat reflect behavior) gives rise to a great range ofindicators with different degrees of behavioralcomponents.

Comprehension of differences between accessi-bility indicators necessitates classification. The cri-teria adopted for such classification is based on thediscussion above, starting with the group of meas-


1 For more information, go to http://www.facts.com/cd/v00087.htm.

ures that address the supply side. The other groupsof measures are perceived measures that representthe behavioral component. This approach to theclassification of accessibility measures has beenused by many researchers (see, e.g., Koenig 1977;Morris et al. 1978). Five major theoreticalapproaches for measurement of accessibility indi-cators can be found in the literature:

1. travel-cost approach,2. gravity or opportunities approach,3. constraints-based approach,4. utility-based surplus approach, and5. composite approach.

Approaches 1 to 3 have been acknowledged byArentze et al. (1994) and others, while Miller(1998; 1999) and Miller and Wu (1999) categorizeapproaches 3 and 4 and derive a new compositeindicator (5).

Travel-Cost Approach

The first class of accessibility indicators embodiesthose measuring the ease with which any land-useactivity can be reached from a location using a par-ticular transportation system (Burns and Golob1976). These indicators have been utilized to indi-cate performance of the transportation infrastruc-ture (Guy 1977; Breheney 1978). The commonaspect for this class of accessibility indicators isdetermined by their configuration, where the indi-cator is simply some proxy of transport cost (net-work or Euclidean distance, travel time, or travelcost). A simple functional form for this class ofmeasures is presented by equation 1.

whereAi is the measure of accessibility at location i,L is the set of all locations, andf(cij) is the deterrence function and cij is a variable

that represents travel cost between nodes i and j.This class of measures has a number of advantages.They are

easy to understand because of the simplicity ofmodel construction,

quite easy to calculate, and

less demanding on data than other indicators.

The following are the most critical disadvantages ofindicators within this class:

they neglect variations in the quality oflocations,

they neglect variations in the value of timeamong travelers,

they are highly sensitive to the choice of demar-cation area (see, e.g., Bruinsma and Rietveld1999), and

they do not consider the behavioral aspects oftravelers (see Hensher and Stopher 1978).

Gravity or Opportunities Approach

Indicators based on spatial opportunities availableto travelers are among the first attempts to addressthe behavioral aspects of travel. A great number ofaccessibility indicators are in this class. The poten-tial to opportunities or the gravity approach isundoubtedly the most utilized technique amongaccessibility indicators (see, e.g., Dalvi and Martin1976; Linneker and Spence 1991; Geertman andRitsema Van Eck 1995; Bruinsma and Rietveld1998; Brunton and Richardson 1998; Kwan 1998;and Levinson 1998). An early attempt was made byHansen (1959), who claimed that accessibility isthe “potential of opportunities for interaction” orliterally “a generalization of population-over-dis-tance relationship” (p. 73). The concept of poten-tial to opportunities is closely associated with thegravity models based on the interaction of massesand has been extensively discussed by Rich (1978).Equation 2 shows a simple form for this class ofaccessibility indicators.

whereWj represents the mass of opportunities avail-

able to consumers, regardless of if they are chosenor not,

is the deterrence function, cij is a variable that represents travel cost

between nodes i and j, andis the travel-cost coefficient usually estimated

from a destination choice model.β

( )f c ij ,β

BARADARAN & RAMJERDI 33

( )Af c

iijj L

=∈∑ 1

1( )

( )AW

f ci

j

ijj L

=∈∑

,( )

β2

Advantages of this class of accessibility measuresare

ease of comprehension,

ease of calculations,

they are less demanding on input data than otherindicators that reflect behavioral aspects, and

the ability differentiate between locations.

Some disadvantages of this class of indicators aretheir

sensitivity to the choice of demarcation area,

deficiency in treatment of travelers with dis-persed preferences, and

ambiguity in what the magnitude of indicatorsexpress (dimension problem).

Constraints-Based Approach

Despite the popularity of potential accessibilityindicators, they have some weak points. One weakpoint with gravity models is that they do notaddress time constraints facing individuals. Theconstraint-oriented approach was developed byHagerstrand (1970) within the space-time frame-work and is based on the fact that individual acces-sibility has both spatial and temporal dimensions.Opportunities or potential to opportunities for anindividual are not only constrained by the distancebetween them, but also by the time constraints ofthe individual.

Miller (1999, 2) defines Potential Path Space(PPS) by stating that: “The space-time prism delim-its all locations in space-time that can be reached byan individual based on the locations and durationof mandatory activities (e.g., home, work) and thetravel velocities allowed by the transportation sys-tem.” Assume an individual located at time t1 innode (X0, Y0). Again assume that at time t2 theindividual has to be back at the same node. Thenthe available time for all activities is given by t = t2– t1. Figure 1 shows the contained volume by twocones that represents the space-time prism or PPS.

The projection of PPS on the two-dimensionalXY-space represents the potential path area (PPA)that corresponds to the potential area that an indi-vidual can move within, given the time budget.

Lenntorp (1976; 1978) developed a so-calledprogram evaluating the set of alternative sample

paths (PESASP) to calculate the number of feasiblepaths between nodes, given the activity schedulesand space-time constraints. The number of feasibleactivity schedules simulated by the program repre-sents a measure of accessibility. In other studies,modified space-time prisms have been employed toindicate the individual accessibility based on vari-ous travel speeds, multistop trip chaining, andchanges in activity schedules (see Hall 1983 andArentze et al. 1994).

A frequently adopted indicator within this classis the cumulative opportunity measure or the so-called isochronic indicators that estimate accessi-bility in terms of opportunities available withinpredefined limits of travel cost, C (Dunphy 1973;Sherman et al. 1974; Breheny 1978; Hanson andSchwab 1987).

This class of indicators addresses some of thelimitations of the earlier models by:

consideration of the temporal dimension ofhuman activities, which leads to indicators thataccount for the individuals time constraints, and

the recognition of multipurpose activity behav-ior by a space-time prism.

Wang (1996) points out four weak points with thisapproach:

assuming a constant speed in all directions is notrealistic and variable speed makes the modelexceedingly burdensome to handle;

the planar space defined as PPA is too abstract—a large PPA is not necessarily better than a small


t

X

Y

t2

t1

(X0 , Y0)

PPS

PPA

FIGURE 1 Demonstration of PPS and PPA

one, if the smaller PPA contains more potentiallocations;

the activity schedules are usually incomplete anddo not cover the whole spectrum of activities;and

even though a time budget is introduced, theindividual’s travel behavior is not fully addressedin this class of measures.

Utility-Based Surplus Approach

This class of accessibility indicators is anotherattempt to include individual behavior characteris-tics in accessibility models. Utility-based indicatorshave their roots in travel demand modeling. Ben-Akiva and Lerman (1979, 654) states: “accessibil-ity logically depends on the group of alternativesbeing evaluated and the individual traveler forwhom accessibility is being measured.” In thatsense, the shortcoming of gravity-based indicatorsbecomes obvious, as all individuals within the samezone will experience the same amount of accessi-bility, regardless of the differences between theirperceived utility of alternatives. Ben-Akiva andLerman (1979, 656) continue: for any single deci-sion, the individual will select the alternative whichmaximizes his/her utility,” Thus a simple def-inition of accessibility is:

wheren is a mutually exclusive and collectively exhaus-

tive individual member of I,j is the destination

andi is the node for which the accessibility is

calculated;and

wherevj is some measure reflecting the attraction of the

alternative j, observable to the modeler,

cij is the cost of travel between i and j, andis the stochastic, random, and unobservable

part of the utility for the individual butunknown for the modeler).

By assuming that the random variables are inde-pendent and identically distributed according tothe extreme value distribution, the accessibility oflocation i for individual n is:

where is a positive scale parameter.The measure of accessibility defined in this way

is in monetary units, which enables the comparisonof different scenarios. Williams (1977) noted thatutility-based accessibility is linked to consumerwelfare. McFadden (1975) and Small and Rosen(1981) showed how this measure can be derived inthe discrete choice situation for the multi-nomiallogit (MNL) model when income effect is not pres-ent. For examples of investigations on utility-basedaccessibility measures see papers by Niemeier(1997) and Handy and Niemeier (1997).

The advantage of this class of indicators is thatthey are supported by relevant travel behavior the-ories. Some disadvantages of this class of indicatorsare:

modeling of utility-based accessibility indicatorsdemands extensive data on locations and indi-viduals’ travel behavior and their choice sets,and

the assumption of nonpresence of an incomeeffect is restrictive.

Composite Approach

Representation of the multiple-purpose property oftrips is lacking in the utility-based measures. Thesedrawbacks have been discussed by some re-searchers. Among them Miller (1998; 1999) sum-marizes the disadvantages of these measures andderives new measures by combining the space-timeand the utility-based models into a compositemodel. Miller’s work has Weibull’s (1976) axio-matic approach as its starting point. Miller callsthese models space-time accessibility measures

µ

(ε = 0ε ij

( ) j j l j i= ∀ ≠1 2, ,... , ,... , ;

Ain

Uj in| .


Ain

i j LUj i

n=∈,

max | ( )3

U v cj in

jn

ijn

ij| ( )= − + ε 4

( )A Ui j L

ein

j in v c

j L

jn

ijn

=∈

= −

∈∑max

,( )|

15

µµ

ln

(STAMs), which are based on the assumption ofuniform travel speed.

STAMs are based on the utility of performing aseries of discretionary activities (e.g., shopping, vis-iting), given the mandatory activities (e.g., work).The following utility function, u(.), defined byBurns (1979) and Hsu and Hsieh (1997), isemployed as the base:

whereak = attractiveness of discretionary activity loca-

tion k,is the parameter for the attraction mass,

is the available timefor participation in activities [T = f(t)],

ti,tj = stop times for mandatory activity i andstart time for mandatory activity j,

tk = [d (xi, xk) + d (xk, xj)] /s is the required traveltime from/to the mandatory activities,

xi = location vector of mandatory activity i,d(xi,xk) = distance from activity location i to

activity location k,s = constant velocity of travel,

is the coefficient for available time, andis the travel time coefficient.

Based on these formulations Miller (1999)defines three different STAMs as:

where

AM1 corresponds to the user-benefit approachwhile AM2 and AM3 correspond to the locationalbenefits approach. AM2 considers the whole choiceset while AM3 assumes that an individual only con-siders the choice that maximizes her utility. Millerand Wu (1999) develop this approach further toincorporate a departure-based, discrete time net-work flow model. While this approach aims atavoiding the problems of the other accessibilitymeasures, its main disadvantage is related to thevast data requirement.

FURTHER ISSUES IN ACCESSIBILITYMODELS

The following discussion summarizes a chapter inBruinsma and Rietveld (1999), in addition to somefurther issues.

Measurement of Spatial Separation

The degree of spatial separation between locationscan be measured several ways. Common proxiesare travel distance, travel time, and generalizedtravel cost. Travel distance and travel time are usu-ally easy and straightforward to calculate, whileoperation with generalized travel cost is more cum-bersome. In the case of generalized travel cost,other than the calculation of distance-dependentcosts, information associated with costs of vehicleuse, fares, taxes, and so forth, are needed. Sincesuch data is not readily available at the disaggre-gate level, mean values must be used, which impliesfurther assumptions.

The calculation of travel time is usually based ona shortest path algorithm. A more precise methodis use of a route choice simulation procedure,which is especially necessary for congested net-works. However, the procedure is data demandingand requires trip-matrices as well as volume-delayfunctions. In the case of public transport, waiting,transfer, and auxiliary times are also relevant inaddition to in-vehicle time and fares.

The functional form of the deterrence variableis also important. For instance, we know that theperception of utility (disutility) derived fromwaiting time is not equal to the in-vehicle time.

λβ

Tt t t

kj i k=− − >

; if

else

0

0

α


( )u a T t a T eij k k k k kt k, , ( )= −α β λ 6

( )AM a T ek kt

k L

k1

17= −

∈∑λ

α β λln exp ( )

AM bkk L

2 8=∈∑ ( )

[ ]

AM bk

k3 9= max ( )

( )[ ]ba T

a T t elsek

k k

k k k=

=

+ −

0 010

if or

ln lnexp( )λ α

λβλ

Furthermore, the deterrence variable does not nec-essarily have to be linear in construction.

Measurement of Attraction Masses

Earlier in this paper, two important questions wereraised, accessibility for whom and to what. Whilethe first question is answered by the choice of themodel (e.g., individual or aggregate), the choice ofattraction mass responds to the second question.The mass of attraction in accessibility models rep-resents the potential utility for opportunities at adestination,2 or in other words, the utility an indi-vidual can derive by visiting a specific location or aset of locations. The choice of appropriate interac-tion mass is crucial for the determination of acces-sibility. In large-scale accessibility studies and in theabsence of other attributes, population is oftenused as the interaction mass variable. Other possi-ble proxies are percentage of gross domestic prod-uct, number of employees, volume of sales, etc.

Choice of Demarcation Area

Arbia (1989) divides the problems related to choiceof demarcation area into two subproblems. Thefirst is related to the effects of scale while the sec-ond corresponds to zoning problems.3 A thirdproblem arises as a consequence of the choice oftotal study area.

The scale problem is related to the number ofunits represented in the study area. Inclusion orexclusion of units will affect the results of the acces-sibility model. The zoning problems relate to theway locations are presented. Expressing locationsas nodes that correspond to urban centers willcause aggregation problems, that is, all individualsin the same zone will have the same level of acces-sibility (Ben-Akiva and Lerman 1979). Fur-thermore, the underlying assumption is that alllocations presented by that node have similar acces-sibility measures (Bruinsma and Rietveld 1998).That also complicates the calculation of internalaccessibility measures. However, the use of geo-graphic information system (GIS) and disaggre-

gated census data can reduce these difficulties. Inthis case other problems might arise, like definitionproblems concerning the grid resolution and issuesrelated to the modifiable areal unit problem.

The choice of total study area is also an impor-tant problem that needs attention. With the deter-mination of the study area, one will consequentlydecide which areas should be excluded. The choiceof a closed study area will ignore the effects fromoutside, which in many cases can be questionable(Bruinsma and Rietveld 1998).

Unimodality versus Multimodality

Uni- versus multimodality is also a relevant consid-eration in modeling accessibility. For instance, for awork trip, a range of travel modes can be appro-priate. In case of trips by air, we can easily imaginethat the traveler actually faces two additional modechoices. One has to determine travel modes to theairport of departure and from the airport of disem-barkation. Multimodality can partially be handledin accessibility models. In a travel-cost approach orgravity approach, multimodality can be embeddedin the calculation of travel time or cost for allmodes. These can be presented separately or by theassumption that the traveler might choose thefastest or the least expensive among alternativemodes. In the case of utility-based and compositeaccessibility models, multimodality can be broughtto the model by the construction of a nested desti-nation/mode choice model.

Time of Day

Differentiation between accessibility measures atdifferent times of day is necessary when the level ofservice varies during the day or when traffic con-gestion is a factor. The variation in accessibility fordifferent times of day can be reproduced by theconstruction of separate accessibility models fordifferent time periods. However, in many cases,especially in the case of long-distance trips, thesevariations could be small and may have only aminor impact on accessibility measures.

Agglomeration Effects

The magnitude of opportunities offered at a loca-tion also encompasses opportunities available insurrounding locations within the individuals’ travel


2 In the case of potential, time-space, utility-based, andcomposite accessibility indicators.3 The spatial arrangement of units or the modifiable arealunit problem.

constraints. Inclusion of agglomeration effects is acomplicated task. However, since agglomerationeffects have a direct impact on the utility derivedfrom the opportunities, the easiest way of approxi-mating these effects is through transformation ofthe attraction mass variable.

A pre-set degree of spatial dependence can beembedded in a variable by means of spatial trans-formation. Different techniques can be used to real-ize these transformations, which can simply becalled spatial averaging (see Anselin 1992). Onetransformation technique is termed the spatial win-dow average.

where is the transformed mass variable repre-

senting the attraction mass of node i (agglomera-

tion effects included) compared with Wi the mass

variable at node i and is a spatial weight

from a contiguity matrix4 up to distance d. This

formulation is not suitable when the mass is in

monetary units.The above formulation is highly sensitive to the

definition of contiguity. As an example, if we definecontiguity by masses within a distance d from alocation, then the above formulation will underes-timate a large agglomeration with many surround-ing settlements compared with another with fewsurrounding settlements. An approach to correctfor this problem is to average the mass of agglom-eration (nominator) by a fixed number, K, for alllocations i. This implies all nodes have the samedegree of neighborhood (K–1).

Dimension Problem

The dimension problem arises because almost allaccessibility indicators (except utility-based and

composite measures) present the accessibility oflocations as nondimensional values that are notcomparable with each other. These nonmonetaryvalues complicate the evaluation of infrastructureimprovements. A method that can be used for com-parison of different accessibility measures is rank-ing. By dividing each accessibility measure by thehighest accessibility measure, indicators willbecome normalized in a way that makes them suit-able for comparison.

A STUDY OF ACCESSIBILITY MEASURESOF EUROPEAN CITIES

The aim of our study is to understand the built-inmechanism of some of the accessibility models dis-cussed earlier, while looking at accessibility meas-ures of European cities with road infrastructure.Even though the discussed accessibility models areoperational, not many of them have been applied inlarge-scale studies. In large-scale accessibility stud-ies, the unavailability of illustrative and homoge-neous data is always a limiting factor. Consequently,one’s choice is limited to more simple and straight-forward models. For this reason, the empiricalstudy presented here is based on the first and thesecond class of the models (travel-cost and gravitytype), with consideration of the agglomerationeffect. Furthermore, variations in accessibilitycaused by different assumptions about the deter-rence variable will be examined.

Data

To decrease the problems associated with thechoice of the demarcation area, all of Europe waschosen as the study area (except for Turkey due tothe absence of appropriate data). Accessibility indi-cators are calculated for more than 4,500 citieswith a population greater than 10,000, located in44 European countries connected to each other bythe road infrastructure. The data source is a modi-fied GIS data layer containing urban centers inEurope5 that includes population data. Travel dis-tance and travel time variables are used as proxiesto the spatial separation variable. These are calcu-lated using a digitized road network from three dif-

( )Ψij d

Wi*


( )

( )W

W W

i

i ij d jj L

ij dj L

* ( )=

+

+∈

∈

∑

∑

Ψ

Ψ111

( )W

W W

Ki

i ij d jj L* ( )=

+∈∑Ψ

12

4 A contiguity matrix represents the degree of neighbor-hood of a location with its surrounding locations.

5 The source for urban centers data is CEC-Eurostat/GISCO.

ferent sources implemented in a GIS-database. Thesources for the road network data are:

1. the IRPUD road network,6

2. the digitized road network for Sweden,7 and3. the digitized road network for Finland.8

Travel distance and travel time are calculatedusing the shortest path algorithm in TransCAD.9

The calculation of travel distance is based on thelength attributes of the links, while travel time isbased on different link speeds, commonly assumedfor different link categories. Hence, the effect ofcongestion is not taken into account in this study.Car ferry links are penalized by an additional traveltime of 45 minutes.

The calculation of internal accessibility meas-ures is necessary. In the absence of appropriatedata, the internal travel distances and travel timesare calculated with the assumption that cities arecircular,10 based on the following equations:

where

and

where d is the diameter of the city. An averagetravel speed of 40 kilometers per hour has beenassumed for all internal trips.

Selected Accessibility Models

One group of accessibility models based on thetravel-cost approach and two groups of gravity-based models will be examined in this work. In allmodel groups, an internal accessibility measure isincluded. For each model group, three deterrencefunctions will be examined:

1. linear in travel time (t),2. exponential in travel time, and3. Box-Cox transformed travel time.11

The first group of measures is based on thetravel-cost approach where the measure of accessi-bility can be interpreted as the level of connectivityof the nodes as:

wheretii is the internal travel time at i, andtij is the travel time between locations.The second group of measures is based on the

gravity approach models (Hansen type) and are:

where p is population.


6 This digitized road network is developed by the Instituteof Spatial Planing in Dortmund, Germany.7 The source of this network is the Swedish NationalRoad Administration (Vagverket).8 The source of this network is the Finnish National RoadAdministration (VTT).9 TransCAD is a transportation-GIS software fromCaliper Corp. (www.caliper.com).10 This formulation of internal distance has been dis-cussed by Rich (1980) and also by Bruinsma and Rietveld(1998).

td

ii =/

( )4

4013

dO

=/

( )π

214

OPopulation

Density= ( )15

at t

i jii ijj L

11 1

16= + ≠∈∑ , ( )

ae e

i jt t

j Lii ij

21 1

17= + ≠∈∑β β , ( )

a

e e

i jt t

j Lii ij3 1 1

1 1= + ≠−

−

∈

∑δ θ δ θ

θ θ, ( )18

11 Box-Cox transformation implies: yx= −θ

θ1

bp

t

p

ti ji

ii

j

ijj L1 19= + ≠

∈∑ , ( )

bp

e

p

ei ji

t

j

j L2 20= + ≠

∈∑β βii ijt

, ( )

bpi

e

p

e

i jt

j

tj Lii ij

3 1 12= + ≠

−

−

∈

∑δ θ δ θ

θ θ, ( 1)

The last group of measures also belongs to thegravity type with the agglomeration effect includedas:

where is the transformed population of loca-tion calculated as:

A location j is assumed to be a neighbor of loca-tion i if tij is less than or equal to one hour. Thechoice of one hour as the threshold is related to thetime constraint a traveler faces making a roundtripduring a working day.12

Conventionally, parameters in the models ofaccessibility should be estimated, but due to theabsence of appropriate data for the whole studyarea, parameters from a Swedish study are used13

(Baradaran 2001). These are:

ANALYSIS OF RESULTS

Relationships between different aspects of theselected measures are analyzed by examination ofcorrelations and other deviation measures and bycomparisons of accessibility maps.

