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FETTER, WILLIAM WOODROW. Effects of Far-Side and Side-Street Bus Stops on the Saturation Flow Rate of Signalized Intersections. (Under the Direction of Dr. Joseph E. Hummer.)

As the use of public transit buses increases, it is important to understand how bus

stops affect the surrounding traffic stream, especially with regards to intersection

saturation flow rate. The HCM 2000 and other sources have addressed the effect of

near-side bus stops, but no one has successfully analyzed bus stops on the far-near-side or near-

side-streets of an intersection. The purpose of this study was to determine the effects that both

far-side and side-street bus stops have on the saturation flow rate at a signalized

intersection.

To determine these effects, a set of analytical equations was derived for each bus

stop type. The methodology for these equations required calculating the number vehicles

processed through the intersection during each of three defined time periods within the

green indication of a cycle. The time periods were divided according to how the buses

blocked the traffic: full blockage (period 1), partial blockage (period 2), and no blockage

(period 3). The average number of vehicles processed during a cycle was determined by

multiplying each of the vehicles processed in a time period by the probability of buses

stopping in that time period and then summing them together. The average number of

vehicles processed was then divided by the ideal number of vehicles processed (obtained

from simulation) to obtain an adjustment factor. Applying this factor to the saturation

flow rate calculated the effects due to the bus stop.

To analyze the ability of the equations to predict saturation flow rates, they were

tested using a variety of variable inputs and compared with CORSIM simulation runs

using the same inputs. Sensitivity tests were also performed to determine how the

equations reacted under a variety of variable extremes. The results from these analyses

were not exactly ideal and, as a result, the equations could only be partially validated.

Overall, while it appears that the method for determining saturation flow rate

according to the HCM is inaccurate, an adequate replacement method has not yet been

(2)
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Effects of Far-Side and Side-Street Bus Stops

on the Saturation Flow Rate of Signalized Intersections

by

William W. Fetter

A thesis submitted to the Graduate Faculty of

North Carolina State University

in partial fulfillment of the requirements for

the Degree of Master of Science

Department of Civil Engineering

Raleigh, NC

2007

APPROVED BY:

_________________________ _________________________

Nagui M. Rouphail

John R. Stone

_________________________

Chair of Advisory Committee

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BIOGRAPHY

The author was born and raised on a farm near Charlotte, North Carolina. On the

farm, he learned the value of hard work and determination and gained valuable life

lessons from his father. At an early age, it was instilled that having a strong educational

background was very important to being successful. Two of his father’s favorite quotes

were “no one can ever take away your education” and “without an education, you’ll

never become successful”. Heeding his advice the author enrolled in several vocational

classes while attending high school, at one point causing him to be enrolled in three

different schools at the same time. The author graduated from Sun Valley High School in

June 2000.

After graduating high school, the author attended the William States Lee College

of Engineering at the University of North Carolina at Charlotte. It was here that the

author discovered transportation engineering and focused most of his studies around it.

While attending classes the author met his future wife, Maya, and the two were soon

engaged. In his last attending years, the author received a large push from several

members of the faculty to attend graduate school at NC State University, specifically

under the direction of Dr. Joseph Hummer. Eventually the author applied and soon was

accepted to NC State. The author graduated with a Bachelor Degree in Civil Engineering

in December 2004.

The author then moved to Raleigh and started attending classes at NC State.

During the summer of 2005, the author married and his wife joined him in Raleigh.

While attending the graduate school the author would work during the day at local

engineering firms and attended graduate school classes in the evening. At graduate school

the author focused his studies on transportation and traffic engineering. The author

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ACKNOWLEDGEMENTS

I would like to extend my appreciation to my advisor Dr. Joseph Hummer who

has provided me with priceless advice and challenged me to see transportation

engineering from different perspectives. I would also like to thank Dr. John Stone and Dr

Nagui Rouphail for the instruction I received in their classes and their participation in my

thesis committee.

I also would like to acknowledge Dr. Rajaram Janardhanam at UNC Charlotte

who pushed me to attend graduate school. He advised me where to go and under whom to

study. Without his encouragement during my undergraduate career, I do not think I

would ever have chosen this path.

I also extend my appreciation to my loving wife Maya Fetter who has stood

beside me while I attempted to divide by time between being a student, a husband, and a

family provider all at once. Without her support, I would never have had the strength to

complete graduate school.

