GIS-based stochastic modeling of physical accessibility using GPS-based floating car data and Monte Carlo simulation

1

Ertugay Kivanc and Duzgun Sebnem, International Journal Of Geographical

Information Science Vol. 25 , Iss. 9,2011

GIS Based Stochastic Modeling of Accessibility

by using GPS based Floating car data and MonteCarlo Simulations

Kivanc Ertugay*, Sebnem Duzgun**

*Research Assistant in Geodetic and Geographic Information Technologies Department, Middle East

Technical University, Ankara, TURKEY,

TEL: 903122105416 FAX: 90 312 2107956 E-MAIL: [email protected]

**Assoc. Prof. Dr. in Mining Engineering, Middle East Technical University, Ankara, TURKEY

TEL: 90 312 2102668 FAX: 90 312 2107956 E-MAIL: [email protected]

Abstract- Although the vital importance of travel cost calculation process in

accessibility modeling, most of the previous studies have heavily used deterministic travelling

costs in calculation of accessibility. This means that accessibility measures are calculated

from constant and generalized travelling impedances and a most likely or average

accessibility result is obtained independent from how many times the process is re-calculated.

This is not realistic, especially when considered highly variable speeds in road segments and

create a poor sense about the accuracy and reliability of the accessibility results. In the light of

the above mentioned facts, a GIS based stochastic modeling of accessibility is proposed

where variations of transportation costs on transportation networks can be taken into account

in a probabilistic manner by using Global Positioning Systems (GPS) based floating car data

and Monte Carlo simulations technique. Compared to previous studies, the proposed

methodology can provide vital information related with the accuracy and the reliability of the

accessibility results and better reality and decision support for the decision makers working on

accessibility, location/allocation and service/catchment area related issues. The methodology

is illustrated with a case study on medical emergency service accessibility in Eskisehir,

Turkey with a comparison between deterministic and stochastic model results.

Keywords: Geographical Information Systems (GIS), Global Positioning Systems (GPS),

Stochastic/Probabilistic Accessibility Modeling, Floating car data, MonteCarlo simulation, ,

Service/Catchment Area, Location/Allocation,

Introduction

The term accessibility (also seen as place, physical or spatial accessibility in the

literature) has long been used by urban and regional planning related disciplines and basically

reflects the relative ease of access to/from several urban services by considering several travel

costs [27,34]. Accessibility measures are concerned with equity and a better distribution of

people and activities in the territory and help to evaluate the location and catchment area of

several urban and regional services like “health, education, recreation, emergency or trade

2

etc.” by considering several transportation modes such as “pedestrian, bicycle, car or public

transport etc.”. Accessibility measures can be accepted as key variables for defining location

and catchment related planning strategies [27,29,31,34].

Although there are many different types and components of accessibility measures in

the literature ranging from simple or complex, calculation of the travel impedances is one of

the most common and vital components of accessibility [see 27,54 for details]. Although its

importance, most of the previous studies, directly or indirectly related with accessibility

modeling, have heavily used deterministic travel impedances in calculation of accessibility.

This means that accessibility measures are calculated from constant, generalized or

approximate travel impedances such as unconstrained Euclidean distances, buffers, voronoi

diagrams etc. or constrained network based distances or times assuming that travelling on a

transportation network has a constant approximate cost, for example 90 km/hour for highways

or 50 km/h for main streets etc. [see

10,13,14,18,20,22,45,46,4,5,6,12,16,17,24,30,47,48,51,52,53,54]. Although these

deterministic approaches can partly support the accessibility modeling process, they are not

realistic from traveling cost calculation point of view, especially when considered highly

variable speeds in road segments, and create a poor sense about the accuracy and reliability of

the accessibility results.

In the light of the above mentioned facts, a stochastic methodology for GIS based

accessibility modeling is proposed by using Global Positioning Systems (GPS) based floating

car data and Monte Carlo simulations technique in the focus of calculation of traveling costs.

Compared to previous studies, the proposed methodology provide vital information related

with the accuracy and the reliability of the accessibility results and better reality and decision

support for the decision makers working on accessibility, location/allocation and

service/catchment area related issues. The methodology is illustrated with a case study on

medical emergency service accessibility in Eskisehir, Turkey with a comparison of

deterministic and stochastic model results.