Examination of Correlations and OtherDeviation Measures

The similarities and differences between models areinvestigated by construction of the correlation14

table (see table 1).Examination of the correlation table shows that

measures in the third group of models (group c,which includes the agglomeration effect) are quitedifferent from the first two groups (group a and b).Within the first two groups, measures based on lin-ear construction of the deterrence variable (a1 andb1) are highly correlated with each other, while hav-ing lower correlation with other measures based onnonlinear construction of the deterrence variable.Similarly, measures based on nonlinear constructionof the deterrence variable are highly correlated witheach other, while they have lower correlation withmeasures based on linear construction of the deter-rence variable. Group c measures that includesagglomeration effects have higher correlation withthe linear measures (a1 and b1).

Similarities and differences between the modelshave also been analyzed using dispersion and skew-ness statistics shown in table 2. The second columnin table 2 represents a dispersion measure,which is constructed as follows:

This measure describes the degree of dispersionof the calculated accessibility measures. This meas-ure is of course dependent on the area of the study.

ϕ,

pi*


cp

t

p

ti ji

ii

j

ijj L1 = + ≠

∈∑

* *

, ( )22

cp

e

p

ei ji

t

j

tj L

ii ij2 = + ≠

∈∑

* *

,β β ( )23

cp

e

p

e

i ji

t

j

tj Lii ij

3 1 1= + ≠

−

−

∈

∑*

, (δ θ δ θ

θ θ24)

*

( )( )

p t hour

p p

Ki ij

i ij d jj i* ≤ =

+≠∑

1

Ψ

( )25

βδθ

===

0.00329

0 07014

0 545

,

. ,

. .

and

12 One should indeed conduct a sensitivity test to evalu-ate the importance of the threshold.13 These parameters are estimated by using a multinomial-logit model with disaggregate data for long-distance tripsin Sweden.

14 Correlation: [ ] [ ][ ] [ ]

[ ]corr X YX Y

X y,

cov ,,= ∈ −

var var11

TABLE 1 Correlation Table for the Calculated Accessibility Measures

a1 1a2 .84 1a3 .86 .99 1b1 .99 .82 .85 1b2 .84 1.0 .99 .82 1b3 .90 .98 .96 .88 .98 1c1 .53 .23 .28 .54 .23 .28 1c2 .36 .09 .12 .35 .09 .12 .95 1c3 .42 .15 .18 .42 .15 .18 .98 .99 1

a1 a2 a3 b1 b2 b3 c1 c2 c3

( )26ϕ =standard deviationmean accessibility

Hence, it is not the magnitude of this measure thatis crucial, but the degrees of similarity or dissimi-larity among these measures that provides the nec-essary information. Table 2 shows that group cmeasures that include agglomeration have a muchhigher -value than other measures. This suggeststhat measures that include agglomeration are dif-ferent from the rest. Among other measures, thenonlinear measures (a2, a3, b2, and b3) have thelowest -values, suggesting that a nonlinear trans-formation of the deterrence variable has a kind ofsmoothing effect on the accessibility measures.

The last column in table 2 represents the skew-ness15 of measures estimated from different mod-els. Skewness helps identify the degree ofasymmetry of a distribution around its mean.Positive skewness indicates that the asymmetricaltail is protracted toward more positive values whilenegative skewness indicates the opposite. Again wecan see that the skewness of the linear measures (a1and b1) and group c measures represent cumulativeprocesses (because they are positive) while the non-linear measures (a2, a3, b2, and b3) show decliningprocesses (because they are negative).

Differences among accessibility models can alsobe investigated by using a numerical taxonomy.Sneath and Sokal (1973, 116) state that “. . . a coef-ficient of similarity is a qualification of the resem-blance between the elements in two columns of thedata matrix representing the character state of twooperational taxonomic units in question.” Two

different dissimilarity coefficients are calculated.These are

mean absolute difference (MAD), which is avariant of Minkowski metrics16 adjusted fornumber of vector elements and specified as

where is the accessibility measure for location iand L is the set of all locations.

dissimilarity index (DSI), also known asLeontief index (after multiplication by 100),specified as

The results are presented in the appendix.However, due to differences in their ranges, thesemetrics are not directly comparable. For compari-son they are normalized in the following way:

where M is the metric and is its transformedform. The result of this transformation are metricsthat vary from 0 to 1. To avoid zeros in the case ofDSI-metric, zeros are replaced with 0.000001.

Figure 2 shows the differences between accessi-bility measures with respect to measure a1, usingMAD and DSI metrics. The examination of differ-ent metrics points to 3 clusters for the 9 accessibil-ity measures. One cluster is a linear deterrencevariable (a1 and b1). The second cluster is a non-linear deterrence variable (a2, a3, b2, and b3). Thethird cluster includes an agglomeration effect(group c measure).

The differences between the examined accessi-bility measures can be caused by either some key

M

Âi

ϕ

ϕ


TABLE 2 Dispersion and Skewness of Accessibility Measures

Model Skewness

a1 0.307 0.39a2 0.018 (–0.80)a3 0.095 (–0.14)b1 0.405 0.76b2 0.041 (–0.80)b3 0.098 (–0.51)c1 1.51 3.01c2 1.61 3.09c3 1.49 2.93

ϕ

15 A skewness coefficient is a measure of asymmetry of a

distribution. Skew = where is the popula-

tion mean and is the standard deviation.σ

µ( )x

i

i −∑ µσ

3

3

16 The Minkowski metric corresponds to the Minkowskiinequality, specified as

il Âi Ai

ril Âi

ril Ai

rr r

= −∑

≤ =∑

+ =∑1 1 1

1 1/ / 1/r

MADL

Â Ai ii L

= −∈∑1

27( )

( )DSI

L

Â A

Â AÂ A

i i

i ii Li i=

−

+

≠ ≠∈∑1

0 0 28, ( )or

( ) ( )[ ]MM M

M M=

−−

min( )max min

( )29

assumptions made in the calculation, such asparameters and internal travel time, or by the func-tional characteristics of the models.17 The exami-nation of relationships between the selectedmeasures by use of correlation coefficients, meas-ures of skewness and dispersion, and other metrics(MAD and DSI) support each other. The followingare some general conclusions that can be drawnfrom the examination of different deviationmeasures.

Differences in accessibility measures are betterexplained by the choice of functional form forthe deterrence variable than by the choice ofmodel approach.

Various methods used to evaluate the differencesbetween measures suggest that models based onlinear functional forms of the deterrence vari-able are not the same as measures based on non-linear designed models.

Nonlinear specification of the deterrence vari-able decreases the level of dispersion among themeasures.

Corrections for the agglomeration effect pro-duce results that are significantly different fromthe other examined approaches.

Comparisons of Accessibility Maps

Finally, different accessibility maps are con-structed using a GIS-platform by construction of

TIN-models.18 Isochor polygons are the result ofthe TIN-model, where the magnitude of accessibil-ity in each polygon will demonstrate its level com-parable to the other polygons in its surroundingneighborhood. Each isochor surface is classified byits rank, where rank 0 corresponds to locationswith the least accessibility and 100 corresponds tolocations with maximum accessibility. The accessi-bility rank19 of each city is used as the Z-value,20

which differentiates the isochors. The dark colorsrepresent highly ranked areas, while the brightareas are ranked lower for accessibility. The con-tinuous range of accessibility ranks is divided into10 equal segments. This, however, makes a visualexamination of small changes on the accessibilitymaps difficult. For the comparison of minor differ-ences of two accessibility maps, one can zoom inareas of interest and use finer segments.

Figure 3 shows an accessibility map of Europebased on model a1 (travel-cost approach and lineardeterrence variable), while figures 4 and 5 showcorresponding maps based on model a2 (travel-costapproach and nonlinear deterrence variable) andmodel b2 (gravity approach and non-linear deter-rence variable). A comparison of these figures sug-gests that the accessibility maps of Europe are moresensitive to the linearity of the deterrence variablethan the approaches for the calculation of theaccessibility measure (travel-cost or gravityapproach).

Figure 6 shows the accessibility map of Europebased on model c1 (gravity approach corrected forthe agglomeration effect and the linear deterrencevariable). Comparison of this figure with previousmaps suggests that the correction for the agglomer-ation effect has changed the relative rankings ofaccessibility values in Europe significantly. Withcorrection for the agglomeration effect, largeagglomerations such as London, Paris, or Moscowget very high rankings compared with the rest of


17 The use of simulated data can make the distinctionsbetween the causes more clear.

18 A TIN (triangular irregular network) is made by con-structing a network using municipality centers as nodeswith links connecting them to neighboring locations.19 The locations are ranked according to their measure ofaccessibility. The least accessible area is ranked to 0 whilethe highest ranked location has the value of 100.20 Here Z-value is the height of each polygon perpendi-cular to the XY-plane.

a1 b3 b2 a3 a2 b1 c1 c2 c30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

MAD DSI

FIGURE 2 Differences Between Accessibility MeasuresUsing MAD and DSI Metrics with Respectto Model a1


FIGURE 3 Accessibility Map of Europe Using Model a1

FIGURE 4 Accessibility Map of Europe Using Model a2


FIGURE 6 Accessibility Map of Europe Using Model c1

FIGURE 5 Accessibility Map of Europe Using Model b2

Europe. In fact Moscow has a significant place onthis map compared with maps presented in figures3, 4, and 5, where the agglomeration effect is notaccounted for. These maps show that the mostaccessible part of Europe is Central Europe (aroundGermany) and accessibility decreases as one movesaway from this area. Note that with a differentscale, the relative rankings of accessibility valueswill change; however, the large agglomerations inEurope will have the highest accessibility values. Ingeneral, visual examination of accessibility mapsconfirm the results from the statistical tests.

Finally, examination of the accessibility maps ofEurope suggest important issues with policy impli-cations for the European Economic Community(EEC). One interesting observation is that accessi-bility measures in border regions of all theEuropean countries seem to be much lower thaninternal accessibility measures. The lower level ofaccessibility measures in the border regions can beexplained by two factors:

the density of cities in border regions is usuallylower than for the interior of a country, and

accessibility in border regions is lower due tolower density of transport infrastructure in theselocations.

Spiekermann and Wegener (1996) have reportedsimilar observations in an accessibility study. Onecan expect that by taking congestion into accountin calculating travel time, these border problemswith respect to accessibility measures shouldbecome less severe, but they would not disappear.Indeed, the accessibility at border regions hasemerged as an important policy issue for the EEC.

Another important observation is low accessibil-ity in the peripheries of Europe, especially in theregions in the east and southeast. The choices of thedemarcation area can at least partly explain thisobservation.

CONCLUSIONS

In this paper, five approaches for measuring acces-sibility were classified based on a literature review:travel-cost approach, gravity approach, con-straints-based approach, utility-based approach,and composite approach. Certain properties ofeach class of accessibility models have been dis-

cussed as have their pros and cons. Basically, acces-sibility measures in these classes differ in threerespects: theoretical foundation, complexity ofconstruction, and demand on data. In general, thesimpler measures are less data dependent, but theyfail to adequately address the subject in a theoreti-cally sound manner. Availability of data is usuallyan important factor in the choice of the appropri-ate measure in an accessibility study. The purposeof a study is another factor that should influencethe choice of the measure. In the empirical part ofthis study, even with the limited number of meas-ures, we have illustrated that the choice of themeasure has an important affect on the accessibil-ity map and hence, the focus on a particular issue.

Furthermore, some important issues relevant inmodeling accessibility are summarized:

measurement of spatial separation,

measurement of attraction masses,

choice of demarcation area,

unimodality versus multimodality,

agglomeration effects,

the dimension problem, and

time of day.

In the empirical part of the study, accessibilitymeasures for more than 4,500 major Europeancities were constructed based on the travel-costapproach and gravity approach with and withoutcorrection for the agglomeration effect. Three dif-ferent functional forms of the deterrence variablewere examined in each approach, one linear andtwo nonlinear in construction. Differences betweenthe calculated measures were studied using statisti-cal and visual techniques. Correlation coefficients,measures of skewness and dispersion, and differentmetrics, mean absolute difference and dissimilarityindex, were used. Finally, accessibility maps ofEurope were produced for all approaches. We candraw some conclusions by examining differentdeviation measures:

the choice of functional form for the deterrencevariable explains the differences in accessibilitymeasures more than the model approach,

a measure with a linear functional form of thedeterrence variable is different from measuresbased on nonlinear functional form,


a nonlinear specification of the deterrence vari-able decreases the level of dispersion among themeasures, and

corrections for the agglomeration effect producesignificantly different results.

This study is subject to many qualifications. Animportant qualification relates to the availability ofnecessary data for the comparison and evaluationof accessibility measures by all identifiedapproaches. The results of this study, however,illustrate the importance of understanding the per-formance of these measures.

Finally, examinations of the accessibility maps ofEurope suggest that the choice of approach influ-ences the relative accessibility of locations, hence,highlighting the importance of issues differently. Itis therefore important to use an approach relevantto the problem. Some important issues with policyimplications for the EEC can be observed fromthese accessibility maps. One important observa-tion is the low accessibility measures in borderregions of all the European countries comparedwith internal accessibility values. This can beexplained by low density of settlements and trans-port infrastructure in border regions. Anotherimportant observation is low accessibility in theperipheries of the Europe, especially in the regionsin the east and southeast.

ACKNOWLEDGMENT

The Swedish National Road Administration sup-ported this research. The authors wish to thanktwo anonymous referees for their helpful com-ments and suggestions.

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TABLE 3 Descriptive Statistics for Simple and WindowAverage Transformed Model for Swedish Municipalities ( = 0.00329)

StandardMin Max Mean deviation

Population 2,859 71,8462 31,020.07 56,370.66Simple model 0 100 3.926 7.87Window average

model 0 100 17.06 16.03

β

TABLE 4 Mean Absolute Difference (MAD) Between Accessibility Measures (Normalized)

a1 0a2 .47 0a3 .38 .09 0b1 .12 .58 .49 0b2 .47 .00 .09 .58 0b3 .36 .11 .01 .48 .11 0c1 .52 .98 .89 .41 .98 .88 0c2 .54 1.0 .91 .43 1.0 .90 .03 0c3 .53 .99 .90 .42 .99 .89 .02 .01 0

a1 a2 a3 b1 b2 b3 c1 c2 c3

TABLE 5 Dissimilarity Index (DSI) Between Accessibility Measures (Normalized)

a1 0a2 .35 0a3 .30 .06 0b1 .15 .48 .43 0b2 .35 .00 .06 .48 0b3 .29 .07 .01 .42 .07 0c1 .90 .98 .97 .85 .98 .97 0c2 .92 1.0 .99 .88 1.0 .99 .25 0c3 .91 .99 .98 .86 .99 .98 .11 .15 0

a1 a2 a3 b1 b2 b3 c1 c2 c3

Appendix

ABSTRACT

In this paper we hypothesize that the local supply oflabor (i.e., labor force participation) is affected,among other things, by the level of accessibility toemployment locations. Specifically, we conjecturethat improved accessibility in a given area, resultingfrom transportation infrastructure investment, willenhance labor participation, given intervening fac-tors such as socioeconomic and locational charac-teristics. We further conjecture that this effect will bemore pronounced in low-income areas where costsof labor-market participation, including transporta-tion costs, constitute a real barrier to market entry.Using a simultaneous equation model, this paperempirically explores the impact of accessibilitychanges on the supply of labor in specific job typesin the South Bronx, New York, an economically dis-tressed area. The major sources of data for this studyare three U.S. Census Bureau data files from the1990 Census Transportation Planning Package.

INTRODUCTION

Can accessibility improved through infrastructuredevelopment actually affect the level of localemployment? If so, what is the nature and extent ofthis change? In this paper, we hypothesize that iftravel time and costs represent a significant barrierto labor-market participation, improved accessibil-

49

Accessibility Improvements and Local Employment: An Empirical Analysis

JOSEPH BERECHMANTel Aviv University

ROBERT PAASWELLCity College

Joseph Berechman, the Public Policy Program, Tel AvivUniversity, Ramat Aviv 69978, Israel. Email:[email protected].

ity, in terms of reduced travel times and costs, canaffect the propensity of potential employees to enterlabor markets, given their residential and employ-ment locations and socio-economic attributes. Wefurther hypothesize that this effect is more promi-nent, and, therefore, more discernible, in economi-cally distressed areas where enhanced accessibility islikely to have a larger impact on labor-market par-ticipation. This paper examines these hypotheseswith the results from an empirical analysis of acces-sibility-improvement impacts on employment usingdata from a low income, high unemployment area inthe South Bronx of New York City.

This analysis stems from the fact that many trans-portation improvement projects are justified by theiralleged positive effect on the local economy, prima-rily an increase in employment beyond that gener-ated by construction of the project. Specifically,transportation investments are suggested for poorareas as a form of economic stimuli under the pre-sumption that increased employment will follow.On the other hand, if improved accessibility doesindeed have a tangible effect on employment, it isnecessary to understand the nature of this impactrelative to the types of employment and socioeco-nomic groups benefiting from such investments.

It is obvious that accessibility is only one of anumber of factors influencing labor-market partic-ipation. Factors such as work skills, education, andfamily size and makeup may have an even greaterimpact on the employability of potential workersthan does accessibility. Therefore, a main objectiveof this analysis is to discern the degree to which thereduction in the cost of travel to specified worksites can influence an increase in labor supply, givenother intervening factors.

It can also be argued that whereas improvedaccessibility may have a positive effect on laborsupply, in affluent areas where income and carownership levels are high, this effect is likely to beinsignificant and quite difficult to detect.1 If it is at

all effective as a means to promote employment,improved accessibility will have a greater impact inpoor areas where skill and education levels arelower than in affluent areas.2 For this reason, wehave conducted our empirical analysis in the SouthBronx, a distressed urban area in New York City.

On a more general level, improved accessibilityhas several potential long-term consequences possi-bly affecting the overall welfare of the area’s resi-dents and should be regarded in a generalequilibrium framework. First, changes in accessibil-ity can affect property values, possibly rising withincreased accessibility, thereby making presentnonowner residents worse off by increasing theirrent level or even forcing them to relocate to fringeareas where rents are lower. Second, improved acces-sibility affects location decisions by both firms andhouseholds. As a result, the argument that improvedaccessibility can induce labor-market entry may nothold since spatial rearrangement may, in turn, alteraccessibility levels to the disadvantage of low-income residents unable to relocate. A related issueis that improved accessibility can cause migration ofresidents of adjacent regions with inferior accessibil-ity level into the impacted area.

Still another element to consider when develop-ing a methodology for analyzing the effects ofaccessibility changes on employment is that trans-portation improvements are the result of publicdecisions, possibly not independent of external fac-tors, such as the wealth levels of different areas.Transportation capital improvement projects areneither ubiquitous nor random since local pressureby affluent constituents can result in greater invest-ments made in their locales relative to areas thatlack such influence. Hence, a more accurate com-parison of areas with and without improved acces-sibility, relative to their impact on employment,requires a consideration of this and similar factors.

In this paper we do not address these issues, eventhough we consider them quite important for theoverall understanding of the relationship betweentransportation improvements and employment.Mainly due to data reasons (see the data in


1 On the other hand, the value of time tends to increasewith income so that the value of accessibility also riseswith income. A counter argument is that at higherincome, trip-makers can influence their travel time bypurchasing the services of high-speed modes, such as aprivate car, express bus or rail, or travel on toll roads, andthat these means are beyond the reach of low-incomecommuters.

2 Vickerman et al. (1995) argue that “. . . a lack of laborskills can be compensated for by the provision of a cheapand efficient public transport system. . . .”

Appendix B) and the specific characteristics of theSouth Bronx, our analysis is a nontemporal andnonspatial equilibrium analysis, which assumesfixed residential and employment locations and agiven population level. It focuses on the moreimmediate response of potential workers tochanges in accessibility. We notice that, in general,the changes noted above in property value, loca-tion, and population shifts are rather complex phe-nomena extending over many years and carryingmixed effects on employment. As such, they requirecomplicated modeling and an elaborate database.On the other hand, potential shorter-term adjust-ments in the level of employment from transporta-tion improvements carry significant implicationsfor policy making, particularly in economically dis-tressed areas with high unemployment rates.