My thanks are also extended to my mother Pamela, my sister Kathryn, and the

rest of my family who have always supported me in my goals. I also extend thanks to my

father, Edward, who provided me with unforgettable life lessons and advice that I will

never forget. It is through these lessons and advice that he has continued to support and

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TABLE OF CONTENTS

LIST OF FIGURES... vi

LIST OF TABLES ... vii

CHAPTER 1 - INTRODUCTION ... 1

Background ... 1

Scope... 2

Project Objectives ... 3

Thesis Outline... 4

CHAPTER 2 - LITERATURE REVIEW... 5

Current Literature... 5

Related Research Topics... 8

Previous Research ... 14

Literature Review Conclusions... 16

CHAPTER 3 - METHODOLOGY ... 18

Model Formulation ... 18

Far-Side Bus Stop ... 19

Side-Street Bus Stops ... 29

Saturation Flow Rate Adjustment Factor ... 30

Experiment Design... 37

Model Analysis ... 39

CHAPTER 4 - ANALYSIS RESULTS... 43

Initial Model Analysis ... 43

Equation Calibration ... 47

Equation Validation... 53

Calibrated Model Analysis ... 54

Sensitivity Analysis... 58

Application to Transit Managers ... 65

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CHAPTER 6 - RECOMMENDATIONS ... 69

Future Work ... 69

REFERENCES... 72

APPENDICIES ... 74

Appendix A: Far-Side Simulated and Equation Calculated Data ... 75

Appendix B: Side-Street Simulated and Equation Calculated Data ... 108

Appendix C: Far-Side Simulated and Calibrated Equation Calculated Data ... 125

Appendix D: Side-Street Simulated and Calibrated Equation Calculated Data ... 138

Appendix E: Far-Side Sensitivity Analysis ... 147

Appendix F: Side-Street Sensitivity Analysis Data... 166

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LIST OF FIGURES

Figure 1. Diagram of Near-Side and Far-Side Bus Stops ... 15

Figure 2. Diagram of Far-Side and Side Street Bus Stops... 19

Figure 3. Diagram of Time and Space Relationship of BT ... 21

Figure 4. Diagram of Stop Bar Location and Vehicle Storage Spaces For Far-Side Bus Stop ... 22

Figure 5. Linear Relationship Between BST and the Number of Vehicles Processed ... 26

Figure 6. Diagram of Time Periods and Relationships... 27

Figure 7. Diagram of CORSIM Network Used in Analysis ... 34

Figure 8. Equation Predicted Saturation Flow Rate Values for Far-Side Bus Stops ... 46

Figure 9. HCM Predicted Saturation Flow Rate Values for Far-Side Bus Stops ... 47

Figure 10. Calibrated Equation Predicted Saturation Flow Rate Values for Far-Side Bus Stops... 56

Figure 11. Calibrated HCM Predicted Saturation Flow Rate Values for Far-Side Bus Stops... 57

Figure 12. Storage Length in Vehicles versus Storage Length in Feet... 58

Figure 13. Sensitivity Plot for Calibrated Far-Side Equations ... 61

Figure 14. Sensitivity Plot for Calibrated Side Street Equations... 63

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LIST OF TABLES

Table 1: Far-Side Bus Stop Case Descriptions for Calibration ... 39

Table 2: T-Test and F-Test Results for Initial Analysis ... 44

Table 3: Initial Difference in Simulated and Predicted Values ... 45

Table 4: Simulated Probabilities of Buses Crossing the Stop Bar During Each Time Period ... 49

Table 5: Predicted Probabilities of Buses Crossing the Stop Bar During Each Time Period ... 49

Table 6. Simulated Probabilities of Buses Stopping in Time Periods When Assumptions are Violated... 52

Table 7: Far-Side Bus Stop Case Descriptions for Validation ... 53

Table 8: T-Test and F-Test Results for Calibrated Analysis ... 54

Table 9: Calibrated Difference in Simulated and Predicted Values ... 55

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CHAPTER 1 - INTRODUCTION

Background

The supply of transportation facilities in the U.S. is not keeping up with the

ever-growing demand. From 1960 to 2004, the total number of vehicle-miles driven annually

increased 400% while the total highway centerline miles inventory has only increased by

12% (1).

One solution to managing growing traffic demand is to increase the use of public

transportation. This would decrease the number of vehicles on the roadways and thereby

reduce congestion on the roads and at the intersections. With recent gasoline prices

becoming a burden on the average driver, bus ridership is steadily increasing by about

3% per year in the US, and is seen more often as an attractive approach to transportation

rather than driving one’s own car (1).