Although the case study is implemented on medical emergency service accessibility,

the primary focus of the study is not evaluation of medical emergency service accessibility in

a detailed manner but to provide a discussion about the accuracy and the reliability of the GIS

based accessibility modeling in the focus of calculation of traveling costs. Therefore, the

proposed methodology can be integrated into various urban services like “health services,

emergency services, recreational services or trade services etc.” by considering several

3

transportation modes such as “pedestrian, bicycle, car or public transport etc.” and can

provide vital information related with the accuracy and the reliability of the accessibility

results and better reality and decision support for the decision makers working on

accessibility, location/allocation and service/catchment area related issues.

GPS Based Floating Car Data Collection

There are several traffic data collection methods to obtain variations in transportation

costs, such as stationary traffic sensors (induction loops, optical systems), space and airborne

techniques (observation from planes, satellites) and GPS based floating car traffic data

collection (position or speed recordings from vehicles moving in the traffic). However,

among the various data collection techniques, GPS-based floating car traffic data method is

the most suitable one for accessibility analyses in which it provides relatively fast, cheap and

accurate position and speed as well as ease in integrating the results in GIS

[38][39][40][41][42][43][44].

Montecarlo Simulations

Uncertainty in the travelling costs can be incorporated into the accessibility analyses

by using simulation. The word “simulation” refers to analyze the effect of varying inputs, on

outputs of the modeled system. A simulation involves hundreds or thousands evaluations of

the model for all possible inputs and gives a probabilistic measure of the outputs. Without the

aid of simulation, the traveling costs in accessibility analyses are calculated by certain cost

parameters and the single accessibility outcome, generally the most likely or average scenario

is obtained independent from how many times the process is re-calculated.

Monte Carlo Simulation (MCS) method was invented by S. Ulam and Nicholas

Metropolis in reference to city of Monte Carlo, Monaco, where is famous with games of

chance and is a well known method which create the random realizations of a deterministic

model many times by generating random inputs. By integrating MCS method into GIS based

accessibility modeling, instead of using deterministic transportation cost values, possible

random transportation cost values can be used to evaluate the probability of an accessibility

4

outcome. By converting constant transportation costs into possible random costs, the

likelihood of the accessibility result and the probability of the outcome can be understood. For

example “there is only a 75% certainty that the place “x” have 15 minutes accessibility” can

be originally predicted when compared with the deterministic model [7][8].

Methodology

The proposed stochastic accessibility model consists of four major steps which are (1) Data

collection, (2) Generation of speed surface, (3) Extraction of speed statistics and (4) Monte

Carlo simulation (Figure 1).

Figure: 1.The flowchart of the methodology

The basic inputs of model are GPS-based floating car traffic data in log file format,

GIS-based transportation network data in digital poly-line format and related service locations

in point format.

The general steps of the model are;

The GPS-based floating car data having certain intervals are obtained in log file

format and needed to be converted to a database file having measurements in the form of

points with x-y coordinates and speed at that point. Then the database file is geo-coded to the

associated GIS layers by using the x- y coordinate pairs in the database file.

Determination of road segments having GPS data or not is an important step for

calculation of network costs in GIS environment. In calculation of costs for the road segments

that have GPS data, the mean and standard deviation of each unique road segment is used.

However for the road segments that have no GPS data, the average mean and standard

deviation of road segments according to road types are used such as highway, boulevard,

5

street etc. Therefore a toolbox is developed in ArcGIS model builder environment which

mainly use the buffer and overlay capabilities of GIS, inserts a new attribute to road data and

add attribute information of 1 to road segments having GPS data and 0 to road segments that

have no GPS data.

The speed surface is created from “point” speed data by using the spatial interpolation

capabilities of GIS. The inverse distance weighted technique, which is one of the most

commonly used interpolation methods, is used for interpolation of GPS points into raster

speed surfaces. The technique is mainly based on the assumption that the speed of any point

in the road segment is mostly affected by the nearest points and less affected by the far points.

This step is necessary in order to able to integrate GPS based “point” data with the “line”

based road data and to extract the speed statistics for each road segment (Figure 2).