In the following section we describe the socio-economic and transportation-related characteris-tics of the South Bronx. The estimated results canbest be understood when considered against thesefactors. In the third section, we briefly present find-ings from studies that measured the effects of acces-sibility improvements on the local economy, mainlyon employment. Section four presents our theoret-ical considerations and modeling approach. Empir-

ical results and discussion appear in section five,and major conclusions are in the final section.

THE SOUTH BRONX: SOCIOECONOMICAND TRANSPORTATION-RELATEDCHARACTERISTICS

While Berechman and Paaswell (1996) offers adetailed description, we begin this analysis with abrief description of the studied area. The SouthBronx, a 336-square block area in the borough ofthe Bronx, New York, is a 30-minute subway tripfrom Midtown Manhattan. Figure 1 displays theboundaries of the South Bronx within the Bronx. Amajor transportation investment project, labeledthe Bronx Center project, was considered for thisarea. Its location is also marked in figure 1.

Although the area contains a community col-lege, a major hospital, courthouses, and boroughoffices, it houses a population whose demographicsand socioeconomic profile show that the region iseconomically disadvantaged. The economic declinecame about through the closing of manufacturingin the 1960s and through the departure of the mid-dle class to suburban regions. A key factor under-lying much of the economic reality of the SouthBronx is its high level of unemployment. As shown

BERECHMAN & PAASWELL 51

Bronx Center

161 St. Sta.

WESTCHESTER

THE BRONX

THE BRONX CENTER New York City The South Bronx Bronx Center Subway lines Subway stations 0 3,000 Meters•

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FIGURE 1 Location of the Bronx Center

in figure 2, in 1990, while 50% of the residents ofthe Bronx (excluding the South Bronx) are definedas “employed and at work,” the corresponding fig-ure for the South Bronx is only 39%. The partici-pation rate, defined here as the number ofemployed people out of the total labor force, was91% in 1990 in New York City, 88% in the Bronx,and 84% in the South Bronx.

As table 1 shows, even in later years the unem-ployment rate (not seasonally adjusted) in theBronx, including the South Bronx, is quite high rel-ative to the other boroughs in New York City.

The median income in the South Bronx is onlyabout 69% of that of the Bronx as a whole andabout 50% of that of New York City.3 The povertyrate (the number of persons in poverty out of totalpersons) is the highest in the New York area, about40% in 1996.

Level of education greatly affects employability.Presently, about 80% of the residents of the SouthBronx have only a high school diploma or feweryears of schooling compared with 67% in the restof the Bronx. This situation is reflected in the occu-

pation profile of the South Bronx residents. Themajority of the labor force is employed in adminis-trative support and service occupations. As the esti-mated results presented later indicate, labor-marketparticipation in these particular occupations ismarkedly sensitive to changes in accessibility.

Transportation options for the area include com-muter rail, rapid rail, and metropolitan bus lines.These, however, are geared to trips ending in mid-to lower-Manhattan. Based on markets existingsome decades ago, they do not necessarily representmarket demands created by the decline of manufac-turing in the Bronx and the growth of services inManhattan. A close inspection of South Bronxtransportation conditions reveals that they are quitedeficient in terms of high travel costs, long commutetimes, and inferior service quality. As shown in fig-ure 1, within the South Bronx many areas are rela-tively far from a subway station, and bus service isinfrequent and expensive. Furthermore, the car-ownership rate in the South Bronx is quite low,about 21% as compared with 49% for the entireBronx borough and 57% for New York City. It isnot surprising, therefore, that residents of the SouthBronx rely heavily on public transit for travel towork. About 63% use public modes (subway, ele-vated train, railroad, or bus), and only 19% use aprivate car. For the Bronx borough (excluding theSouth Bronx), the corresponding figures are 54%and 33%, respectively. The remainder is made upby foot travel and other transportation means.4

Two other important indicators of travel behav-ior are time of departure and length of travel time.Thus, whereas the distribution of time of departure


Bronx tracts* South Bronx tracts0

10

20

30

40

50

60

Employed in the Armed Forces

Employed and at work

Employed but not at work

Unemployed

Not in labor force

Percent

FIGURE 2 Employment Status (1990)

*Excluding South Bronx tracts

3 See Berechman and Paaswell (1996) for a detaileddescription. Data sources are listed in Appendix B. 4 See Appendix B for the source of these data.

TABLE 1 Unemployment Rates in New York’s Five Boroughs, 1996–1998 (percent)

1996 1998

New York City (all boroughs) 8.5 8.1Bronx (including the South Bronx) 11.0 10.2Brooklyn 9.5 9.4Manhattan 7.4 6.9Queens 7.5 6.9Staten Island 7.5 7.6Source: New York State Bureau of Labor Statistics (November1996, July 1998)

for the Bronx residents (excluding the SouthBronx) displays an almost normal curve, the distri-bution of time of departure for the South Bronxresidents is heavy-tailed with many early and latedepartures. On the other hand, the majority of tripsby South Bronx residents are within the middlerange, 30 to 60 minutes, whereas those of Bronxresidents are in the shorter, 0 to 30 minute, andlonger, 60 to 90 minute, ranges.

In summary, these data demonstrate that thesocioeconomic profile of South Bronx residents isquite different from that of Bronx residents as awhole and of the other New York boroughs. Theyare poorer and less mobile and also have lower lev-els of formal education and work skills. Thesequalities effectively reduce their potential employ-ability. This observation has two major ramifica-tions for our analysis. The first is that residents ofthe South Bronx appear more susceptible tochanges in travel time and costs relative to laborforce participation than residents of more affluentareas. The second is that estimated results fromempirical analysis will be best understood ifsocioeconomic and transportation characteristicsare considered.

EFFECT OF ACCESSIBILITY CHANGESON EMPLOYMENT

In recent years, interest in the question of whethertransportation improvements generate economicgrowth, mainly employment, has grown (Banisterand Berechman 2000). Beeson (1992) argued thatin urban areas the degree of labor specializationand division (e.g., diversity of employment), whichaffects labor productivity and use, depends mainlyon the size of the market determined, in turn, bypopulation density and transportation costs.Paaswell and Zupan (1998) showed that increaseddensities in the core (Manhattan) require the highaccessibility provided primarily by rail rapid tran-sit systems. Quite simply, in such extremely high-density areas, an employer can benefit not onlyfrom nearby important support services andamenities but also from a diverse labor forcewithin a reasonable commuting distance. Theauthors showed that few cities in the world,London and Tokyo being exceptions, had that

relationship between employment density andaccessibility. In contrast, in Chicago, a city with ahighly developed rail rapid transit system, oppor-tunities are less than optimal. The more than 50%of the region’s population living in the suburbs areserved by well-developed highway networks,which also encourage dispersion of employment.In the last decade, this dispersion has taken jobsaway from the core, redistributed them through-out the suburbs, and made them accessible only bycar, effectively reducing overall accessibility forpotential employees (Sen et al. 1998). The costs toenter or participate in the job market for the low-income worker in Chicago, then, are higher thanfor his New York counterpart.

The empirical literature pertinent to these argu-ments can be categorized into two broad groups.The first is the Spatial Mismatch Hypothesis(SMH); it focuses on labor force participation ofinner city minority residents. The second, labeledhere the “production function” approach, focuseson the causality between transportation improve-ments and growth as well as the degree to whichsuch association actually exists.

Starting with the pioneering work of Kain(1968), the SMH states that inner city minority res-idents suffer from high rates of unemployment,caused by poor accessibility to employment, whichhas decentralized to suburbs. These minorities,who have low income and low rates of car owner-ship, are unable to relocate to these suburbs due todiscrimination in the suburban housing markets.Under these conditions, improved accessibility canbring about an increase in market participationrates of inner city minorities.

A recent comprehensive review of empiricalresults from SMH studies has concluded that thelack of spatial accessibility to employment canexplain poor labor-market participation rates ofinner city, low-income inhabitants in large metro-politan areas (Ihlanfeldt and Sjoquist 1998).However, this review also suggests that in additionto accessibility, other factors can bring about simi-lar effects. These factors range from the lack ofinformation on job availability at distant employ-ment sites to job discrimination factors. Further-more, it is also suggested that the lack of importantjob skills is at least as important as accessibility in


affecting employment levels among inner city, low-income groups. A similar argument can be madefor the effect of childcare costs, which for low-income groups can be significant. Hence, for policypurposes it is important to discern the relativeimportance of each factor on spatial mismatchsince, in themselves, commuting programs may notappreciably affect deficient market participationamong inner city minorities. Still another empiricalissue is whether all low-skilled workers, mainlyadults, actually are accessibility-deficient. Thisissue is troublesome since most SMH studies havefocused on the analysis of inner city youth.

This study does not intend to examine the SMH.We look at labor-force participation within NewYork City, a unique urban area atypical of U.S.urban areas, and address impacts of costs of travelin boroughs where accessibility may be high andtraditional job markets within reach. Thus, interms of transportation, the South Bronx is not typ-ical as compared with many inner city areas.Workers in the South Bronx have access to trans-portation systems that provide high levels of acces-sibility to the prime locations of employment, thecore of Manhattan. In addition, they have access toa highly developed expressway network that canbring them to nearby suburban counties. The prob-lem discussed here is more local. Because the railnetwork was designed to access the core ofManhattan and the bus network to serve the railstations, public transport within the South Bronxdoes not adequately serve local workers. Thus,while a commute to the core of Manhattan or tothe suburbs can be achieved in a reasonable time, acommute across the South Bronx becomes quitecostly. For this reason, this paper does not attemptto confirm or disprove the SMH.

However, the present analysis accounts for sev-eral factors, also necessary for validating the SMH.In particular, it controls for labor skills, for the levelof education, and for household variables includingage of children. In addition, in this analysis we usean accessibility measure, a function of network-based modal travel times and costs, of time ofdeparture, of car ownership, and of householdincome. We believe that this measure is compre-hensive enough to adequately measure accessibilityto employment in the studied area. Moreover, our

analysis distinguishes between residents who liveand work in the Bronx and those who live in theBronx but work elsewhere.

Within “production function” literature, severalempirical studies have found that changes in acces-sibility (broadly defined) have an insignificanteffect on employment growth (Danielson andWolpert 1991) or on travel-to-work behavior(Ewing 1995). Thus, it was concluded that employ-ment growth took place mainly in outer suburbsand was largely insensitive to highway accessibility(Giluliano and Small 1999). On the other hand,household characteristics such as size, number ofworkers, and income have a stronger impact onwork trip patterns.

Cervero and Landis (1995), who investigatedthe employment effects from the San Francisco BayArea Rapid Transit (BART) system, found thatmost employment growth took place in corridorsnot served by BART and that BART’s locationaladvantage was confined primarily to the servicesector (mainly finance, insurance, and real estate).Employment densities near BART stations werehigher than match-paired freeway interchanges(+12% for suburban and +28% for urban).

Results from these studies do not clearly delin-eate employment changes from accessibilityimprovements. Transportation development gener-ates efficiency gains, transfer effects, and activityrelocation effects (Banister and Edwards 1995;Berechman 1995; Forkenbrock and Foster 1990).Together these effects influence the demand foremployment in conflicting ways. But what aboutlabor supply changes from accessibility improve-ments? Do people, especially in poor areas,respond to accessibility changes by offering morelabor? How do labor skills and labor-market expe-rience affect their willingness to enter the labormarket relative to the effect of reduced transporta-tion costs? Are potential employees in some occu-pations more susceptible to accessibility changesthan employees in other occupations? Next weaddress these questions.

MODELING ACCESSIBILITY ANDMARKET ENTRY DECISIONS

When examining the relationships between accessi-bility improvements and changes in the local


supply of labor, it is necessary to distinguishbetween two types of change. The first is a changein the amount of labor actually provided by exist-ing employees and measured by, for example, thenumber of daily hours worked. The second is achange in the actual number of people in the laborforce, resulting from new market entry.

A common approach to assessing changes inactual labor supplied by existing employees is toconsider work/nonwork activity substitution.Individuals divide their total daily hours betweenwork and nonwork activities, and the latter canfurther be divided between travel and other non-work (leisure time) activities. Travel time, in turn,which confers negative utility, is a function ofaccessibility (by mode). Hence, reduced travel timeresulting from improved accessibility will leavemore time available for work and leisure time activ-ities. Given some reasonable assumptions onwork/leisure time substitution as well as on theeffect on income of reduced travel times and costs,improved accessibility is likely to have a positiveeffect on the actual amount of labor individuals cansupply (Berechman 1994). At equilibrium, the allo-cation of time between work and nonwork activi-ties will depend on the reservation wage rate, thelowest wage an unemployed worker will accept;individual preferences with respect to work/leisuresubstitution; and travel time to work, a measure ofaccessibility.5 Since the focus here is on marketentry due to accessibility improvements, we do notexamine the possibilities of part-time work orworking more or fewer hours. Also the databaseused here (see Appendix B) does not report suchinformation.

A plausible explanation for new labor-marketentry due to improved accessibility is the net-payentry threshold argument. Net pay is defined as theafter-tax total earnings minus the costs associated

with labor-market participation. Accordingly,individuals regard their expected net pay as a keydeterminant in their labor-market entry decisions.The costs of participation include the costs ofchild-care arrangements as well as the time andout-of-pocket expenses associated with travel towork. With other key factors, such as skills andfamily size, kept constant, the net-pay argumentimplies that when given after-tax expected earnedincome, lowering the time and money costs oftravel will also lower entry thresholds, therebypositively affecting the propensity of individuals toenter the labor market. It also follows that thelarger the entry cost share is of total after-taxexpected income, certainly the case for low-incomeindividuals,6 the larger the elasticity of the laborsupply with respect to travel cost reduction will be.Again, we emphasize the short-term and partialequilibrium nature of this analysis since, in thelonger run, changes in the labor supply functionwill affect equilibrium wage rates which, in turn,will affect the actual level of employment.

Empirically, changes in the labor-participationrate can be observed only if individuals willing toenter the labor market, following accessibilityimprovements, actually become employed. For thisto happen, it is necessary for some firms to employthese individuals. In this short-term analysis, weassume a quite elastic labor-demand function sothat an increase in labor supply following accessi-bility improvements will indeed result in employ-ment of workers at present wage rates for firms’location and production technology.

In his well-known study, Cogan (1980) devel-oped a methodology for assessing the effect of thecosts of labor-market participation on entry deci-sions by women. Using 1976 household-panel datafrom the Michigan Panel Income Dynamics surveyand applying a probit model to estimate a reduced-form index of women’s labor force participation,Cogan found that the effect of time and monetarycosts (unrelated to travel) associated with labor-market entry was rather substantial. Specifically, he


6 It might be argued that low wages also imply low valueof time and, hence, low travel costs. In the New Yorkarea, however, direct monetary costs of travel are quitehigh, so their effect on low wage earners probably out-weighs the effect of low value of time.

5 One caveat to this conclusion: many employees are con-strained by employment rules, making it unfeasible forthem to be paid for more than a fixed number of hoursper day, week, or month. These work rules vary betweenfirms and occupations as well as by seniority and laborunion contracts. In the Bronx, a large number of employ-ees are part-time workers, who, for various reasons, suchas lack of skills, cannot increase the number of hours theywork; if they could, they would have done so, consideringtheir income level.

found that estimated at the sample mean, thesecosts were equivalent to 1,151 annual hours to theworker. Overall, his results indicate that the annualcost of participation in the labor market amountsto 16% of women’s average earned income. Theseresults, however, were not categorized by employ-ment type and did not account for transportationcosts associated with market entry.

In this study, we have followed Cogan’s approachto examine the effect of lowering travel times andmoney costs on the supply of labor. Here we test twomain hypotheses: 1) improved accessibility, all elseunchanged, will positively affect individuals’propensity to enter the labor market and 2) thiseffect will vary across employment types and indus-tries. Appendix A provides a discussion of the ana-lytical underpinnings of our modeling approach,primarily on the nature of the supply function,which represents participation decisions in the wage-travel costs space.

We measure accessibility as a combination oftravel time and monetary costs, known as general-ized travel costs, adjusted for the type of modeused. It is important to point out that, to a certainextent, accessibility costs are endogenous variablesin the decision process of potential employees. Thatis, given their location, factors such as mode choice,time of departure, car ownership, and car utiliza-tion are used by individuals to effectuate theirtravel times and costs. On the other hand, modeavailability, bus and train headways, fares, androad tolls are largely exogenous. In the analyticalmodel, we regarded accessibility as an endogenousvariable but have also introduced into the accessi-bility function some exogenous travel variables.

The level of accessibility between residential and

employment locations i and j, respectively, meas-

ured in units of weighted travel time and costs,

denoted by Tij, is specified as a function of the fol-

lowing five components:7 is the monetary costs

of travel by mode, weighted by the proportion of

people using that mode between these locations,

is travel times by mode, also weighted; dij

is time of departure; is car ownership by

households (at residential location i); and is

households’ income level.

The specific accessibility function used in this studyis given by

The weights where is the number

of people using mode m (m = car, transit, walk) forhome-to-work travel between i and j; Lij is the totalnumber of people traveling between i and j.

Equation (2) does not represent a transportationchoice model. That is, often after the implementa-tion of a transportation improvement, for example,a new express bus, travelers may shift route ormode, thereby affecting accessibility. While equa-tion (2) does not account for route or modechoices, it explicitly asserts that whatever trans-portation improvements are made, their accessibil-ity impact is captured through changes in traveltime and costs and time of departure, given caravailability and income.8

Next, we specify the labor-supply function, wheredenotes the number of employees in job type

k, employed in industry type s, residing in locationi, and working in location j, respectively. SeeAppendix A for definitions.

where (equation (2)) and are the errorterms. For the empirical analysis, the accessibilityfunction’s decay factor, , is set to 1.0. Experi-υ

ε 2ε 1

Qijk s,

Lijmw

L

Lijm ij

m

ij= ,

YiH

CiH

w tijm

ijm;

c ijm


7 We have also used a travel time and cost matrix calcu-lated from actual bus and subway information relative toheadways, in-vehicle time, and average walk time to/fromnearest stations. These two matrices are highly correlatedthough on some specific routes there were some signifi-cant variations. We did not find significant differenceswhen we tested the empirical model for each of thesematrices.

8 In any case, conducting route and mode choice analysisrequires an individual choice database, largely unavailable.

( )T f w c w t d C Yij ijm

ijm

ijm

ijm

ij iH

iH= , , , , ( )1

( ) ( )T w c w t

d C

ijm

mijm

ijm m

mijm

ijm

ij iH

= + + +

+ +

∑ ∑η η η

η η η

0 1 2

3 4 5ln (2)YiH + ε 1

Q T Y

W E

ijk s k

ij iH

k jk s

i

,

,,

exp( )= + − + +

+ +

λ λ υ λ

λ λ λ

0 1 2

3 4

ln

ln 51

3

6 2 3, , ( )II

I iF SB=∑ + +λ ε

ments with other values for did not yield signif-icantly different results.

Equations (2) and (3) were estimated simultane-

ously using a two-stage least squares (2SLS) proce-

dure. In the first stage, equation (2), the level of

accessibility, Tij, between residential location i and

employment location j is estimated.9 In the second

stage the number of employees living in i,

working in j, and working in job type k in industry

type s is assumed to be a function of several factors:

1) inverse of the accessibility level, Tij, estimated

from the first stage; 2) income ; 3) the actual

wage rate paid in job type k in industry type s

4) the level of education, measured in

units of school years, Ei; and 5) the number of chil-

dren in 3 age groups (Fl,i;l = 1,2,3): 0-5, 6-13, 14-

18. We have also used a dummy variable, SB, to

indicate whether a person who lives in the South

Bronx also works there (SB = 1) or not (SB = 0).The database used for this analysis is composed of

1990 U.S. Census Bureau data. The major data filesused contain data at the census block group leveland not at the individual household level. The obser-vations pertain to employment, travel behavior, andsocioeconomic attributes of residents of the SouthBronx, New York. Employment is categorized into13 job types in 17 employment sectors. In the studyarea, there are approximately 56,000 census-block-based origin-destination pairs, including persons liv-ing and working in the Bronx and people living inthe Bronx but working anywhere. As already men-tioned, this database does not account for part-timeemployees or for changes in the number of weeklywork-hours actually worked by already employedworkers. A detailed description of the database andits organization, including variables definition,appears in Appendix B.

RESULTS AND DISCUSSION

Our principal hypothesis is that with all else con-stant, reductions in accessibility costs between

places of residence and places of employment willenhance the propensity of individuals in the SouthBronx to participate in the labor force. Thus, themain thrust of the empirical analysis is the estima-tion of point elasticities of labor-force supply inspecific job categories with respect to travel costs,given a set of other intervening variables. The mainresults from the estimation are presented in table 2.

As already mentioned, there are 13 job types.Table 2, however, shows results for four types only.One reason is that some employment types (e.g.,farming) are not well represented in the SouthBronx and thus can be omitted. Another reason isthat not all job types proved sensitive to accessibil-ity changes, that is, the relevant estimated parame-ters were insignificant at 0.05.10 For brevity, table2 lists all variables for each equation but showsonly those parameters that are significant at the0.05 level or better. For the accessibility andemployment equations, the reported parametersare scale-adjusted coefficients as the units of meas-urement of variables in these equations are non-comparable.11

As can be expected, the results of the accessibil-

ity function, equation (2), indicate that overall

accessibility is positively and significantly affected

by public transit, car, and walk travel times.