Because public transportation is on the rise, it is important to evaluate its impact

on the local traffic stream. Transit buses are primarily found in urban areas and make

frequent stops at designated bus stops that are often located near intersections. At a bus

stop, a bus must first slow down, stop to pick up passengers, and then accelerate back up

into the traffic stream. While all of this is occurring, vehicles behind the bus are delayed

or stopped. Depending on the position of the bus, vehicles may be blocked from

proceeding through or making a turn at the nearby intersection. The impact of buses

making stops can be measured in total traffic delay at the nearby intersection. Since delay

is a function of intersection capacity, capacity must first be calculated in order to

determine transit impact.

The Highway Capacity Manual 2000 (HCM) is the standard reference used to

estimate intersection capacity using a series of adjustment factors based on intersection

properties (2). One of these factors, the bus blockage factor, estimates the effect on

capacity due to buses stopping near an intersection based on the dwell time at a bus stop.

The dwell time is defined as the time from when the bus comes to a complete stop at the

bus stop until the time the bus leaves the bus stop. A close review of the HCM, however,

shows conflicting values of the dwell time in different chapters. This leads to questions

(11)

Other sources such as Rodriquez-Seda and Benekohal (3), Wong et. al. (4), and

Holt (5) also have expressed concerns about inaccurate calculations of the effects of

buses on traffic and felt that the blockage factor presented in the HCM (2) was not

satisfactory for all cases and bus stops. By determining what literature had conflicting

information, and what information was not available, areas that needed to be addressed

were determined. By focusing the analysis on those areas the current research gaps were

addressed.

Scope

This project was focused on calculating a saturation flow rate adjustment method

due to the effects of bus stops at nearby signalized intersections. Because intersection

saturation flow rates are a function of capacity and not delay, no delay calculations for

buses and vehicles were performed.

This study was limited to bus stops located on the far-side and on the side-streets

of intersections with respect to the approaching lane segment. The analysis was

performed assuming urban environments, containing intersections with pre-timed

signalized control. Bus routes with short headways were also assumed but the methods

are applicable to any length of bus headway. Actuated signals were not considered in this

study. Only curbside bus stops with no bus bays were analyzed, eliminating the

possibility of traffic maneuvering past a stopped transit bus.

This study was performed on a single lane approach to a “T” intersection where

only through and right-turn movements were permitted. Even though only single lane

roadways were analyzed the methods and concepts produced herein should be applicable

to multilane roads or intersections with four approaches. Application to multilane roads is

possible by applying the evaluation method to the lane containing a bus stop. Since no

other lane or lanes besides the one containing the bus stop will be affected by a bus

stopping, they will not experience the effects due to that stop. Application to multiple

approach intersections is possible by applying the evaluation method to only the approach

in question. If other approaches are present, they are assumed to have negligible effect

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green or in the red indication of the study approach and do not depart until past the start

of the next green phase.

Instead of field verification the transit capable modeling software CORSIM was

used to verify the analytical equations presented. This software is widely accepted and

has been proven effective in simulating similar networks as required in this study

according to other researchers such as Jones et. al (6), Wang and Prevedouros (7), and

Luh (8). The simulated intersection in this study was kept completely saturated at all

times in order to measure the effects from the bus stops. A total of 288 far-side and 192

side street CORSIM runs were made with various alternatives to attempt to capture the

effects of a bus stop under a variety of circumstances.

Project Objectives

This research project proposes to estimate the impact of bus stops on the capacity

of a nearby, signalized intersection. It presents a new method of analyzing the effects of

bus stops, based upon bus stop characteristics and locations, and specific defined time

periods within the cycles green time. This new method is based on series of analytical

equations that can be used to predict the saturation flow rate at nearby signalized

intersections due to the effects of bus stops. The presented models were compared to

CORSIM software simulations of a simple saturated roadway network with a single

travel lane, a single bus stop, and a single bus route. The effect on saturation was

performed by simulating operation for an “ideal network” with no bus stops, and

adjusting the calculated “ideal” saturation flow rate according to the analytical equations

to develop “predicted” saturation flow rate values. Simulations were also performed on a

network with bus stops to obtain the “simulated” saturation flow rates values. The

“predicted” and “simulated” saturation values were then compared and subjected to a

sensitivity analysis. Based on the data presented, conclusions were drawn about the

effectiveness of the equations to properly predict the intersection effects. Conclusions

were also presented to determine whether the new analytical equation method could

substitute for the current method presented in the HCM 2000. Recommendations for

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Thesis Outline

This research project began as a continuation of research carried out by Daniel

Holt in 2004 (5). In Chapter 2, the literature review is presented, establishing the current

status of the topic with regards to previous work. It reveals gaps in current data and

challenges the current accepted practices, presenting areas of focus for this study. Other

research is also presented focusing on the use of CORSIM with regards to similar

research topics. These other sources defend the choice of this paper to use CORSIM for

its modeling purposes.