Figure 2: Production of raster speed surface from GPS data

After the generation of speed surface, the speed statistics of mean and standard

deviation for each road segments are extracted from speed surface by using “buffer” functions

and “zonal statistics” capabilities of GIS (Figure 3). For this process a toolbox is developed in

ArcGIS model builder environment which basically applies buffer for each unique road

segment, create temporary polygon segments and extract the zonal statistics from speed

surface for each unique road segment by using the unique ID’s for linkage.

6

Figure 3: Extraction of speed statistics of mean and standard deviation from created

raster speed surface

The next step is to determine probability distribution function of speed data in order to

be used as an input in Monte Carlo Simulations. Several statistical tests are performed on the

GPS based floating car speed data in order to understand the probability distribution function

of speed data. Then, in order to perform Monte Carlo simulations, a GIS-based road network

having random costs for each road segment is produced by a developed toolbox in MATLAB

environment. The developed toolbox gets “the GIS-based road layer” as an input, calculates

the random costs and adds new attribute fields and random cost attributes to the GIS layer for

each segment.

In the calculation of random costs; the mean and standard deviation of speed for each

road segment, segment length and best fitting distribution function are used. The random

speed value is divided by the segment length for each road segment and the costs are

calculated in “time” (Figure 4).

Figure 4: Calculated random time costs for each road segment in GIS environment

The random cost fields of road layer created in MATLAB environment is used as

input layer in GIS-based network analysis. The accessibility maps for each random cost field

are calculated by isochronal technique, which has a polygon output that connects points of

equal travel time away from a single reference point, converted to binary format as “1” for

accessible and “0” for not accessible areas and summed up by an integrated toolbox

developed in ArcGIS model builder environment in order to obtain the probability scores of

accessibility.

7

The result of the above mentioned approach, based on stochastic modeling of physical

accessibility by using GPS based floating car data and Monte Carlo simulations technique,

could provide vital information related with the accuracy and the reliability of the

accessibility results in GIS based accessibility modeling process and provide better reality and

decision support for the decision makers working in physical accessibility measurement and

evaluation area.

Case Study

The developed methodology is implemented in a case study on medical emergency

service accessibility in Eskisehir city, Turkey (figure 5).

Figure 5: The location of case study area.

The aim of the case study is to implement the developed stochastic accessibility model

on medical emergency services in Eskisehir urban area and discuss the advantages of the

developed stochastic model with the current deterministic model in a comparable manner. The

results are used in analysis and evaluation of the current situation related with the medical

emergency service accessibility.

The city of Eskisehir is one of the biggest cities of Turkey with an urban population of

nearly 600.000 according to official population census of 2008. Eskisehir is governed by the

Eskisehir greater metropolitan municipality, including two main metropolitan districts, which

are Tepebasi and Odunpazari.

The 5 minutes accessibility is considered as input threshold since it is accepted as the

critical time period for saving lives in medical emergency. Finally the produced stochastic

accessibility map is used as a decision support in determination of the critical medical

8

emergency access zones by the help of additional local of medical event distribution and

population distribution maps.

The following data are obtained to implement the stochastic accessibility model:

Digital transportation network data, their hierarchies, 2007 are obtained from

Eskisehir Metropolitan Municipality and integrated into a GIS database in order to perform

accessibility network analyses (Figure 6)

The location of medical emergency service stations, 2007 are obtained and

integrated into a GIS database in order to be used as source points in accessibility network

analyses (Figure 7)

GPS-based floating car traffic data is collected by 2 weeks field work on

08.2007 and on 02.2008 in order to obtain average speed information for road segments in the

network (Figure 8). (GPS based floating ambulance data is collected by another 3 days field

work from three 112 stations on 05.2008 in order to able to make average speed cost

calibrations, however they are not integrated to the model yet.)

Figure 6: Digital transportation network data with related hierarchies (Eskişehir

Metropolitan Municipality)

Figure 7: The location of medical emergency services

9

Figure 8: An example of GPS-based floating car traffic data, collected by one week

field work on 08.2007

The collected speeds from GPS-based floating car data on the road segments are

statistically analyzed to determine best fitting probability distribution. For this purpose more

than 40 probability distributions are tested by using Kolmogorov-Smirnov, Anderson-Darling,

Chi-Squared tests in the EasyFit distribution fitting environment. The goodness of fit tests

show that the Generalized Extreme Value, Normal, Weitbull, Johnson, Beta, Log-Logistic and

Log-Normal Probability distributions are the ones which fit best to the data. The best fitting

distribution of speed data on a road network with similar rank and statistics are listed in Table

1.