Reductions in transit travel times have the greatest

impact while reductions in car

travel times have the least effect

The importance of these results is that in the South

Bronx, considering the low levels of car ownership,

improvements in transit service will have the great-

est impact on accessibility.Interesting results pertain to time of departure.

As the number of people leaving home for work atthe early and late time periods increases, accessibil-ity improves (the negative sign of the 6:30–7:30and 8:30–12:00 departure time variables).Apparently, a rush hour departure time is associ-ated with poorer accessibility as factors such ascrowding, unreliability, and general inconvenience

( . ).η2 0 212Car =( . ),η2 0 807Transit =

( )Wjk s, ;

YiH

Qijk s, ,

υ


9 In the South Bronx, 68.3% of trip-makers travel by pub-lic transit for which monetary cost (fare) is constant rela-tive to trip length and time of day. Therefore, in some runsof the model, the travel cost variable, was omittedfrom the accessibility equation due to lack of variability.

Cijm,

10 It remains to be examined why these sectors are notaffected by travel costs reduction. This is the subject of afollow-up analysis.11 See Montgomery and Peck (1992, chapter 4) for a sta-tistical explanation.

affect accessibility.12 Since New York City publictransit is priced uniformly over time and space,improved transit in vehicle travel times, headway,and capacity is likely to have a profound impact onoverall accessibility.

The relatively low value of the car ownershipparameter reflects the basic real-ity of the South Bronx of a very low level of carownership. Another analysis (Berechman andPaaswell 1997) showed that the car occupancyvariable has an indirect effect on accessibility, ashigher levels of occupancy are associated with

( . )η4 0 04050= −


TABLE 2 A Two-Stage Least Squares Estimation of the Accessibility and Employment Functions

Accessibility (equation 2) Employment (equation 3)

Type of jobExecutive Technician Administrative Transport

Variable Parameter Variable parameter parameter parameter parameter

Mode Accessibility –.237740 –.187414 –.096016 –.079812car .212161 Wage ratetransit .806815 (3) Construction NS .283052 NS NSwalk .413026 (4) Manufacture 1 .129783 .136822 .048485 NSothers NS (5) Manufacture 2 NS .090696 NS .235875Departure12:00–5:59 NS (6) Transport .338492 NS .235395 .5750816:00–6:29 NS (7) Communication NS NS NS NS6:30–6:59 –.140844 (8) Wholesale NS –.145514 .163956 .2566067:00–7:29 –.198046 (9) Retail .285929 NS NS NS7:30–7:59 .286117 (10) FIRE .485281 .447685 .422971 NS8:00–8:29 .103212 (11) Business and repair NS .347708 NS –.3534658:30–8:59 –.126580 (12) Personal Services NS –.142507 .068464 NS9:00–9:59 –.137373 (13) Entertainment .210809 NS .052301 NS10:00–11:59 –.149063 (14) Health NS .858439 .172036 .384054Car ownership0 cars –.042637 (15) Education NS .122671 .074335 .1795011 car –.004050 (16) Other .140571 –.143720 NS .4547752+ cars .017643 (17) Public administration –.141837 .00407 .161577 NSIncome, in $ thousands Education: 0–9.9 .571909 Less than 9th grade NS –.275950 NS NS10–19.9 .521587 Less than 12th grade –.235460 .408651 NS –.68412420–29.9 NS High school diploma NS –.326228 .168903 NS30–34.9 .340198 No college degree NS NS .179568 .21221735–49.9 .367278 Associate degree .146286 NS .166667 –.26863450–74.9 .189123 Bachelor degree NS –.224551 NS –.28802875.0+ –.012188 Graduate degree NS .187507 NS –.538609Constant 44.3827 Childrens’ age:R-Squared .362 Under 3 NS NS NS –.258383

3–5 NS –.235078 NS –.2754076–11 NS –.159645 –.132387 .45536412–17 NS –.425830 .130015 NSIncome, in $ thousands0–9.9 NS .089148 –.055030 NS10–19.9 NS .155627 NS NS20–29.9 .058064 NS –.043658 NS30–34.9 .093460 NS NS NS35–49.9 NS NS NS NS50–74.9 0.082358 NS –.158341 NS75.0+ NS NS NS .121987Constant –4.286843 6.516566 –25.94905 –.841860R-Squared .866 .869 .953 .765

Note: Parameters shown are adjusted coefficients (see text) and significant at 0.05 level or better.NS = not significant.

12 Early departure may also suggest a multi-purpose trippattern. Dropping a child at a day-care center is an obvi-ous example.

reduced travel times. Car ownership by itself, how-ever, does not seem to have such an effect.

Income has an interesting effect on measuredaccessibility. In 1990, in the South Bronx over 65%of the population earned less than $20,000 peryear, and over 45% earned less than $10,000.There is no doubt that at these income levels publictransit is the mode of choice which, compared withcar use, is a slow mode offering lesser accessibility.This explains why we find a significant and positive(i.e., higher travel times) relationship betweenaccessibility and low-income variables (parametervalue is for $10,000 or less, and

for $10,000–$20,000 income level). Asincome increases, there is a gradual shift to privatemodes, associated with greater accessibility, hencethe smaller value of the relevant parameters. Whenincome is at its highest level ($75,000+), its effecton accessibility actually peaks

Turning now to the employment function, equa-tion (3), a key result is that only for some job typesare the accessibility parameters statisticallysignificant and with the correct sign. For example,in table 2, the accessibility parameters of Executive,Technician, Administrative, and Transport types ofjobs are significant and have a negative sign (i.e.,improved accessibility, in terms of reduced costs ofaccess, will increase employment in these job cate-gories). Why is this result important? Actual acces-sibility improvements in the South Bronx seem toaffect labor supply in some job types only but notin others. In assessing the policy impacts of accessi-bility improvements on employment in this area,not all job types should be treated similarly. Wereturn to this issue when we discuss the policyimplications of this analysis.

As expected, the estimated parameters indicatethat a higher wage rate is associated with a greaterpropensity for workers to enter the labor market.This is particularly true for Executive andAdministrative support type jobs in the 17 indus-tries. For Technician and Transport occupations,however, the wage rate effect is positive for onlysome employment sectors and is negative for others(e.g., for Technicians employed in PersonalServices, It is not quite clearhow to explain this result. We surmise that wage

differentials in various industries can suppress thewillingness of one member of a two-employeehousehold to enter the job market when the othermember earns a much higher wage. Another possi-ble explanation is that the increase in accessibilityexpands the search area. People who were unem-ployable at present wage rates in their previoussearch area can now find jobs at a lower wage inthe expanded area.

The parameters pertaining to the variable “levelof education” have a positive effect on labor-market participation though their magnitude is lessthan the impact of other variables. For some jobtypes, Executive and Administrative, the estimatedparameters indicate that having some formal col-lege education positively contributes to employa-bility, whereas for Technician and Transport, theopposite is true 13

Underlying our analysis is the hypothesis thatthe costs of travel and other nontravel expenses anindividual incurs when entering the labor forcerepresent an actual barrier to labor-force partici-pation. Thus, the costs associated with childcarerepresent a major market-entry barrier. A negativesign for the pertinent (and significant) parameter(i.e., indicates that for a given job typehaving more children of a given age group poseshigher market-entry costs. And these, in turn, neg-atively affect the propensity of individuals to beemployed in this occupation. A positive (and sig-nificant) parameter indicates the opposite. By andlarge, the significant parameters of the children-age variable in the employment equation have theexpected negative sign (e.g., for job type“Technician” having children in the age group3–5, One probable explana-tion for the few parameters with a positive sign isthat, for these particular job types, having chil-dren of a certain age does not represent actualcosts while, concurrently, it does induce a greaterlabor-market participation due to income needs.

Except for Executive type jobs and the very lowincome levels of Technician and highest level ofTransport, the income parameter of all other jobtypes was either insignificant or had a nega-( )λ 2

λ 5 0 235078= − . ).

λ 5 0< )

( )λ 4 0< .

λ 3 0142507= − . ).

( )λ k1

( . ).η5 0 012188= −

η5 0 521= .η5 0 571= .


13 We are unable to explain for Technicianwith a graduate degree. Perhaps in this job type overqual-ification has an offsetting impact on employment.

λ 4 0 187507= .

tive effect on participation decisions. The main rea-son seems to be the general low level of income inthe South Bronx that, save for a small percentage ofjobs (Executive being 5.9% of all jobs), is a resultof low wages paid in all other job categories.Above, we saw that the wage rate parameters, byand large, have a positive and a sizable impact onparticipation. Since in the South Bronx wages andincome are highly correlated, participation ratesare largely captured by changes in the wage level.

How can these parameter estimates be used toassess the impact of improved accessibility on laborsupply in the South Bronx? When assessing the sizeof the employment effect from a given improve-ment in accessibility, it is necessary to recall thatour employment model assumes locations as given.Therefore, a specific reduction in travel costs (equa-tion 2) will affect the propensity of potentialemployees at their present residential location i, toenter job type k in industry type s at location j, bythe magnitude of the estimated parameters ( inequation 3) and the actual change in accessibility.Thus, if we assume a certain percentage increase inaccessibility between locations, i and j, thetotal change in labor supply at location j, is

where is the number of potential employees

(the number of employable adults) residing in the

zones affected by the accessibility change (i and j)

who work in job type k in industry type s.To illustrate, consider a particular transporta-

tion development, such as the introduction of anexpress bus to a major employment area j, whichimproves accessibility (i.e., lowers the compositetravel costs measure, Tij) by 10% relative to pres-ent accessibility level (thus, for allpotential employees who reside in i and wouldtravel to work at j. From table 2, there are four jobtypes whose accessibility parameters are statisti-cally significant. Within the South Bronx, theobserved distribution of these four job types is asfollows: Executive (executive, administrative, andmanagerial) makes up 5.9% of the labor force;Technician (technicians and related support occu-pations), 2.1%; Administrative (administrative

support occupations), 22.4%; and Transport(transportation and material moving occupations),5.2%. Jointly, they make up 35.6% of the totallabor force in the South Bronx.14 Hence, for every1,000 potential employees in the relevant i and jarea, 356 are employed in job types that are posi-tively and significantly affected by accessibilitychanges. For these calculations we assume that thisobserved distribution of job types applies also toevery i and j.

Given these figures, from equation (4) we getthat for each 1,000 potential employees, this acces-sibility improvement will induce 4.4 new marketentries in these job categories. That is:

where wk,s is the above proportion of employees ineach job type k in industry s. Thus, under these con-ditions a 10% improvement in accessibility, whichaffects 1,000 potential employees, will stimulate1.23% new market entry in these 4 job types.16 Theaccuracy of these calculations depends, of course,on the degree to which the working assumptionsabove are valid. It is safe to conclude, however, thatoverall the net effect of accessibility improvementson employment in the South Bronx is rather small.In this regard, the results obtained in this studyagree with those reported in the Spatial MismatchHypothesis literature.

CONCLUSIONS

The main objective of this paper was to examinethe effect of improved accessibility from transportinvestment on the local supply of labor in an eco-nomically distressed area. The South Bronx, which,according to key socioeconomic indicators, is suchan area, has been considering a major transporta-tion improvement investment, known as the Bronx

∆Tij = 01. )

Pijk s,

∆Qij

∆Tij ,

λ 1k


∆ ∆Q T Pij ijk

k sijk s= ⋅∑ λ 1 4

,

, ( )

∆ ∆Q T wij ijk

k s

k s= ⋅ ⋅ =∑ λ 1151 000 4 4 5

,

,( , ) . ( )

14 The proportions of job types cited here representobserved figures and not supply figures, which are unavail-able. Therefore, in this example we use the observed per-centages as approximations for the supply figures. 15 = 0.1(0.0590.23774+0.0210.187414+0.2240.096016+0.0520.079812)1,000 = 4.4

16 (4 4

356100

.× ).

∆Qij

Center project. The increases in employment thatderive from transportation investments designed toimprove accessibility also result in a more positiveeconomic future for the area. The question then is,if implemented, will this project indeed bring aboutan increase in employment?

Fundamentally, increased employment fromtransportation investments results from the interac-tion of two main factors. The first is the impact onthe willingness of a potential worker to enter the jobmarket and travel to a specific employment siteonce generalized travel costs have been lessened.The second relates to employers’ demand for labor,which, among other things, is predicated on thelevel of access to a properly skilled labor force. Inthis paper we have examined the first factor, whichessentially amounts to an investigation of the effectof a transportation-cost reduction on labor-marketparticipation, assuming that additional employ-ment will be made available by present employers atpresent wage rates. We have also explicitly assumeda short- to medium-run framework in which house-holds and firms do not relocate in response to theimproved accessibility.

Using an analytical framework similar to that ofCogan (1980) to model market-entry decisions bypotential employees facing significant entry costs,we have estimated a two simultaneous equationsregression model of accessibility and employment.Accessibility is modeled as a function of modaltravel time and costs, of time of departure, of carownership and use, and of income. The employ-ment equation is specified as a function of accessi-bility costs, wage rate by industry, work skills, levelof education, and household demographic charac-teristics. Our database included 1990 census traveland employment data from the South Bronx, NewYork. The empirical estimation has yielded pointestimates that indicate the effects of accessibilityimprovements on labor-force participation by jobtype and employment categories, given residentialand employment locations.

The central conclusion from the empiricalresults is that changes in accessibility costs have adiscernible effect on labor-market participation inthe studied area. However, with respect to job type,the effect of accessibility is not ubiquitous, both interms of magnitude and (statistical) significance.

Depending on skill requirements, offered wagerates, household income, and children of specificage groups, participation in employment sectorssuch as Executive, Technician, Administrative, andTransport are more responsive to travel cost reduc-tion than are other employment types. In fact, theempirical estimation shows that labor supply insome employment types such as Retail andWholesale and Personal Services (statistically) islargely not amenable to changes in accessibilitycosts.

Another important result is that the magnitudeof the estimated net employment effect is rathermodest. However, in an economically distressedarea like the South Bronx, even a relatively smallemployment increase can provide an importantboost to the welfare of area residents. In particular,this is the case for improving women’s labor-marketparticipation following travel costs reductions. Inplaces like the South Bronx, where the proportionof all households headed by a woman is ratherlarge, a reduction in female unemployment is,undoubtedly, of major interest.

Although it was not the intent of the authors tocarry out SMH analysis, the results shown in thepaper do not negate the principal results of thespatial mismatch literature. For example, for occu-pations in which there are a large number of low-skill workers (and low wages) such as serviceoccupations or sales occupations, for the most partaccessibility coefficients are insignificant. Foradministrative and transport type jobs, they aresignificant but quite small. Thus, as the SMH liter-ature confirms, accessibility is not a major factorexplaining labor-force participation in areas likethe South Bronx.

Within the framework of this analysis it isimportant to observe that, even in the short run,location can matter when assessing labor-supplychanges from accessibility improvements. That is, alarge-scale transportation investment, like theBronx Center Project, is likely to strongly affectsome locations but not others, as only a subset ofall origin-destination pairs will experience a conse-quential travel-cost reduction. As a result, onlythose households located within the impacted areaof the planned new rail and bus routes will poten-


tially change their labor-market participation,given all other intervening factors.

A second caveat is that in the empirical analysiswe have used “number of employees” as the laborsupply variable rather than “number of hoursworked.” This practice may have affected the esti-mated results since, in a low-income area like theSouth-Bronx, many people may be employed inpart-time jobs. Therefore, the increase in the supplyof labor can be in the form of more hours workedrather than new entry into the labor market. It alsodoes not tell us whether new workers are part-timeor full-time employees. If data on the number ofhours worked were available, an alternativeapproach would be to investigate the trade offbetween work and nonwork activities from areduction in travel time and cost. It would also per-mit the investigation of the full change in employ-ment resulting from overall equilibrium adjustmentof hours of work.

ACKNOWLEDGMENT

Financial support was provided by the UniversityTransportation Research Center. We wish to thanktwo anonymous referees and the Editor-in-Chief ofthe Journal for their very helpful comments andsuggestions.

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APPENDIX A: A MODEL OF LABOR-MARKET ENTRY DECISIONS

In assessing the effect of reduced travel costs onlabor supply, a key analytical issue is that existingcosts of labor-market entry introduce discontinuityin the labor-supply function. The reason is that anincrease in entry costs will raise reservation wages,thereby reducing the probability that a person willwork. To test these ideas within the context ofwomen’s labor-market participation, Cogan (1980)introduced the concepts of reservation hours andnotional hours of work. The former is defined asthe minimum number of hours a person is willingto work. The latter is the number of hours a personwould choose to work if required to spend at leasta (positive) number of hours in the labor market.We follow a similar approach by formulating thereservation and notional work-hours functions andthe reservation and notional wage-rate functions.To each of these functions we also add an accessi-bility component, our central explanatory factor,estimated from a separate accessibility function.

Within this analytical framework, the labor-

market participation decision is defined as the case

when the amount of a person’s notional hours

exceeds his reservation hours. Let the notional

work hours be denoted by and the reservation

work hours by Labor-force participation

requires that

We conjecture that labor-market participation

decisions by potential employees are based on three

major variables: 1) her/his notional work hours rel-

ative to her/his reservation work hours, 2) her/his

reservation wage rate relative to the offered wage

rate, and 3) the costs of travel to work she/he faces

if deciding to participate. To simplify the analysis,

we assume that each of these variables can be

expressed as a linear function of its determinant

variables but that the supply function must be

upward rising throughout, with respect to the rele-

vant variables.17 These variables (indexed for loca-

tions) are the wage rate offered by job type k, at

location j, household income at location i,

level of employee education in units of num-

ber of school years Ei; employee age, Ai; number of

children, by age category l, at residential location i,

Fl,i; labor-market experience (years employed) Xi;

and travel costs, Tij, between residential and

employment locations (i,j = 1,...,M). Next we define

the notional and reservation work hours functions,

the reservation wage function, and the travel cost

function. We assume that the random disturbance

term, associated with each of these functions (u),

distributes with mean vector zero and an unknown

but constant variance-covariance matrix.

For each household in a residential zone i,

employed in employment zone j, the notional

work-hours equation, given the employment sector

k, is expressed as a function of the market

wage rate, the accessibility costs Tij, and a

vector of socioeconomic variables:

Since accessibility costs are regarded here asendogenous choice variables, the parameter measures only the partial effect of a small change intravel cost on work hours.18 A further caveat is thatsince participation is a discrete choice variable, theparameter actually measures the partial changesin the propensity of potential employees to changework hours.

γ i

γ 6

Wjk ,

hi jk N≠, ,

YiH ;

Wjk ;

h hk jN

k jR

, , .>

hk jR

, .

hk jN

,


h W Y E

A F T

ijk N

jk

iH

i

i l l i ij

,

, ,

= + + + +

+ +

γ γ γ γ

γ γ γ0 1 2 3

4 5 6

ln ln

+∑ u Ai

1 1( )

17 The labor-supply function represents participationdecisions in the wage-travel costs space. Hence, the abovevariables (a) and (b), in fact, are a one-choice variable.18 If accessibility costs were completely exogenous andfixed for each ij pair, the effect of a change in these costscould be interpreted as a full change in hours of work asemployees adjust to their new equilibrium levels.

The reservation work-hours equation is describedas a function of the above variables. That is,

From equations (A1) and (A2), the following reser-vation wage function is derived.19

where:

For a potential employee residing in origin zone i,the wage offer equation at location j is specified asa function of level of education, Ei; age, Ai; andlabor-market experience, Xi (not included in theempirical analysis since the relevant informationwas unavailable). Thus,

To empirically assess the impact of reduced

transportation costs on the propensity of potential

employees to participate in the labor force, we can

follow two alternative approaches. Following

Cogan, we have defined the participation condition

as In terms of the wage functions (A3)

and (A4), this condition is expressed as lnWOj >

lnWRj (given i). Using these functions, we can

derive an explicit form for this condition by prop-

erly grouping all variables in the left-hand side and

the disturbance terms in the right-hand side. The

result would be an index describing the probability

of labor-force participation. Given the above

assumption of the distribution of the disturbance

factors, it is possible to estimate the parameters of

this participation index using a probit analysis.

Such an analysis is quite useful since the participa-

tion index, in fact, provides a reduced-form meas-

ure for the participation function, the combination

of equations (A3) and (A4).

An alternative approach is to use the condition h = max(hN,hR) and the wage-offer equation (A4)to obtain the following expression for the actualhours worked:

where is the wage rate offered in sector k inlocation j.

To carry out empirical analysis following thefirst approach, it is necessary to have a databasecomposed of survey information on specific house-holds relative to their labor-market participationdecisions, their labor-market experience, and theirsocioeconomic attributes.20 Such a database wasunavailable for this study. Therefore, in what fol-lows we use the second approach and simultane-ously estimate equation (A5) with the accessibilityfunction (equation 2 above), using a two-stage leastsquares procedure. In this estimation we assumedthat each new market entry is a full-time employeebecause part-time employment is not considered.Given the database (see Appendix B), such anapproach is quite useful as it directly elicits theimpact of accessibility and its components onlabor-market participation.