In Chapter 3, the author discusses the methodology for the research and presents

in detail the steps used to perform the analysis. The chapter shows the derivations leading

up to the equations used and how those equations were used to calculated saturation flow

rates. It also describes the simulation setup and how it was used to compare with the

equation predictions. The methods for testing the validity of the analytical equations are

also described.

Chapter 4 reveals the results of the analysis for each of the scenarios studied. It

first presents the initial equation results and then discusses how and why they were

calibrated. It then reveals the results of the calibrated equation analysis and discusses

their importance. Finally, a sensitivity analysis is performed and the equations behavior

under a variety of circumstances is examined. The behavior of each bus stop analytical

equation is examined, as well as the CORSIM model it was compared against. The

sensitivity analysis results were also discussed with regards to transit managers and how

the results could be used to locate bus stops.

In Chapter 5, the conclusions from this study are presented. The results are

interpreted with regards to the original intended purposes of the study. A summarization

of the results of the data analysis is given and determination is made to whether or not the

presented methodology is more accurate than current methods.

Chapter 6 discusses recommendations regarding the research conclusions. The

author discusses the effectiveness of the research and its impact on the current

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CHAPTER 2 - LITERATURE REVIEW

This research project aims to determine the likely effects, in terms of saturation

flow rate, that far-side and side-street bus stops have on adjacent signalized intersections.

Before any new analysis was performed, however, a literature review was performed to

establish and identify any previous or current research that relates either directly or

indirectly to this topic. Any literature identified related to the effects of bus stops at

signalized intersections was analyzed for any questions not addressed or any missing

information concerning the topic. Information questioned or found to be lacking was

incorporated into areas to be addressed in the scope and research of this paper.

Current Literature

The Highway Capacity Manual 2000 (HCM) is the nation’s current leading

authority on capacities and levels-of-service for most transportation facilities (2). It can

be used to estimate operational characteristics of signalized intersections with a variety of

geometric, traffic, and signalization conditions.

Specifically, in relation to this research, the HCM can estimate capacity with

regards to bus stops nearby to an intersection. It estimates capacity based on the

saturation flow rate defined as “the flow in vehicles per hour that can be accommodated

by the lane group assuming that the green phase were displayed 100 percent of the time”

(2). It assumes that no lost time, start-up reaction delays, or acceleration headway delays

are experienced and measures saturation flow rate in terms of

passenger-cars-per-hour-per-lane (pcphpl).

Chapter 16 of the HCM deals specifically with signalized intersections and

presents the saturation flow rate estimation equation as:

Rpb Lpb RT LT LU a bb p g HV w

o N f f f f f f f f f f f

s

s= ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ (1)

where,

S = saturation flow rate for subject lane group (pcphpl)

S0 = base saturation flow rate per lane (pcphpl)

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Fw = adjustment for lane width

FHV = adjustment for heavy vehicles in traffic stream

Fg = adjustment for approach grade

Fp= adjustment factor for existence of parking lane or parking activity

Fbb = adjustment for blocking effect of local buses that stop within

intersection area

Fa = adjustment factor for area type

Flu = adjustment factor for area lane utilization

Flt = adjustment factor for left turns in lane group

Frt = adjustment factor for right-turns in lane group3

Flt = adjustment factor for left turns in lane group

Flpb = pedestrian adjustment for left turn movements

Frpb = pedestrian-bicycle adjustment for right-turn movements

The typical accepted value of the base saturation flow rate is 1900 pcphpl. The

HCM equation uses the base saturation flow rate value and adjusts it upwards or

downward according to relevant intersection factors listed in equation 1.

Of the twelve adjustment factors, Fbb, the bus blockage factor, is the only one that

attempts to account for bus transit operations. It is limited to buses stopping to drop-off or

stopping to pick-up passengers at curb-side bus stops within 250 feet of the intersection

stop line. It covers both near-side and far-side bus stops for up to 250 buses per hour

stopping.The equation for Fbb is presented in HCM Table 16-7 as:

N N N

F

b

bb

3600 4 .

14 ⋅

= (2)

where, Nb is the number of buses stopping per hour and N is as defined above.

