i ESTIMATION OF SATURATION FLOW AND LOST TIME AT SELECTED SIGNALIZED INTERSECTIONS OF KARACHI (PAKISTAN) A thesis submitted by Muhammad Jawed Iqbal In fulfillment of the requirement for the degree of Doctor of Philosophy In Civil Engineering Department of Civil Engineering Faculty of Engineering Mehran University of Engineering & Technology, Jamshoro 2009
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i
ESTIMATION OF SATURATION FLOW AND LOST TIME AT SELECTED
SIGNALIZED INTERSECTIONS OF KARACHI (PAKISTAN)
A thesis submitted by
Muhammad Jawed Iqbal
In fulfillment of the requirement for the degree of
Doctor of Philosophy
In
Civil Engineering
Department of Civil Engineering
Faculty of Engineering
Mehran University of Engineering & Technology,
Jamshoro
2009
ii
MEHRAN UNIVERSITY OF ENGINEERING & TECHNOLOGY
JAMSHORO
This thesis written by Muhammad Jawed Iqbal under the direction of his supervisors, and
approved by all the members of the thesis committee, has been presented to and accepted
by the Dean, Faculty of Engineering, in fulfillment of the requirement of the degree of
5.8 Comparison of PCU Values of Shahra-e-Faisal 64 and M.A. Jinnah Road
5.8 Comparison of PCU Values of Shahra-e-Faisal and 64 M.A. Jinnah Road With PCU Values in Other Countries
x
5.10 Measurement of Approach Width 64
5.11 Saturation Flow Data Collection and Analysis 67 (For both Arterials)
5.12 Lost Time 71
Chapter 6 SATURATION FLOW & LOST TIME ANALYSIS 80 & DISCUSSION OF RESULTS
6.1 General 80
6.2 Saturation Flow and Approach Width 80
6.3 Effect of Composition of Traffic 81
6.4 Comparison of Observed & Estimated Saturation Flow84
6.5 Comparison of both Arterials of Present Study 87
6.6 Generalized Model and its Comparison 87
6.7 Comparison of Present Study with Earlier Studies 90
Chapter 7 CONCLUSIONS 92
7.1 General 92
7.2 Future Scope 94
7.3 Recommendations / Suggestions 95
References 96
Appendices 106
xi
LIST OF TABLES
DESCRIPTION PAGE Table 3.1 Summary of Saturation flow with approach widths as given 41 in RRTP-56 Table 3.2 Summary of Effect of Gradient on Saturation flow from 41 Various Studies Table 3.3 Effect of Site Characteristics on Saturation flow as per RRTP-56 42 Table 3.4 Average lane Saturation flow in tcu/h by lane type and 42 Environment given in ARRB Bulletin No.3 (Miller) Table 3.5 Summary of PCU values from various studies 43 Table 3.6 Level of Service Criteria for Signalized Intersections 43 Table 5.1a Summary of Approach Widths which have been studied on 63 Shahra-e-Faisal Table 5.1b Summary of Approach Widths which have been studied on 63 M.A. Jinnah Road Table 5.2 Summary of PCU values observed at Shahra-e-Faisal 64 Table 5.3 Summary of PCU values observed at M.A. Jinnah Road 64 Table 5.4 Comparison of PCU values of Shahra-e-Faisal and M.A.Jinnah 66 Road with Other Countries Table 5.5 Observed Saturation Flow on each Approach on Shahra-e-Faisal 69
(Vehs/hr) Table 5.6 Observed Saturation Flow on each Approach on M.A. Jinnah Road 69
(Vehs/hr) Table 5.7 Observed Saturation Flow on each Approach on Shahra-e-Faisal 70
(PCU/hr) Table 5.8 Observed Saturation Flow on each Approach on M.A. Jinnah Road 70
(PCU/hr) Table 5.9 Lost Time Calculation (McShane & Roess) 73 Table 5.10 Saturation Flow & Lost Time Measurement Form (Akcelik 1993) 76 Table 5.11 Summary of Lost Time Calculated on each Approach on 79 Shahra-e-Faisal
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Table 5.12 Summary of Lost Time Calculated on each Approach on 79 M.A. Jinnah Road Table 6.1 Summary of PCU Values along both Arterials of Karachi 83 Table 6.2 Comparison of Observed and Estimated Saturation Flow 85 on Shahra-e-Faisal Table 6.3 Comparison of Observed and Estimated Saturation Flow 85 on M.A. Jinnah Road Table 6.4 Comparison between Two Models 88 Table 6.5 Comparison of Generalized Model with Faisal & Jinnah Model 89 Table 6.6 Comparison of Saturation flows predicted by present study model 91 with Earlier Studies
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LIST OF FIGURES
DESCRIPTION PAGE Fig 2.1 Fundamental attributes of flow at Signalized Intersections 9 Fig 2.2 Conditions at Traffic Interruption in an Approach Lane 10 of a Signalized Intersections Fig 2.3 Concept of Saturation Flow Rate & Lost Time 12 Fig 3.1 Variation with Time of Discharge Rate of Queue in a fully 27 Saturated green Period Fig 3.2 a) Homogeneous Mix 38 Fig 3.2 b) Heterogeneous Mix 38 Fig 4.1 Typical layout of field data collection equipment set up 48 Fig 4.2 Field data collection set up 49 Fig 4.3 Field data collection screen view 49 Fig 5.1 Road Network of Karachi City 53 Fig 5.2 Data Collection Sites on Shahra-e-Faisal 54 Fig 5.3 Intersections on M.A.Jinnah Road 55 Fig 5.4 Cycle Profile (Lost Time Concept) 72 Fig 5.5 Saturated Headway & Lost Time Measurement 73 Fig 5.6 Observed Discharge across Stop Line 77 Fig 5.7 Average Cycle Profile (Awami Markaz 78 Fig 6.1 Relationship between observed Saturation Flow and 82 Approach Width on Shahra-e-Faisal Fig 6.2 Relationship between observed Saturation Flow and 82 Approach Width on M.A. Jinnah Road Fig 6.3 Graphical comparison of observed Vs theoretical saturation flow 86 on Shahra-e-Faisal Fig 6.4 Graphical comparison of observed Vs theoretical saturation flow 86 on M.A. Jinnah Road Fig 6.5 Generalized Relationship between Saturation Flow and Approach 88
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Width (incorporating both approaches) Fig 6.6 Graphical Comparison of Present Study Model with Previous 90
Models
xv
LIST OF APPENDICES
DESCRIPTION PAGE APPENDIX 1 Headways of Straight-Ahead Motorcycles 107 APPENDIX 2 Headways of Straight-Ahead Passenger Cars 109 APPENDIX 3 Headways of Straight-Ahead Rickshaws 112
APPENDIX 4 Headways of Straight-Ahead Vans 114
APPENDIX 5 Headways of Straight-Ahead Minibuses 116 APPENDIX 6 Headways of Straight-Ahead Buses/Trucks 118 APPENDIX 7 Sample sheet for traffic flow data collection 119 APPENDIX 8 Data sheet for traffic flow at Awami Markaz Junction 120 APPENDIX 9 Data sheet for traffic flow at Drig Road Junction 121 APPENDIX 10 Data sheet for traffic flow at Karsaz Junction 122 APPENDIX 11 Data sheet for traffic flow at Mehran Hotel Junction 123 APPENDIX 12 Data sheet for traffic flow at Regent Plaza Junction 124 APPENDIX 13 Data sheet for traffic flow at Shah Faisal Junction 125 APPENDIX 14 Data sheet for traffic flow at star Gate Junction 126 APPENDIX 15 Data sheet for traffic flow at Tariq Road Junction 127 APPENDIX 16 Data sheet for traffic flow at Kashif Centre Junction 128 APPENDIX 17 Data sheet for traffic flow at Faisal Base Junction 129 APPENDIX 18 Data sheet for traffic flow at Lal Dila Junction 130 APPENDIX 19 Data sheet for traffic flow at Kala Pull Junction 131 APPENDIX 20 Data sheet for traffic flow at Nursery Junction 132 APPENDIX 21 Sample sheet for Saturation Flow calculation 133 APPENDIX 22 Calculation of Saturation Flow (example) 134
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APPENDIX 23 Saturation flow calculation sheet - Awami Markaz Junction 135 APPENDIX 24 Saturation flow calculation sheet – Drig Road Junction 136 APPENDIX 25 Saturation flow calculation sheet - Karsaz Junction 137 APPENDIX 26 Saturation flow calculation sheet – Mehran Hotel Junction 138 APPENDIX 27 Saturation flow calculation sheet – Regent Plaza Junction 139 APPENDIX 28 Saturation flow calculation sheet – Shah Faisal Junction 140 APPENDIX 29 Saturation flow calculation sheet – Star Gate Junction 141 APPENDIX 30 Saturation flow calculation sheet – Tariq Road Junction 142 APPENDIX 31 Saturation flow calculation sheet – Kashif Centre Junction 143 APPENDIX 32 Saturation flow calculation sheet – Faisal Base Junction 144 APPENDIX 33 Saturation flow calculation sheet – Lal Qila Junction 145 APPENDIX 34 Saturation flow calculation sheet – Kala Pull Junction 146 APPENDIX 35 Saturation flow calculation sheet – Nursery Junction 147 Statistical Analyses for Vehicle’s Headway 148 APPENDIX 36 Statistical analyses for Headways of Cars 149 APPENDIX 37 Statistical analyses for Headways of Motorcycles 150 APPENDIX 38 Statistical analyses for Headways of Minibuses 151 APPENDIX 39 Statistical analyses for Headways of Vans 152 APPENDIX 40 Statistical analyses for Headways of Rickshaws 153 APPENDIX 41 Statistical analyses for Headways of Buses/Trucks 154 APPENDIX 42 Average cycle profile at Awami Markaz Junction 155 APPENDIX 43 Average cycle profile at Drig Road Junction 156 APPENDIX 44 Average cycle profile at Karsaz Junction 157 APPENDIX 45 Average cycle profile at Mehran Hotel Junction 158 APPENDIX 46 Average cycle profile at Regent Plaza Junction 159