APPENDIX B: SOURCE AND STRUCTUREOF THE DATABASE

The major sources of data for this study are threeU.S. Census Bureau data files: 1) the 1990 CensusTransportation Planning Package—Urban Element(CTPP), 2) the Summary Tape File 1 (STF 1a), and3) Summary Tape File 3 (STF 3a) (USDOC 1990).The prime source of data used for the analysis inthis paper comes from the CTPP, which containsdata at the census block group level. There areapproximately 56,000 census block group origin-destination pairs used in the analysis: persons livingin the Bronx and working anywhere.

The CTPP data is actually a data set broken intothree different files (see figure A-1). The first file isdemographic data for place of residence (i loca-

Wjk O,

h hk jN

k jR

, , .>

( ) ( )βγ

δ γ ρ σρ ρ ρ= − =105 03

2

l

u N; . ; ~ ,and


ln lnW Y E A

F T u A

jiR

iH

i i

l l il

ij

= + + + +

+ +∑β β β β

β β0 1 2 3

4 5 3 3, , ( )

lnW X E A u AjiO

i i i= + + + +α α α α0 1 2 3 4 4( )

19 For this derivation, h = max(hN,hR), where h is actualhours worked.

20 Using data on residential and employment locations andtheir origin-destination (O-D) interactions introduces sta-tistical complexities into the estimation of a probit model.

h W Y E

A F X

ij jk O

iH

i

i l l ii

i

= + + + +

+ +∑ρ ρ ρ ρ

ρ ρ ρ0 1 2 3

4 5 6

ln ln,

, , + +ρ7 5 5T u Aij ( )

h Y E A

F T u A

k ijR

iH

i i

l l il

ij

,

, , (

= + + + +

+ +∑δ δ δ δ

δ δ0 1 2 3

4 2 2

ln

5 )

tion). The second file is demographic data for placeof employment (j location). The third file is theorigin-destination matrix for every block group inthe New York metropolitan area (a 14-countyregion of New York, 14 counties of New Jersey,and 3 counties of Connecticut). The matrix con-tains all modes of travel, peak and off-peak travel,as well as the number of persons traveling betweenlocations i and j.

The principal variables used in the analysis andtheir ranges are as follows:

I. Mean travel time by mode: mean travel timebetween i and j in minutes by mode

II. Household range of income: number of house-holds within an income range:

1) $0–$9,9992) $10,000–$19,9993) $20,000–$29,9994) $30,000–$34,9995) $35,000–$49,9996) $50,000–$74,9997) $75,000 and above

III. Mode use: number of employed people, 16years of age or older, who use a mode to travel towork:

1) car2) public transit (bus, street car, trolley, subway,

rail, ferry)

3) other (bike, taxi, motorbike)4) walk

IV. Car ownership: number of households thatown x cars:

1) 0 cars2) 1 car3) 2 or more cars

V. Time of departure: number of employed peo-ple, 16 years of age or older, during 1 week prior tothe census, who leave to work at

1) 12 AM–5:59 AM2) 6:00 AM–6:29 AM3) 6:30 AM–6:59 AM4) 7 AM–7:29 AM5) 7:30 AM–7:59 AM6) 8 AM–8:29 AM7) 8:30 AM–8:59 AM8) 9 AM–9:59 AM9) 10 AM–11:59 AM

VI. Type of industry: number of people, 16 yearsof age or older, during 1 week prior to the census,who work in

1) agriculture, forestry, and fisheries2) mining3) construction4) manufacturing, non-durable goods5) manufacturing, durable goods6) transportation


Variables from file1

residential (i)


employment (j)


O-D connections

Database filecreated

Analysis

Residenceweighting factor

Employmentweighting factor

FIGURE A.1 Structure of Database

7) communications and other public utilities8) wholesale trade9) retail trade

10) finance, insurance, and real estate (FIRE)11) business and repair services12) personal services13) entertainment and recreation services14) health services15) educational services16) other professional and related services17) public administration

VII. Wage rate by industry: wage rate for each ofthe above industries, based on NYC ES202 1994data.

VIII. Type of job: number of people, 16 years ofage or older, during 1 week prior to the census, whowork at the following job types

1) executive, administrative, and managerial2) professional specialty occupations3) technicians and related support occupations4) sales5) administrative support occupations, includ-

ing clerical6) private household occupations7) protective service occupations8) service occupations, except protective and

household9) farming, forestry, and fishing occupations

10) precision production, craft, and repairoccupations

11) machine operators, assemblers, and inspectors

12) transportation and material movingoccupations

13) handlers, equipment cleaners, helpers, andlaborers

IX. Educational level: number of persons whohave attained a given educational level

1) less than a 9th grade high school level2) less than a 12th grade level3) high school diploma4) attended college but no degree5) Associates degree6) Bachelors degree7) graduate degree

X. Presence and age of children: number of chil-dren present of different age groups

1) number of children less than 3 years old2) number of children 3 to 5 years old3) number of children 6 to 11 years old4) number of children 12 to 17 years old

The above database contains two interzonalaccessibility matrices, one based on travel time andcosts reported by travelers making home-to-worktrips and the second based on travel time and costscalculated from actual bus and subway informa-tion relative to headway, in-vehicle time, and aver-age walk time to or from the nearest stations.Comparisons of these two accessibility matricesshowed some variations. Therefore, we carried outthe empirical analysis separately for each of thesetwo accessibility matrices though no major differ-ences were found for the estimated parameters.


ABSTRACT

Efforts to improve transportation choices andenhance accessibility at the neighborhood levelhave been hampered by a lack of practical planningtools. This paper identifies the factors that con-tribute to accessibility at the neighborhood leveland explores different ways that planners can eval-uate neighborhood accessibility. A gap between thedata needed to describe important accessibility fac-tors and the data readily available to local planningdepartments points to two complementary strate-gies: a city-wide approach using available data andgeographic information systems to evaluate acces-sibility for neighborhoods across the city, and aneighborhood-specific approach to building adetailed accessibility database. Examples of bothare presented.

INTRODUCTION

Several trends in the 1990s brought new attentionto the importance of alternatives to driving. Federaltransportation policy, as shaped by the IntermodalSurface Transportation Efficiency Act of 1991 andthe Transportation Equity Act for the 21st Centuryof 1998, emphasizes transit, as well as walking andbiking, out of concern for both the environmentand equity of service. The New Urbanism move-

67

Evaluating Neighborhood Accessibility: Possibilities and Practicalities

SUSAN L. HANDY University of Texas at Austin

KELLY J. CLIFTONUniversity of Iowa

Susan L. Handy, School of Architecture, University ofTexas at Austin, Austin, TX 78712-1160. Email:[email protected].

ment has focused attention on how the design ofneighborhoods encourages or discourages walking,among other things, and has given weight to theidea that land-use regulations are also an importantelement of a transportation program. In addition,the relative lack of services in many lower incomeneighborhoods, where auto ownership is often lowas well, has been the target of renewed attention inrecent years. In response, planning agencies are tak-ing a new look at both transportation policies andneighborhood planning in an effort to enhancetransportation choices. Their efforts are hampered,however, by a dearth of applicable planning tools,particularly measures or indicators that can be usedto identify problems and needs, determine the ade-quacy of current policies, or evaluate the impacts ofproposed policies at the neighborhood level.

Planners are beginning to turn to accessibilitymeasures as a way of evaluating the availability andquality of basic services and alternative modes atthe neighborhood level. As generally defined,accessibility reflects the ease of reaching needed ordesired activities and thus reflects characteristics ofboth the land-use system (where activities arelocated) and the transportation system (how thelocations of activities are linked). Extensive aca-demic literature on accessibility measures suggestsmany ways to define and measure accessibility,although examples of the actual use of accessibilitymeasures in planning are relatively scarce. In addi-tion, the literature offers few approaches that ade-quately assess accessibility to different modes oftravel at the neighborhood level. While traditionalmeasures of accessibility focus on the distance toand size of potential destinations, for example,other characteristics of the local environment mayhave an important impact on modes like walkingand biking. Unfortunately, incorporating suchqualities into an assessment of accessibility requiresdata that are not readily available or easy to collect,a real obstacle to developing practical accessibilitymeasures. In addition, traditional measures ofaccessibility combine a variety of factors to pro-duce a single measure of accessibility. Thisapproach is useful for comparisons but masksimportant qualities of the neighborhood that con-tribute to accessibility. As an alternative, planners

might build and analyze an accessibility databaserather than calculate an accessibility measure.

The goals of this paper are twofold: to identifythe factors that contribute to accessibility at theneighborhood level and to explore the optionsavailable to planners for measuring this accessibil-ity. A gap between the data needed to describeimportant accessibility factors and the data readilyavailable to planning departments points to twocomplementary strategies for measuring accessibil-ity: a city-wide assessment of neighborhood acces-sibility using existing data sources and thecapabilities of geographic information systems(GIS), and a neighborhood-specific approach tobuilding a detailed accessibility database. Thispaper begins with a brief overview of the literatureon accessibility measures and a summary of factorsidentified in travel behavior research and planningpractice that may contribute to neighborhoodaccessibility. After establishing a framework forevaluating neighborhood accessibility, the paperturns to an assessment of available data sourcesand a discussion of the two proposed approachesto measuring neighborhood accessibility.

MEASURING ACCESSIBILITY

Accessibility is an important concept for urbanplanners because it reflects the possibilities foractivities, such as working or shopping, available toresidents of a neighborhood, a city, or a metropoli-tan area. Accessibility is determined by attributes ofboth the activity patterns and the transportationsystem in the area. The spatial distribution of activ-ities as determined by land development patternsand their qualities and attributes are importantcomponents of accessibility, as are the qualities andattributes of the transportation system that linksthese activities, such as travel time and monetarycosts by mode. Although most researchers agree onthis general definition of accessibility, they havedeveloped a wide variety of ways to measure it.

The literature on accessibility measures has along history. Most measures can be classified as oneof three basic types (Handy and Niemeier 1997).Cumulative opportunities measures are the sim-plest type. These measures count the number ofopportunities reached within a given distance ortravel time and give an indication of the range of


choices available to residents. Gravity-based meas-ures are derived from the denominator of the grav-ity model used to predict trip distribution; thesemeasures weight the amount of activity at differentdestinations by the cost, time, or distance to getthere. The third type of measure is based on ran-dom utility theory, in which the probability of anindividual making a particular choice depends onthe utility of that choice relative to the utility of allchoices; the accessibility measure comes from thedenominator of the model and reflects the totalutility of all choices. In general, the threeapproaches offer different tradeoffs between thesimplicity and thus ease of comprehension of themeasure and the sophistication with which theactivities and transportation system are character-ized. The more sophisticated measures also requiremore sophisticated data.

In developing a practical technique for assessingneighborhood accessibility, a number of questionsmust be addressed. First, what factors tend to mat-ter most to residents? Clearly it is impossible tomeasure, let alone know, every factor that mattersto every resident. Fortunately, a number of studieshelp to identify the factors that seem to be mostimportant to a majority of residents, and a list ofthese factors is compiled below.

Second, what kind of data are available or canbe collected about these factors? The data com-monly used by planning departments miss many ofthe factors important to neighborhood accessibilityand may not be available in a useful format if theyare available at all. These issues are explored in thesection on data availability.

Third, how can planners make sense of the avail-able data on neighborhood accessibility factors?Traditional accessibility measures can, dependingon their structure, specification, and calibration,combine a number of important factors into a sin-gle, all-encompassing measure of accessibility. Thisapproach, however, may be neither practical nordesirable for planning purposes. The more complexthe measure the more data and analysis skillrequired, limiting the ability of most planningdepartments to develop such measures. The devel-opment of utility-based measures, for example, isprobably beyond the capability of most depart-ments. In addition, much important information is

lost when the data are collapsed into a single oreven a few measures. Traditional measures ofaccessibility may help planners identify neighbor-hoods with relatively high or low accessibility, butthey do not, on their own, point to the specific fac-tors contributing to accessibility. As an alternative,the possibilities and practicalities of developing adatabase of neighborhood accessibility factorsusing either a city-wide or neighborhood-specificapproach is explored in this paper and this effort isdescribed in the section on strategies.

Finally, the use of the neighborhood as the spa-tial unit of analysis presents both opportunities andchallenges. Analysis at the neighborhood levelallows for a more detailed examination of the qual-itative characteristics of the local environment thanwould an analysis at a larger geographic level.However, if neighborhoods are defined by theirnatural boundaries, usually major arterials or openspace, their areas and populations may vary con-siderably. Some normalization by area or popula-tion may be necessary if the goal is to compareaccessibility between neighborhoods. In addition,accessibility may vary considerably within a neigh-borhood depending on the distribution of retailand services relative to the population within andbeyond the neighborhood. Therefore, it is impor-tant also to evaluate accessibility from differentpoints or for different areas within the neighbor-hood. Residents also make use of activities outsideof the neighborhood, not just those found withintheir boundaries. Thus, an assessment of accessibil-ity within the neighborhood would provide onlypart of the picture. On the other hand, an assess-ment of accessibility within and beyond the neigh-borhood must consider what distance beyond theneighborhood is appropriate. These issues arise inmany of the examples presented in the strategiessection of this paper.

The first step in designing a neighborhood acces-sibility database is to identify the factors that con-tribute to accessibility for residents. Although fewstudies address this need directly, we found a num-ber of studies that provide insights into the factorsthat matter to residents and a smaller number thatprovide ways of measuring these factors. Thesestudies can generally be classified in two ways:empirical studies of travel behavior and level-of-

HANDY & CLIFTON 69

service measures designed for use in planning prac-tice. Although both types prove useful in identify-ing potentially important accessibility factors, bothalso have notable limitations. In the case of the for-mer, observed behavior, which is constrained by theavailable options, provides a convenient but imper-fect way of assessing true preferences and priorities.In the case of the latter, the relative importance ofdifferent factors is often assumed rather thantested. Nevertheless, these studies provide animportant starting point.

Activity Factors

The most basic characterization of activity is that aparticular type of activity can be found at a partic-ular location. Cumulative opportunities measures,for example, typically reflect a simple tally of loca-tions of a particular type of activity. Another com-mon approach is to account for the relative amountof activity at each location, usually measured by thenumber of employees or the square footage ofbuildings. This approach is commonly used in bothgravity measures and utility measures of accessibil-ity. But beyond the existence of an activity and theamount of an activity at a particular location, whatfactors influence the attractiveness of a particulardestination to residents?

Our previous research identified several specificcharacteristics that residents consider in evaluatingthe activities in and around their neighborhood;these characteristics range from mostly objective tohighly subjective (Handy et al. 1998; Handy andClifton 2001). The more objective factors of anactivity such as grocery shopping include size ofstore, prices, ease of parking, and range of productselection. More subjective factors include quality ofproducts, crowds, and length of check-out lines.Highly subjective factors like atmosphere also mat-ter. The relative importance of such factors is diffi-cult to assess, however. Not only does theimportance of these factors vary by individual, butit may vary at different times for each individual:residents may use different criteria in evaluatingstores for major food shopping than for a trip tobuy a gallon of milk, for example.

Recker and Kostyniuk (1978) studied factorsthat influence destination choice for grocery shop-ping trips in urban areas. Their study included a

survey of respondents’ perceptions of grocery storesthey frequented on a variety of different attributes.Using factor analysis, they reduced these attributesto four factors: quality (determined by reasonableprices, variety of items, meat and produce quality,and selection of goods), accessibility (determined byease of getting from home to stores and back and tostores from work), convenience (determined byparking facilities, proximity to other shops, hours ofoperation, ease of finding items in stores, andcrowding in stores), and service (acceptance ofcredit cards, check cashing, and ease of returninggoods). In the destination choice models estimated,only the service factor proved insignificant.

Research in the field of retailing provides addi-tional insights into factors that influence a cus-tomer’s choice of a particular establishment. A1980 study by Nevin and Houston, for example,looked at the role of image in the attractiveness ofurban shopping areas. Besides factors such as thequality of stores, the variety of stores, productquality and selection, and general price level, theyfound that the availability of lunch or refreshments,the adequacy of restrooms, the friendliness of theatmosphere, the helpfulness of store personnel, andwhether the center was an easy place to take chil-dren also contributed to the attractiveness of ashopping area.

These studies suggest a list of factors that con-tribute to the attractiveness of a particular activitysite. These factors can be grouped as relating to theactivity itself or relating to the design of the site(table 1). This list is by no means exhaustive, but itgives a sense of the wide range of factors that con-tribute to attractiveness. It is also important toremember that the relative importance of these fac-tors will vary depending on the type of activity.

What activities to include in an assessment ofneighborhood accessibility is also an importantquestion. Most examples of accessibility measuresin the literature use total retail and service employ-ment without further differentiation of activitytypes. Some studies focus on specific kinds of activ-ities, such as grocery shopping (Handy andNiemeier 1997) or health care services (Wachs andKumagai 1973). One study (Handy et al. 1998)gives some indication of the local businesses mostfrequently used by residents of six Austin, Texas,


neighborhoods. Supermarkets and grocery storestopped the list, followed by drug stores, restau-rants, discount stores, convenience stores, videostores, laundromats or dry cleaners, and bakeries.This list can serve as a guide to activities to includein an assessment of neighborhood accessibility.What it leaves out, however, are possible high-priority activities not located in or near those par-ticular neighborhoods.

Transportation Factors

Just as important as the activities found in andaround the neighborhood are the options residentshave for getting to them. Distance and time areused most often as measures of impedance in acces-sibility functions and represent the burden requiredto travel to a particular destination. While distanceand time can be important considerations in thedecision to drive, walk, bike, or ride transit, addi-tional factors contribute to the varying degrees ofaccessibility offered by different modes of travel indifferent neighborhoods. Mode choice models andlevel-of-service measures as well as exploratorystudies suggest a long list of transportation factorsthat contribute to neighborhood accessibility fordifferent modes (table 2). These factors can be cat-egorized as impedance, level-of-service, terminal,and comfort.

Accessibility factors for drivers are, perhaps, themost straightforward. Mode choice models consis-tently show that travel time, or sometimes a gener-

alized travel cost including travel time and mone-tary costs, is the most significant factor to drivers.Factors that influence the travel time or cost,including traffic volume, signalization, directnessof route, and continuity of route, may also beimportant as well as the availability and cost ofparking at the destination. Some drivers may con-sider comfort factors in their perception of accessi-bility. Poor lighting, bad weather, excessively highor low traffic speeds, high volumes of traffic, unap-pealing scenery, inadequate signage, or poor pave-ment condition may contribute to a negativeperception of accessibility. The importance of theseperceptual factors is mostly undocumented. Workby Ulrich et al. (1991), however, shows that thekind of chaotic visual environments found alongmany arterials in metropolitan areas significantlyincreases driver stress.

Mode choice models further show that traveltime is the most significant factor in the decision touse transit. However, most models also show thattransit users differentiate between in-vehicle andout-of-vehicle time, assigning significantly greatercost to the latter. This finding reflects the exposureof the transit user to the elements as well as to theuncertainty of transit service. As a result, amenitiessuch as benches and shelters are important to tran-sit users as are factors that influence the feeling ofsafety while waiting, including lighting, the speedand volume of passing traffic, and crime levels inthe area. A study of customer satisfaction amongriders of the San Francisco, California, Bay AreaRapid Transit (BART) system (Weinstein 2000), forexample, used factor analysis to group over 40attributes of the system into 8 factors influencingsatisfaction, listed in order of relative importance:service and information timeliness, station entryand exit, train cleanliness and comfort, stationcleanliness, police presence, policy enforcement,and parking.

Although pedestrians also are sensitive to traveltime and are limited in how far they can travel bywalking, they are also highly sensitive to the char-acter and quality of the environment throughwhich they walk. One study showed that percep-tions of safety, shade, and the presence of otherpeople were important determinants of the fre-

HANDY & CLIFTON 71

TABLE 1 Activity Factors

Factors related Size and scaleto activity Quality of products/services

Variety of products/servicesPrice of products/servicesHours of operationCrowds/linesInterior designAtmosphere Ownership (local vs. chain)Customer recognition

Factors related Mix of activities at siteto site design Density of activities at site

Parking facilitiesAtmosphereLandscape design

quency with which residents walked in the neigh-borhood (Handy et al. 1998).