The equation relies very heavily on the value of 14.4 embedded within it. This

assumes an average bus blockage time plus acceleration-deceleration time of 14.4

seconds per bus during the green indication for the approach segment. This bus blockage

time can be defined as the amount of time a bus blocks the travel lane from discharging

past the stop bar at the usual saturation flow rate, while picking up or unloading

(16)

reducing the capacity of the lane blocked to zero. From this, we can see that capacity

reduction is directly correlated to blockage time.

A portion of the bus blockage time is designated as the bus dwell time, defined as

the “amount of time required to serve passengers at the busiest doors plus the time

required to open and close the doors” (2). The dwell time could be controlled by boarding

demand, passenger alighting demand, or total interchanging passenger demand. The

HCM recommends using a field observed value of dwell time, but, in its absence, Table

27-14 of Chapter 27 gives suggested dwell times ranging from 15 seconds to 60 seconds,

based on the bus stop location and type. In addition to dwell times, Chapter 27 of the

HCM also recommends a typical value of bus deceleration time of 5 seconds and

acceleration time of 5 seconds (2).

If the 10 seconds of combined deceleration and acceleration time were removed

from the typical 14.4 seconds suggested in Equation 16-4, only 4.4 seconds of passenger

unloading and loading time during the green indication at the bus stop would be left. This

value is far below the Chapter 27 recommended minimum value of 15 seconds, and when

compared to the suggested value of 2 to 5 seconds required for either door opening or

closing, it seems like an unreasonably small time available to serve passengers at a bus

stop.

If we compare the use of 14.4 seconds of bus blockage time in HCM Equation

16-4 to the recommended 15 seconds of dwell time and the 10 seconds of deceleration

and acceleration time recommended in Chapter 27 when calculating Fbb, we again find

discrepancy within the HCM. By holding the number of lanes constant, using 14.4

seconds as the bus blockage time, and increasing the number of buses stopping per hour

from 0 to 60, the Fbb factor decreases from 1 to a 0.76. When 25 seconds (dwell plus

deceleration/acceleration time) is used for the bus blockage factor under the same

circumstances using the same values for buses stopping per hour, the Fbb factor decreases

from 1 to a 0.58. If both of these values were applied to a base saturation flow rate, the

difference between them would be significant. Clearly the difference between a 0.76 and

(17)

This research questions the use of a constant value of 14.4 seconds of bus

blockage time recommended and will see whether it is appropriate for use in analyzing

signalized intersections with adjacent bus stops.

Related Research Topics

In Rodriquez-Seda’s and Benekohal’s study of delay-based passenger car

equivalents for urban transit buses, they also noticed that sufficient data did not exist

concerning the impacts of buses on the traffic stream (3). They found that the HCM’s bus

blockage factor, Fbb, underestimated delay per vehicle and therefore also underestimated

the effects of buses stopping. In addition, they suggested the current suggested HCM

passenger car equivalent value for buses of 2 also underestimated the effects of buses

stopping. Their research suggested an alternative method to estimate the delay caused by

stopped transit buses using a delay-based-passenger car equivalent (D-PCE) value.

They noticed that although the value of Fbb takes into account the impacts of

buses on the traffic stream, it does not account for all the factors contributing to its effect

on the stream. They suggested taking into account bus position within the queue, bus

arrival time within the cycle, and the additional delay experienced by vehicles due to

vehicles changing lanes to avoid the bus stopping. They also discussed the fact that

although the HCM recognizes near-side and far-side bus stops, it does not distinguish

between them within the Fbb equation. Their research was aimed at near-side bus stops

and presented a new method to calculate their effects.

To account for bus position in the queue and the time in which a bus arrives

within a cycle, the cycle itself was broken down into five distinct time periods or cases:

¾ Case 1: G1 – G1. Bus arrives, serves passengers, and departs during the same

green phase.

¾ Case 2: R1 – G2. Bus arrives during red, but when light turns green, the bus is

serving passengers. Then the bus consumes the first part of the green time in the

following cycle.

¾ Case 3: R1 – R1. Bus arrives and serves passengers during red, and departs as light

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¾ Case 4: G1 – G2. Bus arrives during green but the light turns red while the bus is

serving passengers causing a cycle failure. The bus has to wait for the next green

to go through the intersection

¾ Case 5: R1 – R2. Bus arrives during red but is at back of the queue, thus the bus

has to wait until the light turns green to move up in queue to reach the bus stop

and to serve passengers. It might stay until the beginning of the next green cycle

to go through the intersections. The bus causes a cycle failure.