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APPENDIX 47 Average cycle profile at Shah Faisal Junction 160 APPENDIX 48 Average cycle profile at Star Gate Junction 161 APPENDIX 49 Average cycle profile at Tariq Road Junction 162
1
CHAPTER 1
INTRODUCTION
1.1 Preamble Traffic signals are perhaps the most important traffic control devices for at grade
intersection in urban traffic system. Proper installation of traffic signals can reduce
the number of accidents and minimize delays to vehicles at intersections.
Furthermore, traffic signals can increase intersection capacity.
Since last three decades it is found that there is a significant increase in
urbanization and consequent rapid growth of car ownership. Roadways of several
major cities are unable to cater this increased traffic flow.
Therefore, we more often come across with a situation in central areas that the
traffic is congested with formation of long queues, causing delay, frustration and
environmental issues for both the pedestrians and vehicle-users. Such traffic
problems more often become the cause of accidents.
The rapid increase in vehicle ownership in Pakistan in general, and Karachi in
particular has increased the traffic intensity that has created various serious
problems such as congestion and formation of long queues ultimately causing
heavy delays and increase in the number of accidents at various locations on
roadways.
It is usually a challenge to ascertain a particular factor that causes the traffic
problem, because many parameters are involved. However, problems have also
been attributed to the following reasons:
i) Traffic signal installation (timing) in Pakistan is dependent either on
Webster and Cobbe’s formula (British Standard 1966) [1] or on ad-hoc
basis.
ii) Local intersections are not complying with the British Standard practice as
far as traffic behavior, vehicle characteristics and surface characteristics of
the intersection are concerned.
2
iii) Efforts have not been made on national level to develop a formula for
estimation of saturation flow, which simulate our traffic conditions.
In order to solve this problem, it will be necessary to review the traffic signal
timing. For a particular intersection, cycle time is an important parameter to
minimize delay that ultimately causes formation of long queues and accidents. An
important component required for the optimum cycle time is saturation flow. Direct
measurement of saturation flow is obviously desirable to achieve satisfactory
results, but in case of new intersection, results from measurements of saturation
flow are being estimated from the work of outdated researches. In case of
Pakistan, where no standard values of saturation flow are available pertaining to
local traffic conditions, values are being applied from earlier work either carried in
U.K or in USA that does not relate to the actual cycle time needed for local traffic.
A critical need for traffic analysis is a clear understanding of the ability of various
types of facilities to carry traffic. This knowledge, when integrated with
measurements of current traffic demand and forecast of future traffic demand,
allows the traffic engineer to plan and design facilities that can adequately serve
public needs.
Established work has been conducted to estimate the saturation flow and lost time
in developed countries. The procedure in HCM [2] (Highway Capacity Manual) and
other such studies assume that the traffic flow is homogenous and follows lane
discipline. Traffic composition in Pakistan and other developing countries is mixed
in nature with different types of vehicles and the vehicles do not follow lane
discipline. Hence, the procedure for assessing the facility in Pakistan which has
been adopted from developed countries will not be suitable in Pakistan.
Signalized intersections are vital nodal point in transportation network and their
efficiency of operation, in terms of signal timings, greatly influences the entire
network performance. Traffic signals are installed at these nodal points in order to
allocate the right-of-way to different competing streams of vehicles passing
through the intersections. As for the research area in Pakistan, pre-timed signal
controls are in use [3].
3
The HCM presents the results of selected studies that measured saturation flow
rates at various locations throughout the U.S. from 1967 to 1992. The reported
saturation flow rate of each study varies from one another. The average obtained
from measurements of start-up lost times also varies. The large variations in
saturation flow rates and start-up lost times indicate a lack of traffic stability. This
is acknowledged in the HCM. Due to these instabilities, the HCM recommends
that local data collection be performed to produce more accurate estimates of
local saturation flow rates and start-up lost times [19].
It is a known fact that there are close relationships between intersection
characteristics and saturation flow. Empirical relationships have been developed
for estimation of saturation flow and lost time in many countries such as Great
Britain, Australia, U.S.A, Bangkok, Malaysia, India and Bangladesh, etc, but such
relationship has not been developed for Pakistan yet. Therefore, a need was felt
to carry out the research on signalized intersections of Pakistan to derive
empirical relationships between intersection characteristics and saturation flow.
The study reported herein analyzes the capacity of pre-timed signalized
intersections and suggests modifications required in the formula while predicting
the traffic behavior for mixed traffic conditions. The study area of analysis is
concentrated to largest city of Pakistan, known as Karachi.
1.2 Objectives of Study The aim and objectives of the subject study in the city of Karachi are:
1. To collect traffic data and study the traffic flow characteristics at selected
signalized intersections of Karachi in general and at Shahra-e-Faisal
(Faisal Road) and M.A. Jinnah Road in particular.
2. To measure headway and saturation flow of traffic at several
signalized intersections.
3. To determine passenger car unit (PCU) for different vehicle types for
saturated conditions.
4
4. To derive general relationship between intersection characteristic
(approach width) and saturation flow.
5. To measure the lost time at signalized intersections.
6. To compare the subject results with the results of earlier researchers, and
to develop empirical relationship to estimate traffic intensity, i.e., saturation
flow and lost time.
1.3 Methodology Literature review reveals that little work has been done towards the effect of
heterogeneity of traffic on capacity analysis of signalized intersections. There is no
systematic procedure available to deal with mixed traffic in the analysis of
signalized intersections. HCM provides basis for the capacity analysis and is
being widely used in most of the developed countries. The present study attempts
to incorporate changes in the existing formula based on experimental results for
making it applicable to the traffic conditions in Karachi, Pakistan.
As far as data collection is concerned, Video Recording Technique is used to
collect data in the field. Video based technique overcomes many difficulties in
collecting traffic information. The video camera continuously records the traffic
flow. A total of thirteen intersections on Shahra-e-Faisal and five intersections on
M.A. Jinnah Road were selected in Karachi city for the analyses. All intersections
were pre-timed signals.