Several recent efforts to evaluate the pedestrianenvironment also point to important accessibilityfactors. In the LUTRAQ (“Making the Land-Use,Transportation, Air Quality Connection”) studies, aPedestrian Environmental Factor was calculatedfrom four factors: ease of street crossing, sidewalkcontinuity, local street connectivity, and topogra-

phy (1000 Friends of Oregon 1993). In FortCollins, Colorado, a pedestrian level-of-servicemeasure was used to evaluate the traffic impacts ofnew development. This measure incorporated thedirectness of street layout, the continuity of side-walks, the width of street crossings, visual interestand amenities, and security and safety evaluations(Moe and Reavis 1997). Gainesville, Florida,developed a pedestrian level-of-service measure


TABLE 2 Transportation Factors by Mode

Automobile Transit Walking Bicycling

Impedance factorsDistance X X X XIn-vehicle time X XOut-of-vehicle time X X X XCost X XTopography X X

Level-of-service factorsVolume/crowding X X X XSignalization X X X XService frequency XHours of operation XDirectness of route X X X XContinuity of route X X X XInformation availability XSignage X X X XFacility widths X X XVehicle design X X XShelter X X XBenches X X

Terminal factorsParking availability X X XParking cost X XTerminal locations XIntermodal connections X X XTerminal design X X X X

Comfort factorsTraffic speed X X X XTraffic volume X X X XPavement condition X X X XLighting X X X XWeather X X X XShade X X XScenery X X X XCrime/police presence X X XCleanliness X X XConflicts with other modes X X X XOther users X X X X

that included the provision of a pedestrian facility,conflict points with vehicles, amenities, motor vehi-cle level-of-service, maintenance, and transporta-tion demand management or multimodal policies(Dixon 1995). Pedestrian level-of-service is alsoinfluenced by the degree to which sidewalks andcurb ramps meet the requirements of theAmericans with Disabilities Act of 1990. Sidewalkcharacteristics such as driveway crossings, crossslopes, level irregularities, clearance widths, andprotruding objects determine the accessibility ofsidewalks to persons with disabilities (Axelson etal. 1999); parents with strollers; children on skate-boards, scooters, or bicycles; and pedestrians ingeneral.

Bicycle riders are influenced by a mostly parallelset of factors. The Federal Highway Administra-tion’s (FHWA) National Bicycling and WalkingStudy included an assessment of the reasons whybicycling is not used more extensively (USDOT1992). In reviewing a number of surveys on bicycleuse, this study found that primary deterrents tocycling included traffic safety concerns, adverseweather, inadequate parking, and road conditions,and that secondary deterrents included fear ofcrime, lack of bicycle routes, inconsiderate drivers,and inability to bring bicycles on buses. FHWA has,more recently, developed a “bicycle compatibilityindex” to evaluate the appropriateness of a road-way for bicycle use. This index includes the pres-ence and width of a bicycle lane, curb lane width,traffic volume in the curb lane and other lanes, traf-fic speed, parking lane presence and occupancy,truck volume, parking turnover, and right-turn vol-ume (USDOT 1999). Gainesville also developed abicycle level-of-service measure similar to its pedes-trian measure but with slightly different definitionsof each factor (Dixon 1995).

DATA AVAILABILITY

Unfortunately, data for only a few of the accessi-bility factors identified earlier are readily available.Data can usually be found for basic characteristicsof land use and transportation systems, but dataon qualitative and subjective factors are scarce;these factors are hard to assess and the accuracyand stability of the observations are often ques-tionable. The result is a significant gap between the

data needed to describe important accessibility fac-tors and the data readily available to planningdepartments.

Land-Use Data

At a minimum, an accessibility analysis requiresinformation about what kinds of activities existand where they are located. The availability andlevel of detail of land-use data often vary by localplanning department. Data about employment aremore difficult to find than data about residents,which are available through the decennial census.Most metropolitan planning organizations (MPOs)and some cities have developed databases ofemployment by type and by area, census tract ortraffic analysis zone, but the quality of such data isnotoriously poor and the categories of employmentare usually quite broad. Data on floor space by typeof commercial or industrial use can sometimes beextracted from the databases of local tax assessors,and zoning classifications are also sometimes usedas an indication of land use. However, it is oftendifficult to find accurate and specific informationabout current land use in electronic format, andcollecting detailed information through field workcan be laborious and time consuming. In mostcases, data on the quantity of several general cate-gories of activities at the zone or tract level areavailable, if nothing more.

Business and residence telephone directory list-ings provide more specific data on land use and arereadily available in electronic format. For a studyof accessibility in Austin, Texas, neighborhoods,the Select Deluxe CD-ROM was used for the year19961 (Handy and Clifton 2000). These datainclude business or residential name, address,phone number, and geographic coordinates in lati-tude and longitude. Business listings also includeapproximations of the appropriate StandardIndustrial Classification (SIC) codes to the four-digit level.

The use of telephone listings as a source for land-use data offers several advantages. First, the dataare readily available and relatively inexpensive.The CD-ROM can be purchased at many computer

HANDY & CLIFTON 73

1 Select Deluxe CD-ROM is available from ProCD, Inc.,222 Rosewood Drive, Danvers, MA 01923,http://www.procd.com.

software retail stores, and data for the entire UnitedStates cost less than $150 as of this writing. Second,the SIC approximation allows for easy classifica-tion of business types and thus permits disaggre-gate analysis on specific industries or services.Third, the addresses for business and residentiallistings are already geocoded and can be easilyimported into GIS software. Last, the availability ofdisaggregate data for an entire urban area permitsa detailed analysis at both the local and regionallevels. However, using these data for accessibilityanalysis also has its drawbacks. Establishmentswith multiple telephones are overrepresented in thedatabase, and businesses without a phone at thetime of publication are missing from the data set.Also, the SIC codes are only approximations basedon the category under which the business is listed inthe directory.2 In addition, frequent businessturnover reduces the accuracy of the available data,and those listings that do not include an address inthe telephone directory are omitted. Although thesedata provide detailed information about the loca-tion and type of establishment, other land-usecharacteristics such as size, quality, or site designcannot be obtained from this data set.

Transportation Data

The availability and detail of transportation infor-mation also varies widely by planning department.In most areas, zone-to-zone characteristics such astravel time or travel cost are available, but data arenot usually available for travel within neighbor-hoods and for modes other than automobile andtransit. The task of compiling the necessary trans-portation data is complicated by the lack of coor-dination between the various government agenciesresponsible for data on different transportationfactors.

Transportation network files can be obtainedfrom the U.S. Census Bureau in the TIGER/Linefiles. Enhanced and updated network files can beobtained from private vendors, MPOs, or otherlocal agencies. These files allow for distance calcu-lations between points on the network, althoughtravel times are usually more important to resi-

dents. Estimating the travel times between twopoints requires estimations of the average travelspeeds for each link in the network, which for driv-ers is dependent on traffic volume. Data on auto-mobile travel times are available from regionaltransportation planning models usually maintainedby MPOs. These data can be problematic, how-ever; they are not always accurate, are not availablefor most local roads in the network, rarely includetemporal variations, and give zone-to-zone ratherthan point-to-point times. As an alternative, speedlimits can be used to estimate travel time, but speedlimit data are often not available in GIS format. Afew studies have estimated point-to-point traveltimes and distances using the capabilities of a trans-portation modeling package (Handy 1996; Handyet al. 1998) or GIS (Crane and Crepeau 1998).These estimates provide a reasonably accurate indi-cation of driving distances at the neighborhoodscale and also walking and biking distances.

Data for modes other than driving are oftenmore difficult to locate. For transit, data about thelocation of transit stops, routes, capacity, andschedules are usually available but not always inelectronic format. Accurate information about thespatial distribution of benches, shelters, and light-ing, and crime and safety statistics is less oftenavailable. For example, as of this writing, CapitalMetro, the transit authority in Austin, Texas, hasdata on the locations of transit stops in electronicformat but no additional information about thestops, such as presence of bus shelters, that mightbe valuable in an accessibility analysis. Ridershipinformation has been available in electronic formatby route and stop for some time, but bus routeshave been added only recently.

Data on infrastructure for pedestrians and bicy-cling are not generally available, although this situ-ation seems to be changing. Some cities may havean inventory of sidewalks, but such data seemrarely to be in electronic form. In the mid-1990s,the city of Portland, Oregon, completed a city-widesidewalk inventory that required considerable timeand labor. Data on other factors that influence thequality of the walking and biking experience, suchas tree canopy, can sometimes be extracted fromaerial photos. Data on more qualitative factors,such as the scenery and the presence of interesting


2 In an ironic, and we hope inadvertent twist, we founddriving schools (of the sort for ticketed drivers) classifiedas “drinking places.”

houses or gardens to look at, can only be evaluatedthrough field work and the development of criteriaby which to judge such factors. The LUTRAQstudy used such a system to evaluate less qualitativefactors, such as topography and the interconnect-edness of the street network (1000 Friends ofOregon 1993).

The changing attitudes about alternate modesand the availability of federal funding for transit,bicycling, and pedestrian projects have influencedsome planning agencies to focus more attention onthe deficits in modal data. In Austin, Texas, anextensive effort was initiated to collect data aboutthe street conditions and physical characteristicsalong existing and proposed bike routes and theiradjacent streets. Data about traffic volume andspeed, pavement condition, street and lane width,presence and continuity of bike lanes, number ofstop signs and traffic signals along the route, andother objective criteria were compiled. Based onthis information, the street segments were thenranked for bicycle friendliness and published on thebicycle route maps for public distribution. Suchefforts can contribute to the development of a data-base of accessibility factors for use in both neigh-borhood-specific and city-wide analyses.

STRATEGIES

What can a planning department do, given the gapbetween the data needed to describe importantaccessibility factors and the readily available data?Two complementary strategies might prove useful:one is a city-wide approach using existing data andGIS to evaluate accessibility for neighborhoodsacross the city and the other involves a neighbor-hood-specific approach to building a detailedaccessibility database. If the goal is to compareaccessibility across neighborhoods to identifyneighborhoods with deficiencies in accessibility orto evaluate the equity impacts of proposed policies,then a city-wide approach makes sense, eventhough the available data are limited to the mostbasic accessibility factors. If the goal is to develop aneighborhood plan, then the neighborhood-specific strategy might prove useful, even thoughextensive data collection is involved. Planningdepartments might employ both strategies at dif-ferent stages of a planning effort.

City-Wide

Several recent research projects demonstrate someof the ways that existing data can be combinedwith the capabilities of GIS to evaluate accessibilityat a relatively coarse level on a city-wide basis. Inall these examples, researchers point to the powerof visualization as an important benefit of the useof GIS for accessibility analysis.

Talen (1998) used GIS to evaluate the distribu-tion of public facilities, such as parks, in terms ofthe match between the facilities provided and theneeds of residents and in terms of the equity of thedistribution across socioeconomic groups. Fourdifferent measures of access from census blocks toparks were calculated: the gravity model, withparks weighted by size and separation distancebetween origin and each park destination; mini-mizing travel cost, determined by the straight-linedistance between each origin and each park desti-nation; covering objectives, measuring the numberof parks located within a critical distance (essen-tially a cumulative opportunities measure); andminimum distance between each origin and thenearest park. This study demonstrates the power ofGIS as a tool for evaluating accessibility across anurban area and the impact of public facilities planson the equity of accessibility patterns. As Talenpoints out, the analysis can be refined throughmore precise measurement of accessibility, includ-ing an assessment of the quality of the facility orservice, the use of origin zones smaller than censusblocks, and more sophisticated measures of trans-portation. However, the increased costs of data col-lection and analysis may outweigh any benefitsfrom increased precision. “The real benefit of theapproach outlined in this paper is that it is a tech-nique that is readily available to local planners”(Talen 1998).

A study by Grengs (2000) underway at CornellUniversity uses GIS to evaluate accessibility ofinner-city neighborhoods to supermarkets. The ini-tial approach was to use a buffer of a given distancearound a bus line that serves a supermarket andthen analyze the portion of each traffic analysiszone within the buffer area. Assuming that popula-tion and households are uniformly distributedthroughout the zone, the area within the buffer canthen be translated into the share of population

HANDY & CLIFTON 75

within the buffer and, in particular, the share of car-less households within the buffer. Grengs points toseveral limitations of this analysis. First, the analy-sis would ideally account for the affordability andquality of products offered by each supermarket.Second, the buffers were drawn around bus linesrather than bus stops given limitations of the data.Third, only transit trips possible without transferswere considered. Fourth, the approach estimatesequal accessibility for households with and withoutcars. Nevertheless, an application of the analysisapproach to Syracuse, New York, points to theprobability of underestimated disparities in accessi-bility to supermarkets for low-income and African-American households.

The British Government’s Planning PolicyGuidance 13, which encourages plans that pro-mote development at locations accessible by modesother than automobile and that improve access bynon-car modes, has led to the creation of at leasttwo models that evaluate accessibility using GIS.One project evaluated both the accessibility of aparticular residential location to public transit,local accessibility, and the accessibility of locationsto specific destinations using public transit, net-work accessibility (Hillman and Pool 1997). Localaccessibility was calculated as a combination of thewalk time to a transit stop and the average waittime for service at that stop. For each residentiallocation, access to all possible stops was evaluatedand combined into one measure. Network accessi-bility was calculated by defining a set of destina-tions (e.g., schools or shopping centers), identifyingthe transit routes that link the residential zone tothe selected destinations, and estimating the totaltravel time to those destinations. An integrated sys-tem consisting of a GIS and public transit planningsoftware was used to compile an extensive data-base and calculate accessibility measures, but thelack of required data on public transit systems hasbeen an obstacle to the more widespread use of thistool.

A second U.K. project focused on selected desti-nations and determined the number of residentswithin various travel times of a destination by eachtransportation mode (Hardcastle and Cleeve1995). Although data on land uses and road net-works were readily available for this model,

estimates of travel times by mode were relativelycrude, depending on assumptions about the matchbetween the pedestrian network and the road net-work, for example, and about average travel speedsby mode.

In an exploration of the potential for using GISwith available data to assess neighborhood accessi-bility on a city-wide basis, a variety of measureswas calculated for seven neighborhoods in Austin,Texas (Handy and Clifton 2001). Simple counts ofthe numbers of selected types of retail establish-ments located within buffers of various distancearound the neighborhood were used to measureactivity intensity (total number of establishments);diversity (number of types of activities); and choice(number of establishments of each type). Thesemeasures were also normalized for neighborhoodpopulation and for neighborhood area in order tofacilitate comparisons. A more direct assessment ofthe number of retail establishments found in oneneighborhood compared with others was madeusing a location quotient, defined as the share ofestablishments of a certain type within a neighbor-hood relative to the share of establishments of thistype for the city overall. A value greater than oneindicates that the neighborhood has a greater shareof establishments of that type than the city as awhole and may thus be overserved; a value lessthan one indicates that the neighborhood may beunderserved. A high location quotient is not alwayspositive, however. The location quotients for sevenneighborhoods in Austin showed that the low-income neighborhood had over nine times theshare of drinking establishments as the city overall.These analyses demonstrate both the usefulnessand the limitations of relying on existing data andthe capabilities of GIS to assess neighborhoodaccessibility.

Neighborhood-Specific

The available data and the capabilities of GISclearly fall short of providing planners with a fullassessment of the factors that influence neighbor-hood accessibility as listed earlier. Developing acomprehensive neighborhood accessibility data-base, consisting of detailed data about a wide rangeof accessibility factors for all neighborhoods in acity, requires a significant commitment of resources


on the part of a planning department. An intrigu-ing alternative is to make data collection itself animportant part of the planning process and to useneighborhood residents to design and build theneighborhood accessibility database. Not only isthis approach cost-effective for the city, it uses datacollection as way to facilitate public involvementand build technical capacity within neighborhoods,important benefits in their own right.

In Austin’s neighborhood planning program, forexample, residents and other local stakeholders areresponsible for developing their own plan for theneighborhood, with guidance and some assistancefrom city staff. An early task is to compile dataabout existing conditions in the neighborhood,such as inventories of existing land uses and infra-structure and an assessment of the condition ofinfrastructure. In addition, the planning team isrequired to conduct surveys of residents’ concernsand priorities. This approach has many benefits.Such data-collection efforts are labor-intensive andthus need many volunteers from the neighborhoodinvolved. Those who participate learn the kinds ofinformation useful for planning purposes and thetechniques effective in collecting that information.Participants are likely to understand and appreciatethe results more than if city staff simply presentedthe results to them. In addition, participants candecide for themselves which accessibility factorsare of greatest importance. The data produced bythis effort can also be incorporated into a detailedcity-wide database, constructed over time as moreneighborhoods participate.

Providing the neighborhood planning team withdirect access to GIS software and sufficient trainingto use it effectively could be even better and maynot be as costly or impractical as one might think,as demonstrated by a growing number of exam-ples. In 1993, a group of graduate students at theUniversity of Wisconsin-Milwaukee developed aprocess for training neighborhood residents to useGIS to analyze a publicly accessible database ofproperty characteristics, including ownership, zon-ing, land use, assessed value, and other usefulinformation (Myers 1994). One step in the processincluded a walk through the neighborhood to col-lect information about the condition of properties.The project succeeded in providing residents with

the capability to use GIS to analyze and address avariety of problems in the neighborhood. InPhiladelphia, the city has allocated funds toCommunity Development Corporations (CDCs)for GIS hardware, software, and training so thatthe CDCs can better illustrate the quality and char-acter of the environment of the neighborhood(Casey and Pederson 2000). Such examples hint atthe power of GIS not only as a planning tool butalso as a public involvement technique.

CONCLUSIONS

As efforts to promote the use of modes other thandriving grow and as neighborhood planning pro-grams proliferate, planners need new and bettertools to identify problems, highlight inequities, andevaluate potential solutions at the neighborhoodlevel. The concept of neighborhood accessibilityprovides a useful framework for the developmentof such a tool. As defined here, neighborhoodaccessibility includes a wide range of factors thatdescribe both the quantity and quality of activitiesin and around the neighborhood and the charac-teristics of the transportation systems that link oneactivity to another. The key to identifying the fac-tors that contribute to accessibility is to examinetheir relative importance to residents. Although nosystematic effort has been undertaken to catalogthese factors, a review of the literature points to along list of factors likely to be important.

Unfortunately, data are readily available for onlya small subset of these factors. The gap between thedata needed to measure these factors and the datathat are readily available demands a creativeapproach to measuring accessibility. Two strategiesare proposed here: a city-wide strategy using avail-able data and the capabilities of GIS and a neigh-borhood-specific strategy that asks residentsthemselves to build a detailed accessibility databaseas a part of a neighborhood planning process.Several documented planning efforts provideexamples of how these strategies might be imple-mented and the kinds of benefits they can produce.Other strategies may also prove effective. Thispaper provides a starting point and, it is hoped, willlead to new efforts and greater creativity on thepart of others to define and measure neighborhoodaccessibility.

HANDY & CLIFTON 77

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Casey, L. and T. Pederson. 2000. Urbanizing GIS:Philadelphia’s Strategy to Bring GIS to NeighborhoodPlanning. Available at http://pasture.ecn.purdue.edu/~aggrass/esri95/to150/p107.html, as of Oct. 27, 2001.

Crane, R. and R. Crepeau. 1998. Does Neighborhood DesignInfluence Travel? A Behavioral Analysis of Travel Diaryand GIS Data. Transportation Research D 3:4, pp.225–38.

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Handy, S. and K. Clifton. 2000. Evaluating NeighborhoodAccessibility: Issues and Methods Using GeographicInformation Systems, Report SWUTC/00/167202-1.Southwest Region University Transportation Center,Center for Transportation Research, The University ofTexas at Austin, November.

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Handy, S., K. Clifton, and J. Fisher. 1998. The Effectiveness ofLand Use Policies as a Strategy for Reducing AutomobileDependence: A Study of Austin Neighborhoods, ResearchReport SWUTC/98/465650-1. Southwest Region Uni-versity Transportation Center, Center for TransportationResearch, The University of Texas at Austin, September.

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ABSTRACT

This paper explores the development of an accessi-bility measure based on daily travel patterns. Incontrast to traditional zone-based measures, dis-tance is calculated using a predefined travel matrix.The travel pattern for each zone is used as a weightin the accessibility measure. This path-based acces-sibility measure is implemented in a computer pro-gram that is closely coupled to a transport-orientedgeographic information system. The measure isdemonstrated in an application for two Swedishcounties. The properties of the measure are evalu-ated and compared with standard accessibilitymeasures used in the planning process. This papershows that there are differences between tradi-tional measures and the suggested path-basedmeasure and differences in accessibility betweensocioeconomic groups with different travel pat-terns. It is concluded that path-based accessibilitymeasures could be very useful to analyze accessibil-ity for high-mobility groups.

INTRODUCTION

Accessibility implies the ability to physically travelto a resource at a fixed location. The introductionof new technologies, such as electronic commerce,has complicated the definition of presence, but in

79

Path-Based Accessibility

SVANTE BERGLUNDRoyal Institute of Technology

Svante Berglund, Department of Infrastructure andPlanning, Royal Institute of Technology, S-100 44Stockholm, Sweden. Email: [email protected].

this article we are concerned with physical presenceas a result of travel to a supply source. Becauseaccessibility is a crucial positive outcome of thetransportation system,1 how it is measured isimportant.