They developed an equation that takes into account all bus arrival/departure cases

and all bus positions within a vehicle queue. The following equation was presented as a

method of calculating delay-based passenger car equivalence (D-PCE) at near-side bus

stops:

∑∑∑

= −

⎟⎟ ⎠ ⎞ ⎜⎜

⎛ ⋅ ⋅ ⋅

+ =

z

s L

x N

n

C n

s x n B n x b

s

d

P P P d PCE

D

1

0 ,

1 (3)

where,

d-B = total additional bus delay experienced by a queue of N vehicles, d-C = average delay for a car in all passenger car queue of N cars, Pn = probability of bus in position x,

Px = probability of n vehicles queued behind the bus,

Ps = probability of bus arrival/departure case s,

N = last vehicle in queue created by the bus,

L = maximum number of vehicles in a queue, and

n = total number of vehicles behind bus.

To produce the D-PCE value suggested by the model, field data were collected

from near-side curbside bus stops in downtown Chicago. The field data showed that on

average 24 buses per hour stopped to load/unload passengers and that the average bus

blocking time while stopped was 14.6 seconds. When these data were input into the

model for each arrival and departure case, an overall D-PCE value of 10.2 vehicles per

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traffic stream has the same effect of an additional 10 cars being present in the same traffic

stream.

When they compared the D-PCE value produced by the model to that produced

by the HCM and then calculated average delay per vehicle at the intersection as a result,

they found that on average the HCM underestimates the delay per vehicle at signalized

intersections due to buses. Values produced by the HCM in this comparison ranged from

a 53% underestimation to a 2% underestimation of delays.

Their research concluded that the Fbb equation presented in the HCM

underestimates the effect of stopping buses. They claimed that their method for

predicting delay-based passenger car equivalents is a more accurate method when

comparing transit buses that stop at nearside bus stops.

The concept of delay resulting from a bus stop upstream (near-side) from a

signalized intersection was also examined by Wong et. al. (4). They suggested that the

HCM method of reducing the saturation flow rate and the Hong Kong Transport Planning

and Design Manual method of using passenger car equivalents may not be able to model

the delay produced by the near-side bus stops accurately.

To account for this they suggested a simulation based approach that used factors

such as distance from bus stop to the traffic signal, the frequency of buses, the traffic

volume, the bus dwell times, and the signal settings. They suggested the following

formula to account for the delay on a single lane approach:

5 4 3 2 1

0 2

2

) 1 ( ) 1 ( 2 ) 1

( 2

) 1

( α α α α α α

λ λ

c g q

L x

q x x

q x x

c d

b b

s s

s

⋅ ⋅ Ω ⋅ ⋅ ⋅ + − + − + ⋅ −

= (4)

where,

c = cycle length,

λ = g/c, effective green portion of a cycle,

q = flow rate of traffic (veh/sec),

xs = q/λ, degree of saturation at the signal,

xb = q/[(1-Ω)+s], degree of saturation at the bus stop,

L = distance between bus stop and stop line (meters),

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O = average dwell time (sec/vehicle),

Ω = f*O , proportion of time the bus stop is blocked,

g = effective green time (sec), and

αi = unknowncoefficients to be calibrated from simulation

To calibrate the formula simulations were made using the MODSIM simulation

language. A total of 150 runs were simulated varying the parameters L, q, f, O, g and c. A

multivariate regression analysis was then performed to calculate the unknown

coefficients in the model. Putting the coefficients back into the equation transformed the

model into:

53 . 09 .

57 . 27 . 1 07 . 2

2

5 . 106 ) 1 ( ) 1 ( 2 ) 1

( 2

) 1 (

g L

c q

x q

x x

q x x

c d

b b

s s

s

⋅ Ω ⋅ +

− + − + ⋅ −

− =

λ λ

(5)

To validate the new model a total of 16 data sets were observed in the field in

Hong Kong. The observed data were compared with the simulated data and were plotted

against one another on a graph. The two sets of values had an apparent linear relationship

and were therefore considered to have good agreement between them.

Their research concluded that the new model suggested is adequate for use

modeling the delay experienced from a near-side bus stop on a single lane approach.

Koshy and Arasan researched the influence of bus stops on the flow

characteristics of mixed traffic (9). Their study showed that a microscopic simulation

model was appropriate for modeling the effects of bus stops of a typical heterogeneous

traffic stream.