The data recorded films were played back in the laboratory on a large screen with
a slow motion built in facility to retrieve the required information. PCU values are
calculated using regression technique. In addition to the saturation flow, geometric
characteristics (width, gradient, filtration of left turning movements) of the
intersections including parking of vehicles within 40m are also taken into account.
Based on the experimental data, saturation flow model is developed to suit mixed
traffic conditions by regression analysis which simulates local traffic conditions.
5
CHAPTER 2
SIGNALIZED INTERSECTIONS CONCEPT
2.1 General Intersection may be signalized for a number of reasons, most of which relate to
the safety and effective movement of conflicting vehicular and pedestrian flows
through intersection. Three concepts are important in understanding signalized
intersection design and operation:
1) The time allocation of the 3600 seconds in an hour to conflicting
movements and to "lost time" in the cycle.
2) The effect of left turning and right-turning vehicles on the operation of the
intersection.
3) Geometric parameters such as lane width, gradient and site characteristics,
etc.
This chapter discusses the basic principles of traffic behavior at signalized
intersections.
2.2 Terminology and Key Definitions [2] The following terms are commonly used to describe traffic signal operation:
Cycle: One complete sequence of signal indications, start green time on one
phase to start of green again on the same phase is called a cycle.
Cycle Length (C): Total length of time for the signal to complete one cycle.
Phase: The sequence of conditions applied to one or more streams of traffic
during which the cycle receive identical signal light conditions.
Change Interval (Y): The "yellow" and /or "all-red" intervals, which occur at the
end of a phase to provide for clearance of the intersection before conflicting
movement are released.
6
Green Time (G): Time within a given phase during which the "green" indication is
shown.
Lost Time: Time during which the intersection is not effectively used by any
movement or the amount of a time in a cycle, which is effectively lost to the traffic
movement in the phase because of starting delay, and at the end of green phase
with start of amber period. Pedestrian movement at start of phase and the falling
of the discharging rate, which occurs during the amber period.
Effective Green Time: Time during which a given phase is effectively available
for stable moving platoons of vehicles in the permitted movements.
Green Ratio: Ratio of effective green time to the cycle length.
Effective Red: Time during which a given movement or set of movements is
effectively not permitted.
Optimum Cycle Time: The cycle time, which gives the least average delay to all
vehicles using the intersection.
Passenger Car Unit (PCU): Vehicle of different types require variable area in the
road space because of variation in size and performance. In order to allow for
capacity measurements for roads and intersections, traffic volumes are expressed
in PCU. (It is equivalent ratio between another type of vehicle and a normal
passenger car.)
Early Cut Off: To facilitate a right turning movement from one approach, the
green of the opposing arm can be cut off a few seconds before the arm having the
right turn’s movement.
Degree of Saturation: It is the ratio of the design flow to the actual capacity of a
particular approach, weighted by the amount of green the approach receives in a
cycle.
Early Cutoff Overlap: Condition in which one or more traffic streams are
permitted to move after the stoppage of one or more other traffic streams, which
during the preceding stage had been permitted to move with them.
7
Effective Green Period: The time during which a given traffic movement or set of
movements may proceeds; it is equal to the cycle length minus the effective red
time [5].
Flow Factor: The flow factor or `y' value of an approach is the ratio of the design
flow to the saturation flow of the particular approach.
Green Split: The ratio of green time allocated to each of the conflicting phases in
a signal sequence [6].
Intergreen Period: The period between the end of the green display on one stage
and the start of the green display on the next stage is known as the intergreen
period.
Minimum Cycle Time: The minimum cycle time that is just sufficient to pass the
traffic.
Offset: The time difference or interval in seconds between the start of the green
indication at one intersection as related to the start of the green interval at another
intersection from a synchronized system time base[6].
PCU Factor: An average PCU value derived for the convenience of signal
calculation to convert unclassified (by type) vehicle counts from vehicles per hour
units to PCU per hour units.
Saturation Flow: The maximum flow which could be obtained if 100 percent
green time was awarded to a particular approach.
Traffic signals may operate in following basic modes, depending upon the type of
control equipment used:
a. Pre-timed operation: In pre-timed operation, the cycle length, phases,
green times, and change intervals are all preset. The signal rotates through
8
this defined cycle in constant fashion. Each cycle is same, with the cycle
length and phase lengths constant.
b. Semi-actuated operation: In semi-actuated operation, the designated
main street has a "green" indication at all times until detectors on the side
street determine that some vehicles have arrived on one or both of the
minor approaches. The signal then provides a "green" phase for the minor
approach, after an appropriate change interval, which is retained until all
vehicles are crossed, or until a preset maximum side-street allocated green
time is reached. In this type of operation, the cycle length and green times
vary from cycle to cycle in response to demand.
c. Fully- actuated operation: In fully-actuated operation, all signal phases
are controlled by detector actuations. In general, minimum and maximum
green times are specified for each phase. In this type of control, cycle
length and green times may vary considerably in response to demand.
d. Real-time operation: It is an integral part of the urban traffic control
system which takes an input detector data for real-time measurement of
traffic flow, and “optimally” controls the flow through the network.
2.3 Traffic Flow Characteristics at Signalized Intersection At any typical signalized intersection, we can observe a minimum of three signal
lights are seen which are red, yellow and green. Some basic parameters of traffic
flow at typical signalized intersection are presented in Figure 2.1. The figures
implies at typical scenario of one-way approach with cycle of two phases to a
signalized intersection (HSC 2000). [7]
The figure comprises of three portions. A time versus space graph of vehicles has
been shown in first part. The diagram also indicates intervals for the signal cycle
of the particular approach. From the diagram, the timing interval of interest, along
with the labels with the symbols can be seen in second part. An ideal graphical
representation of flow rate along the reference line is provided in the third part
which is indicating the saturation flow.[7]
9
Figure 2.1 Fundamental Attributes of Flow at Signalized Intersections
(Source: HCM 2000)
2.3.1 Performance Measures
The performance measures of a signalized intersection can be evaluated by
stops, delay, and queue length. Each of these factors may be represented as
values, which express totals or averages for the whole intersection or for
individual approaches. These averages are generally expressed on a per vehicle
basis. Other performance measures include throughput and total travel time [8, 9].
Delay, specifically the control delay is the parameter used in the signalized
intersection methodology of the HCM 2000 and the primary measure used in the
number of signalization optimization procedures. Performance measures are
critical part of all intersection design methodologies.
10
2.3.2 Discharge Headway, Lost Time and Saturation Flow
2.3.2.1 Discharge Headway
Before calculating intersection signal timings it is necessary to understand the
vehicle discharge phenomenon, from the intersection when the signal turned on
green. A group of N vehicles at a signalized intersection is illustrated in Figure 2.2.
The vehicles are in queue and waiting for the green signal to be turned on. When
the green light is turned on, the headways of the departing vehicles will be
observed as these vehicles cross the stop line, as shown in the Figure 2.2 [10].
The time interval between the indication of the green light and the crossing of the
first vehicle through the stop line will be the first headway. On the same lines the
second headway is the time interval between the first and second vehicles
crossing the stop line, etc. Generally the headways are measured as the front
wheels of the vehicle cross the stop line. The first headway is relatively long, as it
includes the reaction time and the time required by the first vehicle’s driver to
accelerate. Whereas, the second headway is shorter, because of the overlapping
of second driver’s reaction and acceleration time with the first driver. Each
successive headway becomes smaller. Finally, the headways becomes stable.
This happens when vehicles have fully accelerated while crossing the stop line [10].
Fig 2.2: Conditions at Traffic Interruption in an Approach Lane of a Signalized Intersection (Source: HCM 2000)
11
Veh in Queue Headway
1 h + t1
2 h + t2
3 h + t3
. .
N h + t N
N + 1 h
N + 2 h
. .