Accessibility measures (AMs) can be categorizedin many different ways, but in the recent literaturethere is a tendency to discriminate between zone-based and individual AMs (see, e.g., Hanson 1995,Kwan 1998, and Miller 1999). As the labels indi-cate, zone measures try to capture the overall acces-sibility for a zone, while individual measures try tocapture the accessibility of individuals based ondetailed characteristics of space, available time, andmeans to overcome space. One of the main advan-tages of individual measures is that they can takeinto account the fact that most individuals face amandatory daily travel pattern, such as to and fromwork. Zone-based measures neglect the importanceof mandatory travel patterns on accessibility.

In the simplest form, zone-based measures resultin one figure of accessibility for each zone, whichmay become a target of criticism. In practice, how-ever, different accessibility scores are calculatedbased on gender, socioeconomic status, etc., butthese scores are still averages across a number ofindividuals. Disaggregating population data is oneway of obtaining more realistic accessibility figuresusing zone-based measures.

Individual measures, on the other hand, maylead to as many values of accessibility as there areindividuals in the study area. Individual measuresare conceptually attractive, but face difficultiesfrom an operational standpoint (Hanson 1995).One of the most notable difficulties with obtainingindividual measures is collecting data becauserevealed preference data cannot be used. Infor-mation on time constraints and mandatory activi-ties cannot be obtained from a single travel surveyquestion, but result from a series of questions.Although conceptually the two measures are verydifferent, their mathematical formulation can beidentical (Hanson 1995). The conflict is betweenconceptual elegance and implementation. One wayof increasing the realism of aggregated zonal meas-

ures is to use detailed population data. Anotheroption is to add mandatory travel pattern informa-tion on a zonal level, thus maintaining the opera-tional advantages of zonal measures while bringingin components from individual AMs. This latterapproach will be developed in subsequent sections.

The paper is organized as follows. In the nextsection we take a look at different approaches tomeasuring accessibility. In the third section, analternative AM is defined where a mandatorytravel pattern is taken into account. In the forth sec-tion, data for an empirical example are presentedand implementation of the AM in a GIS software isdescribed. Then an analysis of the properties of thesuggested AM and comparisons with more estab-lished AMs are presented. Finally, the last sectionprovides concluding remarks.

ACCESSIBILITY MEASURES

Regardless of the type of AM, two components arealways present—representation of travel cost (in awide sense) and representation of opportunities atthe destination. Travel cost could be represented asa simple 0/1 variable or defined in detail using aparameterized function. Similarly, description ofthe opportunities can range from a simple descrip-tion of the resource location to detailed address-coded registers of a multitude of opportunities.Population or number of work places are fre-quently used as measures of opportunitites.

Individual space-time accessibility measures(STAMs) (Miller and Wu 2000) have gainedincreasing popularity recently (see, e.g., Kwan1998 and Miller 1999). This is partly due to GISdevelopments that include programming facilitiesand techniques for visualizing individual behavior.Examples of implementation of individual AMs inGIS can be found in Miller (1999), Miller and Wu(2000), and Kwan (1998). Despite the fact thatmost implementation of individual AMs arerecent, the theories behind those AMs are matureand originate from Hägerstrand’s space-timeframework2 (Hägerstrand 1970; see alsoLenntorp 1976). In the space-time framework, the


1 Many other effects, such as pollution, accidents, andconsumption of land, are negative.

2 This is frequently illustrated using the space-time prism(see, e.g., Lenntorp 1976).

mobility of the individual is constrained by trans-portation resources available, which affect accessto opportunities and encourage combining activi-ties with other people.

Mandatory travel patterns, such as going to andfrom work and picking up children, play an impor-tant role in space-time theory. The implications foraccessibility of mandatory travel patterns aretwofold. On the one hand, a mandatory travel pat-tern restricts mobility and prevents the individualfrom reaching certain opportunities, on the otherhand, a mandatory travel pattern brings the indi-vidual to places that may provide opportunitiesand reduce the need for special purpose trips.

Possibilities for overcoming distance and otherobstacles to mobility differ among individualsdepending on where they live and work as well ason their mobility resources. All these restrictionsdefine an area, called the potential path area (PPA),that a specific individual can cover given the set ofconstraints. Despite its conceptual simplicity, thefunctional form of the travel impedance for indi-vidual space-time measures may be a complexsequence of conditions, depending on how manyrestrictions in space and time are taken intoaccount. The PPA simply defines a subset of thetotal study area that should be taken into accountwhen measuring accessibility for an individual.This is in contrast to standard measures where evendistant opportunities can contribute to accessibil-ity, although to a limited extent.

A next step is to determine the utility of oppor-tunities that can be reached. Here, a weightingscheme is necessary. A similar accounting of dis-tance to opportunities can be applied in both indi-vidual and aggregate zonal AMs. The simplestalternative is to put equal weight on all opportuni-ties within a cutoff value of distance in aggregateAMs and let the PPA define the cutoff value forindividual measures of distance (cumulative AMs).Another alternative is to use a gravity-based weightfunction. Accessibility measures based on gravityprinciples adopt a weighting scheme according tosome aggregate travel behavior. Formally, gravity-based measures can be written as follows:

where ai is the accessibility of zone i with regard tothe supply of x across all zones j, and tij is the dis-tance or some other measure of the travel imped-ance between i and j. The shorter the distance thebetter. Common alternatives for f(tij) is the expo-nential function and the power function.Cumulative opportunity measures can be written inthe same form as gravity measures by using

where T is the cutoff value. Cumulative opportu-nity measures are simpler to use compared withgravity measures, because they do not require esti-mation of parameters.

A third alternative is to use an AM based on ran-dom utility theory. The most widely used model ofthis type is the logit model from which the logsumis derived:

In equation (3), the utility is simply a function ofdistance as in previous measures and of the oppor-tunities of zone j. Logit models can handle timeconstraints in the choice set and constrained mod-els have been successfully used by Thill andHorowitz (1997). An application to accessibilitywhere the logsum is used in a time-space frame-work can be found in Miller (1999). In an article byRichardson and Young (1982), the properties ofthe logsum as an accessibility measure are exploredfor linked trips.

The formulation of the functional form of thedistance function has no doubt attracted the mostinterest in the literature. In some respects, percep-tions of opportunities at the destinations are criti-cal. At one extreme you may find opportunitiescharacterized by “the more the better” and at theother extreme “one is enough.” In the first alterna-tive an additive indicator is appropriate, and in thesecond case a maxitive indicator is required (seeWeibull (1980) for a discussion on additive andmaxitive indicators).

BERGLUND 81

( )a x f ti jj

ij= ∑ ( )1

( )f tt T

ijij=

<

1

02

for

otherwise( )

( )a x ti j ijj

= −∑log exp ( )β 3

There are several problems with zone-basedAMs. We must remember that accessibility analysisdoes not differ from any other zone-based analysisof spatial data. The resulting accessibility willdepend on how and to what scale we have aggre-gated our data and zones (i.e., the modifiable arealunit problem). By using zones we cannot explicitlytake individual time constraints into account.Zone-based measures also fail to analyze interac-tions between individuals, which is one of thestrong arguments for individual measures.

AGGREGATE PATH-BASEDACCESSIBILITY

In order to take advantage of the information pres-ent in a predefined travel (to work) matrix, an AMwill be developed wherein the accessibility of eachzone is weighted by a travel matrix. This is illus-trated in figure 1 (left) where the housing area isdenoted h, alternative destinations (e.g., for shop-ping trips) are denoted s, and the travel distance isequal across all alternatives. The AM used in asso-ciation with figure 1 (left) will be a standard aggre-gate AM as in equation (1)

If the alternatives (which we assume) are equal,all alternatives can be chosen with equal probabil-ity. If we add information about a mandatory trip(e.g., a trip to and from work), we have a new activ-ity pattern to consider, figure 1 (right). In this set-ting the available shops will not be indifferent to

the traveler in the example. With path-based meas-ures, it is possible to calculate the extra travel timethe activity requires given the two initial activitiesat i and j. This is an important aspect not taken intoaccount by other types of accessibility measures.The extra travel time caused by going to k (s3) isgiven as

where i is allowed to be equal to j, which means a

trip was not made or that job and home are in the

same zone. In this case there will be no difference

between a traditional zone-based AM and a (non-)

path-based AM. A modified distance measure like

this can be found in Richardson and Young (1982).

If i j and k is along the road from i to j, the extra

time equals the time consumed by activity l, and

will be denoted by tl. The total extra time con-

sumed by activity l at an arbitrary k will equal

If it is impossible (or difficult) to obtain

some reasonable estimate of we could use some

other stop penalty. The probability of making an

additional trip or stop is not modeled in the appli-

cation below. Changes in that respect, however,

will not alter the fundamental properties of the

path-based AM. Just changing the distance meas-

t kl ,

t tk ij kl

| .+


h1s1

s2

s3

4

4

4

h1s1

s2

s3

w1

10

7

4

4

4

4

FIGURE 1 Illustration of the Difference Between Traditional Accessibility Measures (left) and Path-Based Measures (right)

( )t t t tk ij ik kj ij| ( )= + − 4

ure by taking one possible trip pattern into account

will not add much realism to our AM. To gain

something more, we must weight the AM by incor-

porating information on probabilities for manda-

tory destinations using a trip pattern that is not

evenly spread across all destinations. The next

component is, thus, a travel matrix Fij, where i rep-

resents the residential zone and j represents the

work zone. This matrix could be observed from a

travel survey or estimated by some model.

where we can then

write a path-based AM weighted by the trip pattern

:

We noted above that is a predefined travelmatrix that could be obtained from a survey (asavailable in Sweden) or be the results of an earlierestimation. But, if the matrix is estimated, it mayoriginate from a process like Fij = Fi Pj|i. If wesubstitute the right side of (5) into (6) and use theassumed model for Fij we will obtain:

which will simplify to

One important determinant of our AM will bethe number of trips outside the residential zone. Ifthe travel pattern only consists of within-zone trips,

will be zero except for the diagonal. Then ourAM will equal traditional zone-based AMs. If thetravel pattern consists of trips between any pair ofzones, the path-based accessibility score will beequal to or higher than scores of traditional AMs.The usefulness of the suggested AM will, thus,depend on zone size because the share of within-

zone trips can be expected to be proportional to thezone size. If we disaggregate into groups thatcan be expected to have different mobility charac-teristics, the analytical power will increase.Segmentation can be made with regard to socioe-conomic status or education. Yet another alterna-tive is to transpose the weight matrix and obtain anaccessibility score for the work zones.3

Our suggested AM is still a zone-based measureand suffers from the same problems as other aggre-gate AMs (mentioned in the previous section). Forexample, using a path-based measure of this typewill not capture interactions between individuals.What could be done is to impose a complex weight-ing scheme and argue that the realism of our AMhas increased. This, however, would not alter thefundamental properties of zone-based AMs (e.g.,we still do not capture interactions between indi-viduals). Instead, the argument for our measure isthat we maintain the operational properties ofaggregate AMs while adding information on oneimportant daily activity—trips to work.

EMPIRICAL EXAMPLE, DATA, AND PROGRAM

In order to illustrate our measure we provide oneapplication with an observed travel pattern and oneapplication with an estimated travel pattern. For theempirical example we used two sets of data—onefrom the Stockholm region and one from the countyof Jämtland about 600 kilometers (km) northwest ofStockholm (see maps in figures 2 to 4). For charac-teristics of the two regions, see table 1. The regionaldivision is based on small area marketing statisticszones of varying size. In the city centers, the zonesconsist of just a few blocks, while in the peripherythe largest zones are over 100 km2. The two appli-cation areas are different in two important aspects:1) for the Stockholm region we used an estimatedmatrix as the travel pattern weight , while weused a matrix from a total survey for Jämtland; and2) Stockholm is an urban region with more than 1.7million inhabitants with a dense population, whileJämtland is rural and sparsely populated.

One of the contributions of the AM put forwardin this article is the weighting of the travel paths. As

( )ω ij

ω ij

ω ij

ω ij

ω ij

( )F Fi ijj j ij= =∑ ∑, ,ω 1

BERGLUND 83

ω ij ij iF F= / ( )5

( )a x f ti ijj

k k ijk

= ∑ ∑ω | ( )6

( ) ( )aF P

Fx f ti

i j i

ijk k ij

k

= ∑ ∑|| ( )7

( )a P x f ti j ij

k k ijk

= ∑ ∑| | ( )8

3 This option is available in the software developed forthis paper but is not used in the application below.

shown in the section on aggregate path-basedaccessibility, this can be done using observed orestimated travel flows of a compulsory trip pattern.In the application for Jämtland, we used a matrixobtained from a total survey, the 1990 census—thelast year in which data with mode choice are avail-able on a geographically detailed level. Our data setcontains variables for gender, education, and mode.To restrict the empirical example, only the carmode was considered. For the Stockholm region,we used estimated matrices for men and women asweights for trips by car.

Two different types of opportunities wereselected: one where “more is better” (additive) andanother where “one is enough” (maxitive). For theadditive opportunity, the number of jobs in retailtrade was used. As the maxitive opportunity, phar-macies were used. Pharmacies were selectedbecause this type of opportunity is independent of

the size or number of opportunities.4 In this study,alternative ways of distributing prescription drugswere not taken into account.5 Access to retail tradeand access to pharmacies were measured to thecentroid of the STAMs that contains the relevantopportunity.

Network data were obtained from the Swedishroad administration and the Swedish Institute forTransport and Communications Analysis (SIKA).In the sparsely populated region we used free flowtravel times, while in the Stockholm region we usedtravel times from the afternoon peak hour. In ourexample, we have used a precalculated travel timematrix. Another alternative is to include the short-est path algorithm in the calculation of the AM andavoid storage of the travel time matrix. This mightbe an alternative for GISs that cannot handlematrices, but is not a restriction in our case.

We defined the general form of our AM in termsof one opportunity (xj) and one impedance func-tion f(tk|ij) or f(tij). In the applications presentedbelow, we used the simple formulation from equa-tion 2 (cumulative opportunity) and the logsumfrom equation 3. For the cumulative opportunitymeasure, we used a cutoff time of 25 minutes. Thereason behind choosing cumulative opportunity isthat, despite its shortcomings, this is a frequentlyused measure in applied work. An alternativemeasure is the logsum, which is a natural alterna-tive in association with transport models. The log-sum is a parameterized AM and needs estimationof the parameters of a logit model. This model wasestimated using data from the national travel sur-vey6 (RVU 94) where information on secondarytrips was available. In order to concentrate on theAM, a simple model with travel time as impedanceand number of workplaces (wk) in retail trade at kas attraction was estimated, uk|ij = 0.3603log wk–0.2265tk|ij, where uk|ij is the utility of going to k


0 200 400

Kilometers

Jämtland

Stockholm

FIGURE 2 Application Areas

4 It is not reasonable to regard a destination with twopharmacies as twice as good as a destination with onepharmacy. For retail trade in general, it could be a rea-sonable assumption that a large destination (e.g., a shop-ping mall) constitutes a more attractive alternative than asmall one (e.g., a single store).5 In some sparsely populated areas, drugs are distributedby a local shop or post office the day after an order hasbeen placed.6 This travel survey is sample based.

conditioned on a trip from i to j. Most secondarytrips are short, and the destination is either close tohome or close to work, consequently our parame-ter is rather high (–0.2265). We used these esti-mates for both applications.

In a nested logit model, the secondary trips willmost likely be in a nest below the destinationchoice. In such a model structure, different levelsshould be coupled by the inclusion of a logsumterm. It is, however, not likely that someone would

choose their place of work with regard to the serv-ice supply along the road between home and work.We have, thus, not included any logsum term fromthe secondary trips into the utility function of thedestination choice model.

The application platform is a transport-orientedGIS, TransCAD7 (TC). Beside the standard GIStool box, TC contains routines for transportationanalysis, such as different modeling tools. TC alsoprovides an internal matrix database format (lack-ing in most GISs), which simplifies our application.The program8 that computes the accessibility iswritten in TC’s internal programming language(Caliper script) and integrated in a “tool box”where different AMs are available (see Berglund1999). The usage of a native GIS programminglanguage makes it possible for us to offer a close

BERGLUND 85

100

Kilometers

Retail trade0–11–55–1010–2525

500

FIGURE 3 Location of Pharmacies and Employment Within Retail Trade in Jämtland County

40

Kilometers

Retail trade01–55–1515–5050200

FIGURE 4 Location of Pharmacies and Employment Within Retail Trade in the Stockholm Region

TABLE 1 Characteristics of the Application Areas

Jämtland Stockholm

Inhabitants 135,584 1,725,756Km2 49,347.5 5,812.3Inhabitants/km2 2.75 296.91Nodes 1,000 4,400Links 2,000 9,000Zones 150 900Time Free flow Afternoon peak hourMode Car Car

7 Available at http://www.caliper.com.8 The program is available from the author on request.

integration between GIS and the computationalroutines. The program can only run within TC.9

COMPARATIVE ANALYSIS OF AMS

Using aggregate path-based accessibility measures,accessibility with regard to spatial location (whichis traditional) and impacts of socioeconomic status(education) and mobility pattern (based on groups)will be analyzed.

In order to explore some of the properties of thepath-based AM, it is compared with existing andwell known AMs. Such AMs are the nonpath-based equivalent of the AMs selected for this study.In previous studies, comparisons between differentAMs were made using correlation coefficients (see,for example, Kwan 1998). The fact that two AMsare correlated does not indicate quality but mayprovide an intuitive sense of their properties.Remember that the case with no compulsory tripswill yield the same value of path-based accessibil-ity as the corresponding traditional AMs. Thus,low mobility groups are expected to have a path-based accessibility similar to standard zone-basedaccessibility.

In standard AMs, the only factor that deter-mines accessibility is the location of the zone inrelation to the opportunities. This might imply acontinuous pattern of accessibility. Given equalaccess to mobility resources, the differencesbetween socioeconomic groups will be negligible.For path-based measures, the resulting accessibilitywill also depend on the travel pattern associatedwith the population in each zone and its socioeco-nomic composition. It is well known that differentsocioeconomic groups have different mobility pat-terns and that different travel time sensitivities areobtained when estimating models.

When we weight the AM with the travel pattern,we expect to discover inequalities in accessibilitythat are difficult to uncover using other types ofAMs. This will also result in less continuous pat-terns of accessibility, and adjacent zones will showdifferent accessibility depending on socioeconomiccomposition. We can check this by using a test for

the degree of similarity between adjacent zones(spatial autocorrelation). The most widely used testfor global spatial autocorrelation is Moran’s I(Moran 1948; Cliff and Ord 1972). The value ofMoran’s I will be in the range +1 to –1. Moran’s Iwill be positive when neighboring areas have simi-lar attributes and negative when the attributes aredissimilar. The hypothesis is that the path-basedmeasures score lower than the conventional AMs.

Results

Let us first look at the correlation coefficients intables 2 through 5. The first two letters of the codein the “variable” column of tables 2 through 5 referto the type of AM, where CU = cumulative oppor-tunity and LS = logsum. Letters 3 and 4 refer to theopportunity: RT = retail trade and PH = pharmacy.Letter 5 refers to gender: M = men, W = women. Intables 2 and 3, the last letter in the code indicateseducational level: L = low, I = intermediate, and H= high. Finally, AA is the traditional zonal measurethat is unweighted. Three questions are nowconsidered.

Is there a difference between the weighted meas-ures and the traditional ones, i.e., to what extentare the traditional AMs (in bold face in tables 2and 3) correlated with the weighted AMs?

The coefficients with regard to retail trade rangefrom 0.788 to 0.922 (cumulative opportunity) and0.511 to 0.833 (logsum). The differences are moreobvious for accessibility with regard to pharmacies,with overall lower coefficients indicating less simi-larity between the path-based measures and thezone-based measures. The same pattern holds forthe AMs weighted by estimated matrices. The mapsin figures 5 and 6 illustrate the difference betweentraditional AMs and weighted AMs. For theweighted AM, a larger area in the central regionobtains high accessibility scores while the scores forthe unweighted AM declines toward the periphery.A notable difference between the two types ofmeasures can be found in the northeastern part ofthe region where the weighted AM scores highwhile the unweighted is quite low. This pattern canbe attributed to the fact that the most importantcommuting flows (or commuting probabilities asestimated by the model) move toward areas wherepharmacies can be reached.


9 Since this AM goes over a loop that is n × n × n (seeequation 6), where n is the number of zones and GIS pro-gramming languages are not very computationally effi-cient, we also wrote an alternative program in FORTRAN.

Does accessibility differ between groups depend-ing on travel pattern, i.e., to what extent is thepath-based AM for different groups correlated?

Looking at the correlation between cumulativeopportunity measures of retail trade (table 2, upperleft) with different weights, the answer wouldprobably be, “they are not very different.” Takingweights 1 to 6 into account, the coefficients rangefrom 0.866 to 0.976. Looking at the parameterizedmeasure (the logsum, table 2, lower right), theanswer is different. The same 6 groups (8 to 13)yield correlation coefficients ranging from 0.371 to0.864. Turning to the example with accessibility to

pharmacies, the differences are more pronouncedfor the cumulative opportunity measures and lessobvious for the logsum. In the example with esti-mated matrices as weights (tables 4 and 5), we findthat the differences between men and women arevery small, and it appears that our model that gen-erated the weight matrix has not been able to cap-ture differences between genders. One reason isthat our AM does not take mode choice intoaccount, which would seriously affect the accessi-bility for women.