Their research claimed that although several studies researching the impact of

buses on homogenous traffic flow have been presented, none have been made for

heterogeneous traffic flow. In response to this, they developed a model called

HETERO-SIM to simulate the vehicular speed, acceleration, deceleration, and passing of vehicles in

a traffic stream near a bus stop. They used this model to analyze curbside bus stops, bus

bays, and bus bulbs. To insure a heterogeneous flow, they provided the model with

inputs such as traffic volume, traffic composition, dimensions of vehicles, vehicle

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Field data from Chennai City, India were collected for use in validating the

model. Values of speed, volume, traffic composition, and dwell time were recorded for a

period of one hour. When the average speeds were compared between the observed and

simulated values, the data were found to be satisfactorily similar with minimal error.

Thus it was assumed that the model accurately predicted traffic effects due to bus stops.

By varying the values of dwell time, flow rate, and type of bus stop, the model

was used to predict the resulting impacts on the traffic stream. The results indicate that as

expected, bus bay stops experience less effect on average vehicle speeds as a result of

increasing traffic flow volume than curbside bus stops. Generally it was found that as

flows rates increase from 0 to 2,400 vehicles per hour, average vehicle speeds decrease

about 25%.

Their research concluded that a microscopic simulation model could be used to

replicate the flow of a heterogeneous traffic stream of an urban road affected by curbside

bus stops, bus bays, and bus bulbs.

A comparison study of three micro-simulation packages was performed by Jones

et. al (6). This study compared the COMSIM, SimTraffic, and AIMSUN packages to

determine their strengths and their weaknesses regarding one another.

Each software package was evaluated using three case studies in Birmingham

Alabama. Each of the case studies represented a different corridor type; interstate,

signalized principal arterial, and urban collector. Data such as volumes, signal control,

geometry, and speeds were collected from each of the case study locations.

Each of the software packages was assessed according to hardware/software

requirements, difficulty/ease of coding, data requirements, and relevance/accuracy of

resulting performance measures.

This study concluded that each of the models can provide reasonable traffic

simulation results although they vary in their capabilities and the amount of setup

required. The specific conclusion with regards to CORSIM was that its ability to model

complex situations makes it suitable for modeling complex urban networks. It was also

found capable of modeling the impacts of transit, parking, and traffic incidents. Some of

(22)

the need for extensive calibration and validation of the network. Another limitation was

that its traffic assignment capabilities were found to be limited to single network types,

and do not function with a combination of surface street and freeway networks. This was

felt a serious limitation if regional models were to be analyzed on CORSIM.

Wang and Prevedouros compared the simulation programs INTEGRATION,

TSIS/CORSIM, and WATSim with regards to analysis of mixed arterial and freeway

networks (7).

They compared the software packages using three case studies in Honolulu,

Hawaii. The three case studies included a congested on-ramp merge with an upstream

signal, a freeway divergence point, and a freeway weaving section with a signalized

intersection at a nearby off-ramp. For each of the cases traffic volumes, link speeds,

signal control, and corridor geometry data were collected from both video and field

collection.

Each software package was evaluated according to the resulting measures of

effectiveness (MOEs) for each case study. The study found that all of the models were

able to simulate all MOEs effectively on freeway segments, on-ramps/off-ramps, and

intersection links. Only CORSIM and WATSim were found to be able to replicate field

observations on weaving segments.

When studying the case of an on-ramp merge with an upstream signal they found

that CORSIM required an unusually large lane capacity, 3,100 vphpl, to produce outputs

similar to field collected data.

When analyzing the case of the freeway divergence point they found that the

distance needed to implement a mandatory lane change parameter has a significant

impact on freeway diverging sections. For the networks studied, the default distance to

implement a mandatory lane change for CORSIM was too short.

Analysis of the freeway weaving section with a signalized intersection at a nearby

off-ramp case study showed that CORSIM was able to satisfactorily simulate the

pre-timed signal operation. The study also found that CORSIM speeds tended to be slightly

(23)

The study concluded that, overall, all of the study software produced satisfactory

and comparable MOEs for most of the network links studied. They also concluded that

CORSIM has the most realistic lane-changing behavior of the three models.

Luh researched a case study in near Pensacola, Florida with regards to simulation

of roadway and traffic operations using CORSIM (8). His goal was to compare the MOEs

produced by the HCS software to MOEs produced by CORSIM.

The first case study used in the analysis was along an interstate and involved two

closely spaced interchanges and an adjacent surface street with traffic signals. A

comparison of HCS and CORSIM MOEs showed that the most of the levels-of-service

(LOS) were similar for the freeway segments except for a few locations. Luh found that

the locations where the LOS differed were directly impacted by congestion at locations

either upstream or downstream of the study location. Because the HCS software analyzes

locations individually, congestion nearby has no affect unlike CORSIM, which considers

multiple intersections at one time.