. .
n h
the saturation headway is defined as the level headway attained by the vehicles
passing during the green phase [10].
Figure 2.3 shows conceptual plot of headways of vehicles entering the
intersection versus the position of the vehicle in the queue.
12
Figure 2.3 Concept of Saturation Flow Rate and Lost Time (Source: HCM 2000)
The behavior at a signalized intersection can be modeled by considering that each
vehicle requires an average of “h” seconds of green time to cross the intersection.
A related term of saturation flow rate has been arise from this assumption. If each
vehicle requires h seconds of green time, and if the signal remains green, then s
vehicles/hour could cross the intersection, where s is the saturation flow rate [10].
Thus:
s = 3600 h
where: s = saturation flow rate, vehicles per hour of green time per lane
(vphgpl)
h = saturation headway, seconds
The units of saturation flow rate are “vehicles per hour of green time per lane.” It
can be multiplied by the number of lanes to yield units of vehicles per hour of
green time” [10]. If the signal were always green, the saturation flow rate would be
the capacity of all the lanes.
13
From the conceptual plot of headways it is clear that the fifth vehicle following the
beginning of a green should be used as the starting point for saturation flow
measurements. The value h represents the saturation headway, estimated as the
constant average headway between vehicles after the fourth vehicle in the queue
and continuing until the last vehicle that was in the queue at the beginning of the
green has cleared the intersection [5]. The saturation headway is the time interval
that a vehicle in the stopped queue takes to pass through a signalized intersection
on the green signal, assuming that there is a continuous queue of vehicles moving
through the intersection.[2]
2.3.2.2 Lost Time
Delay in start and stoppages at end of a phase indicate that a portion of the cycle
length is not being completely utilized. This is called lost time (time which is not
effectively serving any movement of traffic). Total lost time is a combination of
start-up and clearance lost times.
Start-up lost times occur when a signal indication first turns from red to green,
drivers in the queue do not instantly start moving at the saturation flow rate. This
start-up delay results in a portion of the green time for that movement not being
completely utilized. This start-up lost time (has a value that is typically around 2
seconds).
When green phase finishes, drivers hesitate while crossing the intersection, thus,
green time is not effectively utilized. This causes delay and drop in saturation flow.
This time lost at the end of green phase is termed as clearance lost time. Start-up
and clearance lost times are summed to arrive at a total lost time for the phase,
given as:
tL = l1 + l2
Where:
tL = total lost time for a movement during a cycle in seconds,
l1 = start-up lost time in seconds, and
l2 = clearance lost time in seconds.
Lost time remains fixed, regardless of cycle length. For shorter cycle lengths, the
cycle length will comprise a larger percentage of the lost time, and will result in a
larger total of lost time over the course of a day than for longer cycle lengths.
14
Longer cycle lengths usually have more phases than shorter cycle lengths, which
may result in similar proportions of lost time.
2.3.2.3 Effective Green and Red Times
For analysis purposes, the time during a cycle that is effectively (or not effectively)
utilized by traffic must be used (the green, yellow, and red signal indications are
not directly useful for analysis). Effective green time is the time during which a
traffic movement is effectively utilizing the intersection [5].
The effective green time is calculated as [2]
g = G + Y + AR − tL
Where:
g = effective green time for a traffic movement in seconds,
G = displayed green time for a traffic movement in seconds,
Y = displayed yellow time for a traffic movement in seconds,
AR = displayed all-red time in seconds, and
tL = total lost time for a movement during a cycle in seconds.
Effective red time is the time during which a traffic movement is not effectively
utilizing the intersection. The effective red time is calculated as:
r = R + tL
Where:
r = effective red time for a traffic movement in seconds,
R = displayed red time for a traffic movement in seconds, and
tL = total lost time for a movement during a cycle in seconds.
Alternatively, the effective red time can be calculated as follows, assuming the
cycle length and effective green time have already been determined:
r = C − g
Where:
r = effective red time for a traffic movement in seconds,
C = cycle length in seconds, and
g = effective green time for a traffic movement in seconds,
15
Likewise, the effective green time can be calculated by subtracting the effective
red time from the cycle length. The capacity at signalized intersection is based on
saturation flow rate, the lost time and the signal timing.
2.3.2.4 Saturation Flow
Saturation flow is important in transportation engineering because it is used in the
evaluation of the intersection performance, to estimate the intersection capacities
and for setting the timings of the traffic signal. The saturation flow rate is “the
equivalent hourly rate at which previously queued vehicles can traverse an
intersection approach under prevailing conditions, assuming that the green signal
is available at all times and no lost times are experienced [2].” According to a
special report of the Australian Road Research Board [98] on traffic signal capacity
and timing analysis, the saturation flow rate “represents the most important single
parameter in the capacity and timing analysis of signalized intersections”.
The definition of the saturation flow rate can be confusing because the rate at
which the first few stopped vehicles enter an intersection after a signal changes to
green is well known to be less than the flow rate of subsequent vehicles.
Consequently, the extra time consumed by the first few vehicles is considered as
“lost time” and is treated as a separate factor in capacity and signal timing
determinations.
The base saturation flow rate is usually calculated empirically by simply starting
measurements of queue dispersion after the first three to five vehicles, and their
accompanying lost times, are skipped. This treatment has led to the base
saturation flow rate being perceived as a constant value subject to adjustment
factors which cause the rate to be increased or decreased due to any special
conditions specific to an intersection approach site under study. Similarly, the
estimated lost time incurred in the start-up of the first three to five vehicles can be
increased or decreased due to any special characteristics existing at a given
intersection approach.
Saturation flow rates are not usually measured directly. Instead, headways
between successive vehicles are measured and averaged, and the saturation flow
16
rate is calculated from the average saturation headway by dividing it into 3,600 s
per hour. The saturation headway is defined by the HCM as “the average
headway between vehicles occurring after the fourth vehicle in the queue and
continuing until the last vehicle in the initial queue clears the intersection”. The
time at which the last vehicle in the initial queue clears the intersection [5] can be a
cause of confusion because the HCM defines the headway screen line as the stop
line and the measurement benchmark as the front wheels of a vehicle, which is
not a position where the last vehicle “clears the intersection”[19].
2.4 Capacity and Level of Service Concepts The capacity analysis is carried out to ascertain the maximum traffic that can be
accommodated by given facility. It is also intended to estimate the maximum
amount of traffic that can be accommodated by a facility without compromising the
operational qualities. The definition of operational criteria is accomplished by
introducing the concept of level of service. Range of operating conditions is
defined for each type of facility and is related to the amount of traffic that can be
accommodated at each service level.
2.4.1 Capacity The capacity of a lane in an intersection is the number of vehicles per hour of
green time that can pass through the intersection. In a fully-utilized intersection,
time is lost because of start-up time (the headway for the first 4 or 5 cars is larger
than h) and slowdown. Thus, the effective green time is nh, where n is the number
of vehicles that pass through the intersection on the green phase and h is the
saturation headway time. The proportion of actual time available for movement in
lane i during a complete cycle is nh/C where C is the cycle length. The capacity is
computed by multiplying the saturation rate by this quotient [10]. That is,
C i = S i nh
C where: Ci = capacity of lanes serving movement i, vph or vphpl
17
Si = saturation flow rate for movement i, vphg or vphgpl
n = average number of vehicles that pass through the intersection
on the green phase
h = saturation headway, seconds
C = signal cycle (green, yellow, red) length, seconds
The Highway Capacity Manual 2000 defines the capacity of facility as " the
maximum hourly rate at which persons or vehicles can reasonably be expected to
traverse point or uniform section of a lane or roadway during a given time period
under prevailing roadway, traffic, and control conditions”.
Prevailing roadway, traffic, and control conditions, which should be reasonably
uniform for any section of a facility, define capacity as “Any change in the
prevailing conditions will result in the change in capacity of the facility”.
Capacity is defined on the basis of "reasonable expectancy." That is stated
capacity for a given facility is a rate of flow that can be repeatedly achieved during
every peak period for which sufficient demand exists and that can be achieved on
any facility with similar characteristics [11].