Will the map of accessibility be more heteroge-neous with path-based AMs?

BERGLUND 87

TABLE 2 Correlation of Accessibility Scores for Retail Trade in Jämtland (see page 86 for explanation of row codes)

Variable 1 2 3 4 5 6 7 8 9 10 11 12 13

(1) CURTML(2) CURTMI .954(3) CURTMH .866 .879(4) CURTWL .950 .932 .870(5) CURTWI .941 .948 .887 .966(6) CURTWH .940 .942 .871 .963 .976

(7) CURTAA .904 .852 .788 .918 .922 .917

(8) LSRTML .889 .840 .757 .780 .772 .786 .699(9) LSRTMI .785 .855 .719 .722 .749 .745 .626 .859(10) LSRTMH .422 .394 .556 .411 .378 .416 .346 .490 .377(11) LSRTWL .833 .833 .805 .884 .846 .852 .740 .787 .735 .560(12) LSRTWI .822 .878 .824 .847 .896 .865 .745 .767 .828 .371 .864(13) LSRTWH .655 .692 .686 .671 .694 .721 .586 .646 .666 .458 .708 .772

(14) LSRTAA .852 .847 .836 .871 .899 .891 .851 .741 .686 .511 .833 .831 .759

TABLE 3 Correlation of Accessibility Scores for Pharmacies in Jämtland (see page 86 for explanation of row codes)

Variable 1 2 3 4 5 6 7 8 9 10 11 12 13

(1) CUPHML(2) CUPHMI .840(3) CUPHMH .652 .659(4) CUPHWL .782 .800 .697(5) CUPHWI .743 .798 .614 .887(6) CUPHWH .744 .794 .688 .844 .776

(7) CUPHAA .676 .644 .571 .670 .707 .705

(8) LSPHML .777 .715 .528 .609 .575 .604 .535(9) LSPHMI .683 .786 .533 .575 .616 .589 .508 .908(10) LSPHMH .526 .598 .790 .574 .505 .599 .499 .702 .720(11) LSPHWL .728 .743 .649 .839 .750 .759 .625 .824 .809 .726(12) LSPHWI .690 .727 .597 .748 .811 .717 .660 .799 .850 .700 .917(13) LSPHWH .697 .735 .628 .719 .697 .817 .631 .808 .828 .739 .900 .905

(14) LSPHAA .726 .662 .625 .741 .760 .735 .868 .593 .528 .563 .672 .706 .682

In table 6, Moran’s I for the AMs are presented.Table 6 shows a mixed pattern. For accessibility toretail trade, except for women in the Jämtlandapplication, the traditional AMs are spatially morehomogeneous and show a more continuous acces-sibility surface. Access to pharmacies shows theopposite pattern. This is not surprising since loca-tion of pharmacies is a 0/1 variable (a zone eitherhas one or not and no zone has more than one) forthe cumulative opportunity measure. Hence, therewill be zones with an accessibility score of 1 or of 0(remember, pharmacies are assigned a maxitiveAM). The very low value for Moran’s I is not a sur-prise in this case. Taking the opportunities along apath into account will even out the accessibilitybetween the zones. Again we can see a similar pat-tern between the two applications.

Low and High Accessibility Mobility Patterns

Using path-based AMs, it is possible to detect dif-ferences in accessibility related to differences inmobility patterns. From an initial calculation, one

zone was selected (see figures 7 and 8) with quitedifferent accessibility for two groups—men withlow and high education.10 The zone under consid-eration has no pharmacies, is quite distant fromeverything else (this is a sparsely populated area),and is separated from the regional center by a lake.To reach more qualified service from this zone, atrip is necessary.

The two groups under consideration have quitedifferent mobility patterns. The most significantdifference is that for the group with high educationthe rate of commuting out of the residential zone is85 percent, while it is 56 percent for the groupwith low education. The commuting patterns (seefigures 7 and 8) indicate a stronger concentration


TABLE 4 Correlation of Accessibility Scores for Retail Trade in Stockholm(see page 86 for explanation of row codes)

Variable 1 2 3 4 5 6

(1) CURTM 1.000(2) CURTW .999 1.000

(3) CURTAA .592 .599 1.000

(4) LSRTM .822 .818 .381 1.000(5) LSRTW .827 .823 .388 1.000 1.000

(6) LSRTAA .749 .751 .615 .836 .840 1.000

TABLE 5 Correlation of Accessibility Scores for Pharmacies in Stockholm(see page 86 for explanation of row codes)

Variable 1 2 3 4 5 6

(1) CUPHM 1.000(2) CUPHW 1.000 1.000

(3) CUPHAA .465 .467 1.000

(4) LSPHM .892 .891 .436 1.000(5) LSPHW .891 .890 .435 1.000 1.000

(6) LSPHAA .538 .539 .817 .488 .486 1.000

Max = 100

0–25

25–50

50–75

75–100

FIGURE 5 Access to Pharmacies in the Stockholm Region (unweighted logsum)

10 For this zone, the accessibility score was about twiceas high for the highly educated group compared withthe group with low education.

Note: Accessibility is presented as an index where 100 is the highestaccessibility score.

of the commuting flows to the service centers forthe highly educated group than for the less edu-cated group. In this case, with a low local level ofservice, commuting to service centers will yieldhigh accessibility.

CONCLUSIONS

In this paper an accessibility measure has been pre-sented where accessibility is calculated with regardto a mandatory travel pattern for each zone. It isshown that there are quite large differences inaccessibility between groups with different travelpatterns if an observed matrix is used as a weight.In our example with estimated matrices the differ-ences between groups were negligible. It is ofcourse difficult to capture details in travel patterns

by a model. The differences between traditionalAMs and the path-based AMs are not as evidentfor the cumulative opportunity measure as for thelogsum. The same pattern holds for the AMsweighted by estimated matrices.

The pattern of similarities between adjacentzones shows a mixed result. For access to retailtrade, neighboring zones can have very differentaccessibility scores depending on the mandatorytravel pattern. For the case of pharmacies (using amaxitive AM), the path-based AMs show a moresmooth pattern.

When could a path-based AM be useful?

For low-mobility groups who work close tohome, the path-based component will not changethe accessibility score much and will not be veryuseful (but not less useful; see the aggregate path-based accessibility discussion). For high-mobilitygroups, a path-based AM can capture accessibilityobtained along the daily travel path and, thus, isuseful. A situation where a path-based AM couldbe useful is in transition regions outside urbanareas where part of the population is active in sec-tors where jobs are found locally (mainly tradi-tional sectors of the labor market) and others findtheir employment within sectors located in theurban center. If an estimated matrix is used as aweight, the model must be able to capture differ-ences depending on socioeconomic status.

BERGLUND 89

Max = 100

0–25

25–50

50–75

75–100

FIGURE 6 Access to Pharmacies in the Stockholm Region (logsum weighted by travel pattern for women)

TABLE 6 Moran’s I for AMs Used by Gender and Education (L = low, I = intermediate, H = high)

Retail trade Pharmacy___________________ __________________Group Cum. opp. Logsum Cum. opp. Logsum

Jämtland county

Men L 0.86 0.60 0.46 0.65Men I 0.83 0.50 0.41 0.61Men H 0.78 0.44 0.48 0.48Women L 0.90 0.65 0.68 0.68Women I 0.91 0.67 0.73 0.73Women H 0.90 0.42 0.66 0.65Unweighted 0.90 0.80 0.38 0.48

Stockholm region

Men 0.90 0.80 0.70 0.70Women 0.90 0.80 0.70 0.71Unweighted 0.95 0.83 0.57 0.69

Note: Accessibility is presented as an index where 100 is the highestaccessibility score.


FIGURE 7 Mobility Pattern: Low Accessibility to Pharmacies (Men With Low Education) (56% commuters)

FIGURE 8 Mobility Pattern: High Accessibility to Pharmacies (Men With High Education) (85% commuters)

REFERENCES

Berglund, S. 2001. Computing Accessibility in GIS—ProgramDocumentation. Technical report. Department ofInfrastructure, Royal Institute of Technology.

Cliff, A. and J.K. Ord. 1972. Testing for Spatial Autocor-relation Among Regression Residuals. GeographicalAnalysis 4:267–84.

Hanson, S. 1995. Getting There: Urban Transportation inContext. The Geography of Urban Transportation. NewYork, NY: Guilford Press.

Hagerstrand, T. 1970. What About People in RegionalScience. Papers of the Regional Science Association24:7–21.

Kwan, M.-P. 1998. Space-Time and Integral Measures ofIndividual Accessibility: A Comparative Analysis Using aPoint-Based Framework. Geographical Analysis 30:3.

Lenntorp, B. 1976. Paths in Space-Time Environment: ATime Geography Study of Movement Possibilities ofIndividuals: Lund, Studies in Geography 4. Lund,Sweden: CWK Gleerup.

Miller, H.J. 1999. Measuring Space-Time Accessibility

Benefits Within Transportation Networks: Basic Theory

and Computational Procedures. Geographical Analysis

31:187–212.

Miller, H.J. and Y.-H. Wu. 2000. GIS Software for Measuring

Space-Time Accessibility in Transport Planning and

Analysis. GeoInformatic 4:141–59.

Moran, P. 1948. The Interpretation of Statistical Maps.

Journal of the Royal Statistical Society 10B:243–51.

Richardson, A.J. and W. Young. 1982. A Measure of Linked-

Trip Accessibility. Transportation Planning and Tech-

nology 7:73–82.

Thill, J.C. and J.L. Horowitz. 1997. Modelling Non-Work

Destination Choice Sets Defined by Travel-Time

Constraints. In Recent Developments in Spatial Analysis.

Eds. Fisher and Getis. Heidelberg, Germany: Springer

Verlag.

Weibull, J.W. 1980. On the Numerical Measurement of

Accessibility. Environment and Planning A 12:53–67.

BERGLUND 91

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Guidelines for Manuscript Submission

BDavid Banks Bureau of Transportation Statistics, USDOT, Washington, DCWilliam Bannister Bureau of Transportation Statistics, USDOT, Washington, DC

CEd Christopher Metropolitan Planner, Olympia Fields, IL

FStephen Fienberg Carnegie Mellon University, Pittsburgh, PA

GDavid Gillen Wilfrid Laurier University, Waterloo, Ontario, CanadaGenevieve Giuliano University of Southern California, Los Angeles, CAThea Graham Bureau of Transportation Statistics, USDOT, Washington, DCMichael Greenwald University of Wisconsin, Milwaukee, WI

HMark Hallenbeck Washington State Transportation Center, Seattle, WA

KKazuya Kawamura University of Illinois, Chicago, IL

LJung-Taek Lee University of Illinois, Chicago, ILHerbert Lee III Duke University, Durham, NCMark Levenson U.S. Consumer Product Safety Commission, Bethesda, MDTimothy Lomax Texas Transportation Institute, College Station, TX

MSue McNeil University of Illinois, Chicago, ILPaul Metaxatos University of Illinois, Chicago, IL

SRick L. Schmoyer Oak Ridge National Laboratory, Oak Ridge, TNAshish Sen Bureau of Transportation Statistics, USDOT, Washington, DCQing Shen University of Maryland, College Park, MDBrian Sloboda Bureau of Transportation Statistics, USDOT, Washington, DCTony Smith University of Pennsylvania, Philadelphia, PASiim Soot University of Illinois, Chicago, ILP.S. Sriraj University of Illinois, Chicago, IL

WLynn Weidman Bureau of Transportation Statistics, USDOT, Washington, DCJack Wells Bureau of Transportation Statistics, USDOT, Washington, DC

YPeg Young Bureau of Transportation Statistics, USDOT, Washington, DC

ZAthanasios Ziliaskopolous Northwestern University, Evanston, IL

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REVIEWERS for Volume 4

AAccessibility

competition and, Vol. 4(2/3): 19–29

concepts and applications, Vol. 4(2/3): 15–30

definition of, Vol. 4(2/3): 16

gravity-based measures,Vol. 4(2/3): 33, 69

improvements, local employment and,Vol. 4(2/3): 49–66

indicators,Vol. 4(2/3): 32–36

modeling,Vol. 4(2/3): 31–48

neighborhood, evaluating,Vol. 4(2/3): 67–78

path-based,Vol. 4(2/3): 79–91

performance measures,Vol. 4(2/3): 31–48

space-time measures,Vol. 4(2/3): 1–14, 34, 80

travel-cost approach,Vol. 4(2/3): 33

utility-based measures,Vol. 4(2/3): 35, 69

Accidentscosts to drivers,

Vol. 4(1): 87–90, 99–100interstate, increased speed limits and,

Vol. 4(1): 1–26Air pollution

costs from highway transportation,Vol. 4(1): 91–92, 100

Austin, Texasneighborhood accessibility assessment,

Vol. 4(2/3): 70–71, 76–77

BBalkin, Sandy

speed limit increases, fatal interstate crashes and,Vol. 4(1): 1–16, 24–26

Baradaran, Siamakaccessibility performance measures,

Vol. 4(2/3): 31–48Bartin, Bekir

New Jersey highway transportation costs,Vol. 4(1): 81–103

Baysian methodsestimating traffic volumes,

Vol. 4(1): 27–36Berechman, Joseph

accessibility improvements, local employment and,Vol. 4(2/3): 49–66

New Jersey highway transportation costs,Vol. 4(1): 81–103

Berglund, Svantepath-based accessibility,

Vol. 4(2/3): 79–91Bicycling

accessibility and,Vol. 4(2/3): 67–68, 73, 74–75

Box-Jenkins ARIMA time series,Vol. 4(1): 13–15

Bronx, New YorkVol. 4(1): 51–53

CCargo transportation

train waybill data models and statistics,Vol. 4(1): 75–79

Carload Waybill Sample,Vol. 4(1): 76

Census Transportation Planning Package,Vol. 4(2/3): 64

Clifton, Kelly J.evaluating neighborhood accessibility,

Vol. 4(2/3): 67–78Competition

accessibility and,Vol. 4(2/3): 19–29

Congestioncosts to drivers,

Vol. 4(1): 87–90, 99–100modeling,

Vol. 4(2/3): 6–8transportation management professionals view,

Vol. 4(1): 51–73see also Traffic

Costshighway transportation,

Vol. 4(1): 81–103Crashes, see AccidentsCTPP, see Census Transportation Planning Package

DDavis, Gary

traffic volume estimates,Vol. 4(1): 27–38

Demand managementtransportation management professionals view,

Vol. 4(1): 31–37Drivers

congestion and accident costs,Vol. 4(1): 87–90, 99–100

EEmployment

accessibility improvements and,Vol. 4(2/3): 49–66

Environmentcosts from highway transportation,

Vol. 4(1): 91Europe

accessibility performance measures,Vol. 4(2/3): 31–48

97

INDEX for Volume 4

FFARS, see Fatality Analysis Reporting SystemFatalities

literature review,Vol. 4(1): 2–3

speed limits and,Vol. 4(1): 1–26

Fatality Analysis Reporting System,Vol. 4(1): 3

Federal-Aid Highway Act of 1956,Vol. 4(1): 52

Ferguson, Erikcongestion, demand management, and mobility

enhancement, Vol. 4(1): 51–73

Fontaine, Michael D.speed limit increases, fatal interstate crashes and,

Vol. 4(1): 16–21

GGoodness-of-fit statistics,

Vol. 4(1): 75–79Great Britain

Planning Policy Guidance 13,Vol. 4(2/3): 76

HHandy, Susan L.

evaluating neighborhood accessibility,Vol. 4(2/3): 67–78

Harris, Brittonaccessibility concepts and applications,

Vol. 4(2/3): 15–30Harvey, Andrew

speed limit increases, fatal interstate crashes and,Vol. 4(1): 22–24

Highway transportationcosts,

Vol. 4(1): 81–103Highway Trust Fund,

Vol. 4(1): 52Highway user fees

New Jersey,Vol. 4(1): 99–102

IInfrastructure


Intelligent transportation systems,Vol. 4(1): 61

Intermodal Surface Transportation Efficiency Actof 1991,

Vol. 4(2/3): 67

JJämtland, Sweden

accessibility measures applied to,Vol. 4(2/3): 83–89

LLabor supply

accessibility improvements and,Vol. 4(2/3): 49–66

Land usecreating scenarios for cluster analysis,

Vol. 4(1): 39–49data, accessibility analysis and,

Vol. 4(2/3): 73–74Ledolter, Johannes


Lee, Herberttrain waybill data models and statistics,

Vol. 4(1): 75–79Loglinear models,

Vol. 4(1): 75–79

MMiller, Harvey J.

measuring space-time accessibility,Vol. 4(2/3): 1–14

Mobility enhancementtransportation management professionals view,

Vol. 4(1): 51–73Motor vehicles

operating costs,Vol. 4(1): 86–87

NNational Bicycling and Walking Study,

Vol. 4(2/3): 73National Highway System Designation Act,

Vol. 4(1): 2, 14National Maximum Speed Limit,

Vol. 4(1): 2, 3, 16, 18Neighborhood accessibility

evaluating,Vol. 4(2/3): 67–78

New Jerseyhighway transportation costs,

Vol. 4(1): 81–103New York

South Bronx,Vol. 4(2/3): 49–66

NMSL, see National Maximum Speed LimitNoise


OOrd, J. Keith

speed limit increases, fatal interstate crashes and,Vol. 4(1): 1–16, 24–26

Ozbay, KaanNew Jersey highway transportation costs,

Vol. 4(1): 81–103

PPaaswell, Robert


Portland, Oregonsidewalk survey,

Vol. 4(2/3): 74–75

98

Path-based accessibility measures,Vol. 4(2/3): 79–91

Public transit ridershipletter,

Vol. 4(1): v

QQu, Tongbin Teresa


RRailroads


Ramjerdi, Faridehaccessibility performance measures,

Vol. 4(2/3): 31–48

SSaito, Mitsuru

creating land-use scenarios,Vol. 4(1): 39–49

San Francisco Bay Area Rapid Transitcustomer satisfaction among riders

Vol. 4(2/3), 71employment growth, in relation to,

Vol. 4(1): 54School bus ridership

letter,Vol. 4(1): v

Smith, Joshuacreating land-use scenarios,

Vol. 4(1): 39–49South Bronx, New York


Space-time accessibilityas indicator,

Vol. 4(2/3): 34–35measuring,

Vol. 4(2/3): 1–14Spatial Mismatch Hypothesis,

Vol. 4(2/3): 53–54, 61Speed and speed limits

increased, fatal interstate crashes and,Vol. 4(1): 1–26

Spiegelman, Clifford H.speed limit increases, fatal interstate crashes and,

Vol. 4(1): 16–21Stockholm, Sweden

accessibility measures applied to,Vol. 4(2/3): 83–89

Stokes, Charles J.urban transit ridership,

Vol. 4(1): v

TThakuriah, Piyushimita (Vonu)

introduction to volume 4, numbers 2/3,Vol. 4(2/3): v

Trafficvolume estimates,

Vol. 4(1): 27–38see also Congestion

Trains, see RailroadsTransportation, see specific modes, e.g., Highway

transportation, Railroads, Urban transitridership, etc.

Transportation dataaccessibility analysis and,

Vol. 4(2/3): 74–75Transportation Equity Act for the 21st Century,

Vol. 4(2/3): 67Transportation networks

measuring space-time accessibility in,Vol. 4(2/3): 1–14

Transportation planning systemscreating scenarios for cluster analysis,

Vol. 4(1): 39–49Transportation sketch planning,

Vol. 4(1): 39–49Transportation system management

professionals view,Vol. 4(1): 51–73

Travel demand managementprofessionals view,

Vol. 4(1): 51–73Travelers and travel behavior

space-time accessibility, measuring,Vol. 4(2/3): 1–14

UUrban transit ridership

letter,Vol. 4(1): v

VViele, Kert


WWalking

accessibility and,Vol. 4(2/3): 67–68, 71–73, 74–75

Wu, Yi-Hwameasuring space-time accessibility,

Vol. 4(2/3): 1–14

YYang, Shimin

traffic volume estimates,Vol. 4(1): 27–38

ZZimmerman, Karl


99

CONTENTS




ISSN 1094-8848

PIYUSHIMITA (VONU) THAKURIAH—guest editor

Introduction to the Special Issue

YI-HWA WU + HARVEY J MILLER Computational Tools forMeasuring Space -Time Accessibility Within Dynamic FlowTransportation Networks

BRITTON HARRIS Accessibility: Concepts and Applications

SIAMAK BARADARAN + FARIDEH RAMJERDI Performanceof Accessibility Measures in Europe

JOSEPH BERECHMAN + ROBERT PAASWELL AccessibilityImprovements and Local Employment: An Empirical Analysis

SUSAN L HANDY + KELLY J CLIFTON EvaluatingNeighborhood Accessibility: Possibilities and Practicalities

SVANTE BERGLUND Path-Based Accessibility

ACCESIBILITY

Documents

university of texas

information of high

quality of life

th street swwashington

special issue

accessibilitythe views

public domain

bts product catalog