Table 1: Results of distribution fitting tests applied to GPS based floating car data

For the sake of simplicity normal distribution is used as the distribution of speed data

to be input to MATLAB environment and to produce random costs for Monte Carlo

simulation. As described in the methodology part, the random costs fields are created in

MATLAB environment and used as input layer in GIS-based network analysis. The

accessibility maps for each random cost field are calculated by isochronal technique, which

10

has a polygon output that connects points of equal travel time away from a single reference

point. The results converted to binary raster format as “1” for accessible and “0” for not

accessible areas and summed up by an integrated toolbox developed in ArcGIS model builder

environment in order to obtain the probability scores of accessibility.

As accessing a call in 5 minutes is the critical threshold for medical emergency

service, the 5 minutes medical emergency service maps are produced for both deterministic

model1 and the developed stochastic model

2 (figure 9, figure 10).

Figure 9: Deterministic modeling of accessibility

Figure 10: Stochastic modeling of accessibility

1 In calculation of costs in deterministic model, the static costs are used for the roads that have the

same type, which are accepted as 53 km/h for highways, 44km/h for boulevards, 34 km/h for main streets 31km/h

for streets and 20 km/h for dead-end streets.

2 A total number of 1000 simulations are performed for preparation of stochastic accessibility maps

because of a considerable change is not observed in the results after 1000 simulations.

11

The results of a simulations clearly show the advantages of stochastic modeling in

terms of accuracy and reliability. The results give important information about the accuracy

level of the accessibility maps by the help of the probability values. The reliability of the

results is better in stochastic modeling because of the usage of GPS based floating car data

based dynamic costs instead of deterministic static costs and the simulations performed.

When the deterministic and stochastic accessibility model results are overlaid in GIS

environment, the differences can easily be observed. Many urban areas in the accessible zone

in deterministic model are in the inaccessible zone or vice versa according to the results of

stochastic model. For example the locations in the north-west and south parts of the urban

area seem to be in the inaccessible area in the deterministic model; however they are in the

90%-100% probability accessible area in the stochastic model. Similarly it can be observed

that although the north-east and south-west parts of the city are in the accessible area in the

deterministic model, they are in the 20%-30% probability accessible area in the stochastic

model. It can be said that the differences can reach up to 2 km length which can be considered

as an important difference from reliability point of view (figure 11).

Figure 11: The comparison of stochastic and deterministic modeling of accessibility

After the generation of stochastic accessibility map of the Eskisehir urban area region,

the next step in the research (still continues…) is the integration of the produced stochastic

accessibility map with the population distribution maps (obtained from Odunpazarı

municipality for the 2007 year) and medical emergency incident distribution maps (obtained

from 112 command and control center of Eskişehir for the 2007 year). The integration will

clearly produce a final map having scores from the accessibility, population and medical

12

incidence distribution maps and provide vital guidance for decision makers to decide on

newly planned medical emergency stations or the current location of the medical emergency

stations...

4 RESULTS AND CONCLUSION

The results and conclusion obtained from the study can be summarized as follows;

The developed GIS-based stochastic accessibility modeling improved the usage and

decision making capabilities of accessibility maps by providing better understanding

of the accuracy of the accessibility modeling as well as considering the uncertainty in

the results.

Although the developed accessibility model is applied on medical emergency service

accessibility, it can easily be adapted to other urban related services such as central

business district accessibility, recreational accessibility, trade center accessibility or

educational accessibility etc.

Despite the fact that there are several traffic data collection methods, GPS-based

floating car traffic data collection is unique in terms of its fast and accurate data

obtaining and integrating possibilities with GIS. After the outputs are integrated into

the digital road networks, an effective decision support is possible for many urban

related accessibility measurement and evaluation.