The capacity of highway facility is an important characteristic. Operating
conditions at capacity are, however, generally poor. Few facilities are designed to
operate at or near capacity because of poor operating characteristics and the
difficulty in maintaining capacity operations without breakdown. Thus, the ability to
analyze the traffic carrying ability of facilities under better operating is major
aspect of capacity analysis. Capacity may be defined in terms of persons per
hour, passenger cars per hour, or vehicles per hour depending upon the type of
facility and type of analysis.
2.4.2 Level-of-Service The Highway Capacity Manual 2000 defines level of service (LOS) as term, which
denotes a range of operating conditions that occur on transportation facility when
it is accommodating range of traffic volumes.
18
Highway Capacity Manual describes service quality in following terms:
(i) Speed and travel time. One of the most easily perceived measures of service
quality is speed, or travel time. On freeway, speed is very evident measure of
quality, while on surface street systems, the driver is very sensitive to total
travel time.
(ii) Density. Density is not often used in traffic analysis. A density describes the
proximity of vehicles to each other in the traffic stream and reflects ease of
maneuverability in the traffic stream, as well as psychological comfort of
drivers.
(iii) Delay. Delay can be described in many ways. It represents excess or
additional travel time due to travel time of controls.
(iv) Other measures. A variety of other measures are used to describe service
quality. In some cases, measures used are not directly related to drivers or
passengers. Such measures generally rely upon volumes or flow rates.
Six level of service (LOS) are defined for capacity analysis and are designated A
through F, with LOS A representing the best range of operating conditions and F
the worst [8]. Safety is also a parameter, used to establish level of service.
The specific terms in which each level of service is defined vary with the type of
facility involved. In general LOS A describes a free flowing condition in which
individual vehicle of the traffic stream are not influenced by the presence of other
vehicles. LOS F generally describes breakdown operations (except for signalized
intersections), which occur when flow arriving at a point is greater than facility's
capacity to discharge flow [12]. Level of service B, C, D, and E represent
intermediate conditions, with lower bound of LOS E often corresponds to capacity
operations.
Each facility has five service flow rates, one for each level of service (A through
E). For LOS F, it is difficult to predict flow since stop-start conditions often occur.
Service flow rate is the maximum hourly rate at which person or vehicles can
reasonably be expected to traverse a point or uniform segment of lane or roadway
during given period under prevailing roadway, traffic, and control conditions while
maintaining a designated level of service. The service flow rates are generally
based on a 15-min period [13].
19
2.4.3 Factors Affecting Level of Service
2.4.3.1 Base Conditions
Many of the procedures in HCM 2000 provide formula or simple tabular or graphic
presentations for set of specified standard conditions, which must be adjusted to
account for any prevailing conditions not matching those specified. Base
conditions assume good weather, good pavement conditions, user familiar with
facility, and no incident impending traffic flow [14].
Base conditions for uninterrupted flow facilities are:
a. Lane width of 3.6 m,
b. Clearance of 1.8 m between the edge of the travel lane and the nearest
obstruction or the objects at the road side and in the median,
c. Free-flow speed of 100km/h for multilane highway,
d. Only passenger cars in the traffic streams (no heavy vehicles),
e. Level terrain,
f. Absence of no-passing zone on two-lane highway, and
g. No impediment to through traffic due to traffic control or turning vehicles.
Base conditions for intersection approaches include [14]:
a. Lane width of 3.6 m,
b. Level grade,
c. No curb parking on the approaches,
d. Only passenger cars in the traffic streams and no local transit buses
stopping at the travel lanes,
e. Intersection located in a non-central business district area, and
f. No pedestrians.
20
In most capacity analysis, prevailing conditions differ from the base conditions,
and computation of capacity, service flow rate, and level of service must include
adjustment to reflect this. Prevailing conditions are generally categorized as
roadway, traffic, or control.
2.4.3.2 Roadway Conditions
Roadway conditions include geometric and other elements. These include:
a. Number of lanes
b. The type of facility and its development environment,
c. Lane widths,
d. Shoulder widths and lateral clearance,
e. Design speed,
f. Horizontal and vertical alignments, and
g. Availability of exclusive turn lanes at intersection.
2.4.3.3 Traffic Conditions
Traffic conditions that influence capacities and service levels include vehicle type
and lane or directional distribution.
a. Vehicle Type: whenever a vehicle other than passenger cars exists in the
traffic stream, the number of vehicles that can be served is affected. Heavy
vehicles adversely affect traffic in two ways:
(i) They are larger than passenger cars and therefore occupy more roadway
space, and
(ii) They have poorer operating capability than passenger car, particularly with
respect to acceleration, deceleration, and the ability to maintain speed on
upgrades.
21
b. Directional Distribution
Directional distribution and lane distribution also affect capacity, service flow rates,
and level of service.
2.4.3.4 Control Conditions
For interrupted flow facilities, the control of the time available for movement of
specific traffic flow is critical element affecting capacity, service flow rates, and
level of service. The most critical type of control on such facilities is the traffic
signal. Operations are affected by the type of control in use, signal phasing, and
allocation of green time, cycle length, and relationship with adjacent control
measures.
22
CHAPTER 3
LITERATURE SURVEY ABOUT DEPARTURE HEADWAY,
SATURATION FLOW AND LOST TIME
3.1 General This chapter reviews the literature regarding the work, which has been carried-out
on the saturation flow and lost time all over the world, the behavior of varying
cycle profile and junction capacity (traffic flow).
The concept of capacity and level of service are central to the analyses of
intersections, as they are for all types of facilities. It is necessary to consider both
capacity and level of service to evaluate the overall operation of signalized
intersections. As per HCM 2000 level of service is based upon the average control
delay per vehicle for various movements within the intersections. Literature
review of departure headway, saturation flow, delay, level of service, etc., is
presented in this chapter under respective headings.
3.2 Departure Headway
A lot of research work has been carried out regarding departure headway to
analyze traffic characteristics like passenger car unit, delay, saturation flow rate,
and lost time. This is because the knowledge of departure headways at signalized
intersections plays a pivotal role in assessing the intersection capacity analysis
and signal timings [15].
Though there are many definitions which have been proposed by various
researchers from time to time, the term of departure headways at signalized
intersections can defined as “the time intervals between two successive vehicles
passing stop line or any predetermined reference line at the intersection” [15]. The
values of various basic parameters in connection with signalized intersection
operation, such as delay, saturation flow and lost time, are generally the basic tool
of measurements of departure headways. Improper headways can results in
23
errors in estimation of saturation flow and lost time which will consequently result
in traffic accidents, delays, congestion, and economic losses [15].
Hung [15] has acknowledged the earlier work of Greenshield [16] as a pioneer work
regarding departure headway study in the filed of traffic engineering. A camera
with 16-mm lens was utilized to take a series of time-motion pictures at short
successive time intervals in New Haven, Connecticut and New York City while
studying traffic performance at intersections. Greenshield [16] made 2,359
observations and his recommendations for departure headways from first to fifth
vehicles in a queue are 3.8, 3.1, 2.7, 2.4, and 2.2 seconds. He did not consider
the effect of left-turning movements and heavy vehicles. After fifth vehicles the
departure headway touched to 2.1 seconds [15].
Hung [15] has referred the earlier work of Gerlough and Wanger[17] who studied the
departure headways at signalized intersections in Los Angeles. They developed a
simulation model to analyze the traffic signals at individual intersections. The
summary of the headways for the first to twentieth vehicle ranges from 3.85 to
2.28 seconds [15].
Carstens [18] carried out his research at four signalized intersections in Ames and
Iowa with manual counts. He studied starting delay and headway of vehicles.
Altogether 2,093 signal cycles were analyzed which revealed average headway of
straight through passenger cars 2.29 seconds per vehicle [15].
Yean-Jye Lu [19] has used a time recorder and stop watches at one signalized
junction in Austin, Texas, to collect departure headways. The departure headways
of protected left turns were in range of 2.43 to 2.09 sec for the vehicles in the first
through fourth queue positions respectively. A headway of 1.8 sec was recorded
when the vehicles were in a queuing position up to fifth vehicle and onward. He
studied three classes of vehicles i.e., large cars, small cars, trucks / buses [15].
Lee and Chen [20] conducted their survey with the help of video camera. In their
study the average headways ranges from 3.80 to 1.76 sec. They suggested six
24
important factors which influence the departure headways. The detail is given in
their research paper [15].
Massoum Moussavi and Mohammed Tarawneh [21] have studied departure
headways for 10,000 vehicles in six cities of Nebraska. The departure headways
ranges were 2.90 to 1.75 for straight through vehicle [15].
Niittymaki et al [22] studied departure headways at Finland while studying
saturation flow at signalized intersection. His research revealed a mix type of time
headway for 1st, 2nd and 3rd vehicles in the queue, after 3rd vehicle headway
reached at 2.0 seconds [15].
Overall conclusion of all the above studies pertaining to departure headways are
indicating that departure headways are varying from site to site and from country
to country. However, it can be concluded that for each saturation flow, lost time
and passenger car unit study, the departure headway study is quite essential.
3.3 Capacity Miller [23] stated that “the capacity of an approach to any intersection is the
maximum sustainable rate at which vehicles can cross the intersection from that
approach (under consideration) under the prevailing roadway and traffic
conditions”. The actual rate on which the vehicles cross any reference line is also
same as the capacity, if the traffic flow is continuous throughout the full green
period. Therefore, it is important when discussing the capacity of signalized
intersection, to state the prevailing conditions of roadway and traffic, and actual
rate at which vehicles cross the stop line.
Individual lane group’s capacity is defined as capacity at intersection which is
defined as “The lane group capacity is the maximum hourly rate at which vehicles
can reasonably be expected to pass through the intersections under prevailing
roadway, traffic and signalization conditions” [7]. While referring to traffic
conditions, it generally include vehicle type distribution, volumes on each
approach, use of bus stops and their locations within intersection area, distribution
25
of vehicles by movement, parking movements on approaches, and and pedestrian
crossing flows. Roadway conditions include the width and number of lanes,
grades, basic geometric parameters of the intersections, and lane use [7].
Signalization condition refers to signal phasing, timing, and type of control.
3.4 Level of Service
In the 1965 Highway Capacity Manual, levels of service at signalized intersection
were related to load factor. Load factor presented some problem such problem as
its insensitivity to low service volume, absence of any rational; basis for defining
break points, and difficulty in identifying loaded cycle. Sutaria and Haynes [24] used
road user opinion survey that involves depicting and rating different traffic situation
at carefully selected single signalized intersection. Over 300 drivers rated
randomly arranged film sequences of two types - a driver view (micro view) and
an overall view (macro view) of an intersection. Later on these films were
reviewed, segment by segment, in terms of appropriate level of service. Statistical
analyses indicated that average individual delay correlated better with level of
service. The hypothesis for load factor as a better predictor of Level of Service
was tested and was rejected through the latest results.
Chandra et al. (1996)[25] studied the parameter to define level of service for mixed
traffic at signalized intersections. Due to many problems associated with the
measurement and interpretation of delay at signalized intersection LOS
parameters were redefined. Degree of saturation and percent of vehicle stopping
in the approach were considered the appropriate parameters. Data collected at
eight signalized intersections in Delhi were analyzed. They developed the
graphical relationship incorporating the average stopped delay, saturation green
ratio and the degree of saturation (DOS). Break points in the range of DOS for
different LOS have been determined based on these parameters. DOS was also
related to the percent stopping to define six LOS for mixed traffic flow at signalized
intersections.
The control delay per vehicle is calculated for each lane group, then on the basis
of this average control delay it is estimated for each approach and on the similar
26
lines aggregated for the whole intersection. This control delay is directly
concerned with the Level of Service. The criteria for which is given in Table 3.6 [13].
Level of service A: describes operation with very low control delay. This level of
service occurs when progression is extremely favorable and most vehicles arrive
during green phase. Many vehicles do not stop at all.
Level of service B: this level generally occurs with good progression, short cycle
length, or both. More vehicles stop than LOS A causing higher level of delay.
Level of service C: the higher delays may result from only fair progression,
longer cycle length, or both. Individual cycle failures may begin to appear at this
level. The number of vehicles stopping is significant.
Level of service D: at this level the influence of congestion becomes more
noticeable and longer delays may result from some combination of unfavorable
progression, long cycle lengths, or high v/c ratios. Many vehicles stop and
individual cycle failures are noticeable.
Level of service E: at LOS E delays will be high indicating poor progression, long
cycle length, and high v/c ratios. Individual cycle failures are frequent.
Level of service F: this level is considered to be unacceptable to most drivers
and often occurs with over saturation, i.e., when arrival flow rate exceeds the
capacity of lane groups. It may also occur at high v/c ratios with many individual
cycle failures. Poor progression and long cycle lengths may also be major
contributing causes to such delay levels.
3.5 Saturation Flow Saturation flow is a vital traffic performance measure of the maximum rate of flow;
it is most oftenly used in intersection design and the control applications.
Saturation flow is an important performance measure of junction operation at
macro level. The potential capacity of an intersection when operating under 'ideal'
conditions is also indicated by saturation flow [26].
27
The saturation flow is the uniform flow of vehicles through an approach while the
full green time is lapsed still few vehicles are in queue waiting to cross the
junction. Researchers have expressed Saturation flow in Passenger Car Units
(PCU) per hour of green time. Its value depends on the prevailing roadway and
traffic conditions. The roadway includes the layout of the intersection, the width of
approach, the number and width of lanes, site conditions and also the gradient.
The traffic condition includes the traffic composition, the number of right and left
turning vehicles, the presence of parked vehicles and many other related factors
which vary from area to area and site to site.
3.5.1 Cycle Profile
Figure 3.1 represent an ideal plot of saturation flow at a typical signalized
intersection. When green light turns on at traffic signal, initially there is a very little
gap as the first driver reacts to the signal. In the beginning the rate of vehicles
crossing the stop line increases as per the speed of the cars they are following.
Soon the vehicles attain a steady state where they cross the stop line at a
constant gap or headway [26].
Fig. 2.1 Variation with Time of Discharge Rate of Queue in a fully Saturated Green Period.
RedAmber
Amber Red
Time
Effective Green Time
Saturation Flow
Final Lost TimeInitial Lost Time
Rat
e O
f D
isch
arge
of
Que
ue in
Sa
tura
ted
Gre
en P
erio
d
Fig. 3.1
28
This steady state is illustrated as the plateau in this profile. In a saturated
intersection, too long queue will be formed, during red indication of signal which
will not be clear in the green period and hence the cars will be following one each
other at constant spacing during the green period. This flow will start decreasing
when the signal turned on amber light. Now the flow rate will decrease at an
increasing rate as in the beginning vehicles carry on through the stop line on
amber light and then stop as the signals turned on red light. The saturation flow is
then calculated by converting the curved profile into a rectangle from which the
dimensions can be measured. This is done through the concept of lost time and
effective green time. Here the lost time will be the time from the start of green light
to a point where vehicles are crossing at half the maximum flow and the sum of
time from where vehicles are flowing at half the maximum flow at the end of
saturation to the start of the red period [26].
3.6 Relationship of Saturation Flow to Optimum Signal Time The relationship of saturation flow to optimum signal cycle time can be found from
the theoretical analysis that the saturation flow is one of the parameter of the
formula for optimizing signal cycle time. For setting fixed time signals to minimize
the delay two formulas have been proposed one by Webster & Cobbe[1] and other
by Australian Road Research Board[98] Both formulas yield more or less similar
results. The main equations are:
C = 1.5 L + 5……………………………………………3.1
1 –
n
1 I
Yi
C = L + 2.2 L/S ………………………………………3.2
1 –
n
1 I
Yi
Where,
C = Optimum Signal Cycle Time (sec)
L = Total Lost Time Per Cycle (sec)
Yi = Representative movement for ith phase ( qi/Si)
n = Number of phases
29
S = Saturation Flow in PCU per sec.