The GPS-based floating car data collection can be performed more detailed for

different dates and hours for more detailed representation of accessibility according to

rash hours, normal hours, weekends, special dates etc. The detail of data collection

depends on the aim, the budget and the required detail of the study

The ARCGIS Model Builder 9.3 software and MATLAB programming environments

are used in the implementation of the model. A total of 1000 simulations are

performed within nearly 10 hours time in Pentium 3 Ghz, 3.5 gb ram desktop

computer. However the elapsed time can be decreased by lower input data detail,

higher PC configuration or advance programming capabilities.

5. FUTURE WORK

13

The main objective of the study is achieved by development of GIS Based Stochastic

Modeling of Physical Accessibility. The improvement provide vital information related with

the accuracy and the reliability of the accessibility results and provide better reality and

decision support for the decision makers.

A further step for the study can be the integration of the produced stochastic accessibility map

with the population distribution and medical emergency incident distribution maps. The

integration will clearly produce a final map having scores from the accessibility, population

and medical incidence distribution maps and provide vital guidance for decision makers to

decide on newly planned medical emergency stations or the current location of the medical

emergency stations

6.REFERENCES

[4]Sylvie Dubuc.,(2007) “Gis-Based Accessibility Analysis For Network Optimal

Location Model”, Article 407, Cybergeo, Systems, Modelisation Geostatistiques

[5] Mitchel Langford, Gary Higgs, Jonathan Radcliffe, Sean White., (2008) “Urban

Population Distribution Models And Service Accessibility Estimation”, Computers,

Environment And Urban Systems 32 66-80

[6] Juliao, Rui Pedro., (1999) “Measuring Accessibility Using Gis” Geo-Computation-

99,

[7] Hoffman, P., (1998), The Man Who Loved Only Numbers: The Story Of Paul

Erdos And The Search For Mathematical Truth. New York: Hyperion, Pp. 238-239.

[8] Metropolis, N. And Ulam, S., (1949), "The Monte Carlo Method." Journal of the

American Statistical Association 44 (247):, 335-341.

[10] Hélène Charreirea, Evelyne Combierb., (2008), Poor prenatal care in an urban

area: A geographic analysis, Journal of Health and Place 15 p:412-419

[12] David O'Sullivan, Alastair Morrison, John Shearer (2000), Using desktop GIS

for the investigation of accessibility by public transport: An isochrone approach, International

Journal of Geographical Information Science, Vol. 14, No. 1. (January pp. 85-104.

[13] Wei, Luo, (2004), Using a GIS-based floating catchment method to assess areas

with shortage of physicians, Health And Place 10 p:1-11

[14] Jessica Scott, Ann Larson, Felicity Jefferies and Bert Veenendaal, (2006), Small-

area estimates of general practice workforce shortage in rural and remote Western Australia,

Australian Journal of Rural Health, Volume 14 Issue 5, Pages 209 – 213 Published Online: 10

Oct 2006

[16] Brabyn, Lars (2002), Modelling Population Access to New Zealand's General

Practitioners, International ESRI User Conference, San Diego.

[17] Sylvie Dubuc, (2007) GIS-based accessibility analysis for network optimal

location model », Cybergeo, Systems, Modelling, Geostatistics, Article 407,

[18] Konstadinos G. Goulias, (2007), An Optimal Resource Allocation Tool for Urban

Development Using GIS-based Accessibility Measures and Stochastic Frontier Analysis,

University of California, Santa Barbara California PATH Research Report, UCB-ITS-PRR-

2007-7

14

[20] John Fortney, Kathryn Rost and James Warren (2000), Comparing Alternative

Methods of Measuring Geographic Access to Health Services, Journal Health Services and

Outcomes Research Methodology, springer, Volume 1, Number 2 / June, 2000, p: 173-184

[22] Joseph P Messina , Ashton M Shortridge , Richard E Groop , Pariwate

Varnakovida and Mark J Finn, (2006), “Evaluating Michigan's community hospital access:

spatial methods for decision support”, International Journal of Health Geographics 2006, p:5-

42.