3.7 Estimation of Saturation Flow There are many factors affecting the saturation flow, i.e., approach width,
gradient, traffic composition, right turning traffic, left turning traffic, pedestrian,
parked vehicles and site characteristics.
3.7.1 Effect of Approach Width As per RRTP-56 [1], the saturation flow is expressed in terms of PCU per hour,
with no turning traffic and no parked vehicles present on the approach. The
summary of saturation flow with respect to approach width is given in Table 2. 1.
For approach width greater than 17 feet the saturation flow varies linearly and is
given by:
S= 160 W, pcu/h (W= Width in ft)……………… (3.3)
S = 525 W, pcu/h (W= Width in meters)………. (3.4)
In this context the Australian Road Research Board has also done considerable
research as Leong [27] studied 23 approaches in Sydney metropolitan area the
width of approach was from 3.6 to 9.3 m. Leong[27] stated through his research
that if the approach width ranges from 2.75 m to 3.5 m, then there had been no
effect on saturation flow, this is because there is only a single queue of vehicles,
which could be accommodated within this width.
Leong’s equation is as given below:
S = 1700 veh/h, per lane ……………(3.5)
Sarna and Malhotra [28] presented the results and analysis of the studies on
saturation flow conducted at a number of different intersections with varying
approach road widths. They developed the relationship between the saturation
flow and the approach road width at signalized intersections. Effect of approach
30
volume and increasing percentage of bicycles on the saturation flow was also
studied. It was suggested that flaring of the approach should be done to increase
discharging capacity. The study has shown that the saturation flow increases with
the increase in approach volume.
Miller [23] measured saturation flow at seven main cities of Australia at signalized-
intersections. He observed that the saturation flow increased up to 3.05 m
approach width and than remained constant up to 3.95 m as explained in
Australian Road Research Board bulletin No.3.
Branston [29] studied seven single lane sites, two two-lane sites and one three lane
sites. Like RRTP-56, which gives three different site characteristics, he has also
given three different formulae for the different times of the day and visibility, i.e.,
off peak periods, dark peak periods, and dry light peak periods.
S = 885 + 222W For off peak periods …………… (3.6)
S = 960 + 222W For dark peak periods …………. (3.7)
S = 1045 + 222W For light peak periods ………..... (3.8)
All the above formulas as described by Branston underestimate saturation flow
when compared with the Road Research Laboratory’s recommended formula
given in RRTP-56.
Abu-Rehmeh [30] carried out a study of over 23 signalized approaches in city of
Sheffield. The width of those approaches varied from 2.5 to 6.7 m. Analysis of this
study showed that the width had an effect on saturation flow; however his results
were just nearer to the lowest limit of RRTP-56 given formula.
Through the Regression Analysis he developed the following equation:
S = 475 W pcu/h …………………….. (3.9)
Where, W is the width of approach in meters.
Chang Chien [31] carried out a study over 17 approaches in Bangkok. The width of
approaches varied from 2.80 to 3.50 m. Linear relationship was developed
between Saturation Flow and lane width as:
S = 643 W pcu/green hour ………….. (3.10)
31
Research by Cuiddan and Cuiddan & Ogden [32] developed a new method for
collecting saturation flow data for the design and analysis of signalized
intersection. They have used a portable computer and dedicated software named
SATFLOW for saturation flow measurement and analysis. Data were collected for
a total of 40,000 saturation headway in 160 lanes at 71 sites through out the
Melbourne Metropolitan area.
Ibrahim et. al. [33] had carried out a study to determine the ideal saturation flow at
signalized intersections under Malaysian road conditions. They adopted the
similar method of measuring saturation flow as given by Road Research
Laboratory. The averaged flow values were then regressed with lane widths to
obtain a linear regression model as shown below [34]:
S = 1020 + 265w; R2 = 0.876………….. (3.11)
Where, S = measured saturation flow rate in pcu/hr
w = lane width (m)
R = Constant (Y intercept)
3.7.2 Effect of Gradient Gradient is the average slope between stop line and a point 200 ft. before the stop
line. As per RRTP-56 “ for each 1% of uphill gradient the saturation flow has been
decreased by 3%, and for each 1% downhill gradient the saturation flow increases
by 3%”.
Dick [35] investigated the effect of gradient on saturation flow having measured
approach gradient by using engineer’s level and staff. The result of Dick’s
experiment showed, increase of 1% gradient produces a decrease of 3% in
saturation flow where the gradient continued through the junction.
Heyes and Ashworth [36] carried out an experiment on the effect of gradient on
capacity in Queensway Mersery road Tunnel at Liverpool and they found that 6%
uphill gradi/ent had an effect of 13% reduction in capacity. Leong [27] studied
32
limited gradient effect in Australia and he concluded that 4% up hill gradient
reduced the saturation flow by 9%.
Al-Samarrai [37] studied three sites in city of Sheffield and his results at two sites
showed that 1% uphill gradient decreases the saturation flow by 2% and 1%
downhill gradient increased the saturation flow by 0.33%.
Khaskheli [38] in his study at a flared approach without an additional traffic lane
showed an increase of 5.1% in saturation flow for each 1% downhill gradient.
However, another flared approach with one additional traffic lane showed an
increase of 4.4% in saturation flow for each 1% downhill gradient.
The summary of all the research work that has been carried out in context of
gradient effect on saturation flow is given in Table 3.2.
3.7.3 Effect of Site Characteristics Sites are classified as good, average or poor according to the descriptions given
in Table 3.3.Standard saturation flow is based on observation of ‘average’ sites.
Miller [23] also collected data from many approaches at various locations having
different environmental conditions and measured headway by lane. Four
environments; central business district, industrial, suburban shopping and
residential and three lane types; including left, through and right turning were used
in his experiments. These are defined below.
a. Central business district (CBD)
Central business district of a city with large numbers of pedestrians, high parking
turnover, cars and taxis, pick up and setting down, bus stop, some loading and
unloading of commercial vehicles.
33
b. Industrial
Usually at the edge of the city center. Development includes high industry,
warehouse and other commercial activities. Smaller number of pedestrians than
for CBD but with interference caused by loading unloading of goods vehicles,
vehicle interring and leaving industrial premises with a low parking turnover.
c. Suburban Shopping
Suburban shopping street with moderate numbers of pedestrian and parking
turnover.
d. Residential
Residential or parkland development. Perhaps a hotel or shop or a corner service
station but very few pedestrian. Ideal or nearly ideal conditions for free movement
of vehicles.
Table 3.4 is the basic table of saturation flow for the 12 combinations of lane type
and environment, containing average value.
3.7.4 Effect of Composition of Traffic For measuring the saturation flow in pcu per hour of green time, the information of
pcu equivalents for different type of vehicles is an essential element. In this
regard, Webster & Cobe [1] has carried out an extensive work at the Road
Research Laboratory, and measured the pcu values, which are expressed in
RRTP-56. The summary of all the findings in this context are given in Table 3.5.
Lee and Chen[20] studied the entering headways in small city Lawrence, Kansas
and six factors were examined. Entering headway values from total of 1,899 traffic
queues were recorded by using video camera equipment. From the data, mean
entry headway of vehicle 1 through 12 were found to be 3.80, 2.56, 3.25, 2.22,
34
2.16, 2.03, 1.97, 1.94, 1.94, 1.78, 1.64, and 1.76 sec., respectively. He found the
following observations:
(i) Signal type has little influence on entering headway at signalized intersections.
(ii) Time of the day (a.m. or p.m.) has little influence on entering headways.
(iii) The inside lane of an approach has slightly lower entering headways than
does outside lane.
(iv) The entering headways at approaches with speed limits of 20 mph are
significantly higher than those at approaches with higher speed limits. (>=30
mph). For approaches with speed limits higher than 30 mph, the influence of
speed limit on the headway is noticeable.
(v) In general, streets that have higher speed limits and less roadside friction
have lower entering headway values.
(vi) When queue lengths increase, the general observation is that the entering
headway values decrease.
Taylor et al. (1989) [39] used video-based equipment to estimate the character
speeds and headway. This technique provided cheap, quick, easy, and accurate
method of investigating traffic systems. Investigation of headways on freeway
traffic allows the potential of this technology in a high-speed environment to be
determined. Its application to the study of speeds in parking lots enabled its
usefulness in low-speed environments to be studied. The data obtained from the
video was compared to traditional methods of collecting headways and speed
data.
The departure headways of approximately 10,000 vehicles from straight-through,
exclusive left and exclusive right-turning lanes at 22 intersections in six cities in
Nebraska were collected in the study of Massoum Moussavi and Mohammed
Tarawneh [21]. A microcomputer was used to collect, extract and analyze the data.
The average departure headways obtained in this study were 2.90, 2.04, 2.10,
2.04, 1.87, 1.91 and 1.75 sec respectively, for the first through seventh vehicle in
a stopped queue at signalized intersections. The researchers made comparisons
of the departure headways in different cites and emphasized the variability of
departure headways at signalized intersections [40].
35
Niittymaki et al. [22] found that the departure headway of first vehicle was less than
1.5 sec in the study of saturation flow in Finland. The headway of the second
vehicle in queue was more than 2.5 sec. The third one is around 2.2 sec. After the
fourth and fifth vehicle, the departure headway became constant, less than 2.0
sec. Their study aimed at updating the saturation flow values. The effects of
geometric and traffic composition factors, such as percentage of turning vehicles,
traffic composition, lane width and approach grade were examined [40].
Hossain [41] used micro simulation technique to model traffic operation at
signalized intersections of developing cities. The model was calibrated and
validated on the basis of data collected from Dhaka, the capital of Bangladesh.
Leong et. al. [42] have developed a new statistical approach for finding the PCU
values of different vehicles at signalized intersections with respect to Malaysian
traffic conditions.
3.7.5 Effect of Right Turning Traffic Without opposing flow and with exclusive right turning lanes, it is observed that
the saturation flow of a stream turning through a right angle depends on the radius
of curvature, and is given by: [1]
S = 5/r 1
1800
pcu/h for single file stream………………. (3. 12)
S = 5/r 1
3000
pcu/h for double file stream………………. (3.13)
Where r = radius of curvature (m)
3.7.6 Effect of Left Turning Traffic If the proportion of left turning vehicles is more than 10% of the traffic, a correction
could be made for the excess over 10% by assuming each left turning vehicle
equivalent to 1 .25 straight ahead vehicles [1]
36
3.7.7 Effect of Parked Vehicle
If a vehicle is parked within 10 m. from the stop line there has to be a reduction in
saturation flow. The reduction in saturation flow is equivalent to a loss of carriage
way width at the stop line and can be expressed approximately as follows: [1]
Effective loss of carriageway width = 5.5 — K
25) -(Z 0.9 ft ………… (3.14)
Where Z (>25 ft.) is the clear distance to the nearest parked car from the stop line
and K is green time in sec.
Priyanto [43] in his study investigated the effect of parked vehicles on saturation
flow, extra delay and driver behavior in terms of gap / lag characteristics in
merging behind the parked vehicle. This study covered three approaches.
Saturation was not affected on the right hand lane but it was affected on left
(blocked) and middle (adjacent) lanes. It was found that the use of flashing hazard
indicators caused drivers in the blocked lane to accept shorter gaps and also to
merge further up stream. The later increased the effective length of bottleneck,
which resulted in overall increase in extra delay.
3.8 Heterogeneous Traffic The composition of traffic in developing countries is mixed, with a variety of
vehicles, motorized and non-motorized, using the same right of way. The
motorized or fast moving vehicles include passenger cars, buses, trucks, auto-
rickshaws, scooters and motorcycles; non-motorized or slow moving vehicles
including bicycles, cycle-rickshaw, and animal drawn carts.
Since 1950s, considerable research has been made to develop traffic flow models
for roadways with mainly homogeneous traffic, representing the composition of
traffic primary in developed countries (Khan and Maini) [44]. Very limited studies
have been done to develop an understanding of traffic flow for non-lane-based
heterogeneous or mixed traffic condition in developing countries. Some efforts
have applied a variation of practices developed for homogeneous traffic by
converting heterogeneous traffic by to equivalent passenger car-units and then
applying procedures for homogeneous traffic. However, these efforts have
37
produced mixed results. Recent efforts include the development of microscopic
simulation models.
3.8.1 Comparison of Heterogeneous and Homogeneous Traffic Flow The differences that characterize mixed traffic system are owing to the wide
variation in the operating and performance characteristic of vehicles. The traffic in
mixed traffic flow can be classified as fast-moving and slow moving vehicles or
motorized and non-motorized vehicles. In urban areas, mixed traffic flow often is
also accompanied by substantial pedestrian movement, encroachment at
intersections, street parking, business demand of abutting properties, and narrow
roads.
Lane markings, if present, are typically not followed by mixed traffic flow. Figure
3.2 shows the homogeneous and heterogeneous traffic flow. Traffic does not
move in single lane. Moreover, there is a significant amount of lateral movement,
primarily by smaller-sized motor vehicles. Vehicles do not follow each other within
lanes; hence the concept of relating headways and linear densities is not
meaningful. Vehicles traverse in both the lateral and transverse directions.
At intersection specifically, smaller vehicles such as bicycles, motorcycles, and
scooters use the lateral gaps between larger vehicles in order to reach at the head
of the queue and to discharge quickly (Khan and Maini). [44]
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Figure 3.2 a) Homogeneous Mix b) Heterogeneous Mix
3.9 Passenger Car Unit (PCU) The unrestricted mixing of various classes of vehicles along a road creates many
problems to the traffic engineers and planners. One type of vehicles in the traffic
stream cannot be considered equivalent to any other type, as there is large
difference in their vehicular and flow characteristics The space of the carriage way
is shared by vehicles depending upon their size, speed, headway and lateral gap
maintained by them. The non-uniformity in the static and dynamic characteristics
of the vehicles is normally taken into account by converting all vehicles in terms of
common unit. The most accepted one such unit is passenger car unit (PCU).
3.9.1 Factors Affecting PCU Values PCU value of a class of vehicle may be considered as the ratio of the capacity of a
road with only that class of vehicles on the road to the capacity with a straight
ahead passenger cars only, under identical conditions.
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PCU value depends on the following factors:
(i) Vehicle characteristics:
Physical and mechanical, such as length, width, power, acceleration,
deceleration and breaking characteristic of vehicles.
(ii) Stream characteristics:
(a) Mean stream speed
(b) Longitudinal and lateral clearance distribution
(c) Speed characteristic of the stream
(d) Percentage composition of different classes of vehicle
(iii) Roadway characteristics:
(a) Horizontal alignment, grade, location etc.
(b) Stretch: mid-block, signalized intersection etc.
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 2654 / (15 x 7 x 10) = 2.5276 Vehs / sec = 9100 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 2887 / (16 x 7 x 10) = 2.57 Vehs / sec = 9280 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 2434 / (16 x 7 x 10) = 2.17 Vehs / sec = 7824 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 2787 / (15 x 7 x 10) = 2.65 Vehs / sec = 9555 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 1833 / (12 x 4 x 10) = 3.054 Vehs / sec = 10994 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 2285 / (12 x 8 x 10) = 2.3805 Vehs / sec = 8570 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 1302 / (12 x 4 x 10) = 2.7125 Vehs / sec = 9765 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 893 / (12 x 4 x 10) = 1.8604 Vehs / sec = 6697 Vehs / hr
Saturation Flow = (Total Flow in Saturated intervals) / (Total of the Samples of the Saturated Intervals) = 883 / (12 x 4 x 10) = 1.8395 Vehs / sec = 6622 Vehs / hr