[24] Nadine Schuurman , Robert S Fiedler , Stefan CW Grzybowski and Darrin

Grund (2006), “Defining rational hospital catchments for non-urban areas based on travel-

time”, International Journal of Health Geographics 2006, p: 5:43

[27] Makrí, Maria Brodde., (2002) “Accessibility indices and planning theory”

Eighth International Conference on Urban Transport and the Environment for the 21st

Century, URBAN TRANSPORT VIII, p 37-46

[29] Juliao, Rui Pedro., (1999) “Measuring Accessibility Using Gis” Geo-

computation-99 Conference, Mary Washington College, Virginia, USA

[30] Emelinda, M. Parentela., Shashi K. Sathisan., (1995) “Gis-Based Allocation of

Emergency Response Units Along A Transportation Route” Conference Proceedings,

International ESRI User Conference, San Diego.

[31] Kuntay, Orhan., (1990), “Erişilebilirlik Kesin Bir Öncelik,” Planlama Dergisi

(Journal of The Chamber of City Planners), 90/1-2, 7 (in turkish)

[34] Halden, Derek., Mcguigan, David., Nisbet, Andrew., Mckinnon, Alan., (2000)

“Guidance On Accessibility Measuring Techniques And Their Application”, Scottish

Executive Central Research Unit, ISBN: 1842680013

[38] Daoqin Tong, Benjamin Coifman, Carolyn J Merry, (2009), “New Perspectives

on the Use of GPS and GIS to Support a Highway Performance”, StudyTransactions in GIS ,

13(1): 69–85

[39] Glen M. D’Este, Rocco Zito & Michael A. P. Taylor, (1999), “Using GPS to

Measure Traffic System Performance”, Computer-Aided Civil and Infrastructure Engineering

14 255–265

[40] G. Mintsis , S. Basbas, P. Papaioannou, C. Taxiltaris, I.N. Tziavos, (2004),

“Applications of GPS technology in the land transportation system”, European Journal of

Operational Research 152, 399–409.

[41] Cesar A. Quiroga (2000), “Performance measures and data requirements for

congestion management systems”, Transportation Research Part C 8 287±306

[42] Michael A.P. Taylor *, Jeremy E. Woolley, Rocco Zito, (2000), “Integration of

the global positioning system and geographical information systems for traffic congestion

studies”, Transportation Research Part C 8, 257±285

[43] R. Zito, G. D’este And M. A. P. Taylor, (1995), “Global Positioning Systems In

The Time Domain: How Useful A Tool For Intelligent Vehicle-Highway Systems?”,

Transportation. Research Part C. Vol. 3, No. 4, pp. 193-209,

[44] G. Derekenaris , J. Garofalakis , C. Makris , J. Prentzas , S. Sioutas , A.

Tsakalidis, (2001) “Integrating GIS, GPS and GSM technologies for the effective

management of ambulances”, Computers, Environment and Urban Systems, 25 , 267±278

[45] Luis Rosero-Bixby, (2004), “Spatial access to health care in Costa Rica and its

equity: a GIS -based study”, Social Science & Medicine, Volume 58, Issue 7, April, Pages

1271-1284

[46] Sedigheh Lotfi , Mohammad Javad Koohsari (2009), “ Measuring objective

accessibility to neighborhood facilities in the city (A case study: Zone 6 in Tehran, Iran)”,

Cities 26 133–140.

15

[47] Mohammad H. Vahidnia*, Ali A. Alesheikh, Abbas Alimohammadi, (2009)

“Hospital site selection using fuzzy AHP and its derivatives”, Journal of Environmental

Management, 90, 3048–3056

[48] J.R. Ritsema van Eck*, T. de Jong, (1999), “Accessibility analysis and spatial

competition efects in the context of GIS-supported service location planning”, Computers,

Environment and Urban Systems

23 75±89

[51] Wei Luo, Fahui Wang, (2003), “Measures of spatial accessibility to health care in

a GIS environment: synthesis and a case study in the Chicago region” Environment and

Planning B: Planning and Design, volume 30, pages 865 ^ 884

[52] Matthew R. McGrail, John S. Humphreys, (2009), “Measuring spatial

accessibility to primary care in rural areas: Improving the effectiveness of the two-step

floating catchment area method”, Applied Geography 29, 533–541

[53] John Radke, Lan Mu (2000), Spatial Decompositions, Modeling And Mapping

Service Regions To Predict Access To Social Programs”, Geographic Information Sciences,

Vol. 6, No. 2

[54] Mark F Guagliardo (2004), “Spatial accessibility of primary care: concepts,

methods and Challenges” International Journal of Health Geographics 2004, 3:3