Luh concluded that CORSIM was an “excellent tool” for traffic operational

analysis, especially when considering traffic operations at an intersection that is under the

influence of an adjacent intersection.

Previous Research

This report is a continuation of research started by Holt in 2004 (5). In his

research, he suggested that the current procedure for calculating saturation flow rate at a

signalized intersection due to the effects of bus stops was inadequate. He argued that the

HCM’s (2) method for calculating the bus blockage factor, Fbb, contained discrepancies

with regards to suggested values and that a new method should be developed.

Holt’s work distinguished between bus stops according to their location on the

approach to an intersection. He identified two bus stop locations, near-side bus stops and

far-side bus stops. Figure 1 illustrates the difference between near-side and far-side bus

(24)

Direction of Traffic Flow

Near-Side Bus Stop

Far-Side Bus Stop

Figure 1. Diagram of Near-Side and Far-Side Bus Stops

His research presented a set of analytical equations, based on the bus stop

location, to be used instead of the traditional calculation method using Fbb to calculate

saturation flow rate adjustment factors. He simulated a CORSIM network with a two-lane

intersection approach with a curbside bus stop. In his analysis one of his network lanes

contained buses stopping and the other lane contained no buses stopping. By extracting

data from the lane with no buses stopping and applying it to the equations presented he

predicted the saturation flow rate and compared that with data obtained from the lane

with bus stops.

His research concluded that the proportion of right-turning vehicles, the distance

of the bus stop from the intersection, and the number of stopping buses had a direct effect

on the saturation flow rate. He suggested that new methods should be used to calculate

the effects of bus stops and that those methods should take into consideration the location

of the bus stop.

Recognizing the importance of Holt’s study and the methods his study contained,

this author decided to continue Holt’s research with a few modifications made to the

research methods. This author felt that by making changes to the analysis a stronger case

(25)

made was to utilize a one-way approach segment with only one travel lane. By using this

one-lane approach setup, CORSIM will not be able to allow vehicles to change lanes and

pass the bus while the bus is making a stop. Although Holt did not mention in his study if

vehicle passing did occur, this may have affected the saturation flow rate being measured.

Also, because the approaching lane will be only one lane, a comparison will not be made

between two lanes, one containing buses and one containing no buses; it will instead be

made between two networks, one containing stopping buses and one containing no

stopping buses. With these changes made this research will attempt to determine the

effects of bus stops on the saturation flow rate at signalized intersections.

Literature Review Conclusions

Holt, Rodriquez-Seda and Benekohal, and Wong et. al. all suggested that the

HCM 2000 is inadequate for predicting the effects of bus stops. Therefore, a need exists

to verify what exactly the effects are. In all three of studies, new methods were suggested

taking into account several factors concerning the buses stopping, the surrounding traffic

stream, and nearby traffic signals. This research will also seek to use similar aspects of

nearby traffic and intersection parameters in order to predict bus stop effect.

The suggestion by Rodriquez-Seda and Benekohal that the effects of a bus stop

are a function of when the bus stop arrives and departs in the cycle is interesting. Because

the signal phases control traffic flow through the intersection and buses can stop anytime

within the phases it seems logical to conclude that the time of bus stop within the cycle

plays a large part in the effect of the bus stop. Holt also made a similar assumption.

Koshy and Arasan showed the effects of micro simulation when modeling the effects of

bus stops. They asserted that micro-simulation can accurately predict the effects of bus

stops and the same assertion will be made in this study.

It is also important to note that none of the literature examined the effect of

far-side bus stops or far-side street bus stops. The Rodriquez-Seda and Benekohal and Wong et.

al. studies only examined near-side bus stops, and although the HCM mentions both

near-side and far-side bus stops it does not distinguish between the two in its calculations.

(26)

research. As part of this research, distinctions between the bus stop types will be made

(27)

CHAPTER 3 - METHODOLOGY

As explained in the Literature Review chapter, current research does not

adequately cover the effects of bus stops on the saturation flow rates of signalized

intersections. The current method in the HCM 2000 uses inconsistent dwell times within

separate chapters that seem unreasonable when examined, and does not take into account

bus stop location with respect to the intersection. Subsequent research by Rodriquez-Seda

and Benekohal, Wong et. al., and Holt have all realized this delinquency with the HCM

and have attempted to suggest alternative methods. None of the suggested methods

however, except for Holt’s, based their suggested methods on derived analytical

equations used to calculate a saturation flow rate adjustment factor. This method is based

on Holt’s work and seeks to expand his research.

This section of the research presents a new method for estimating the effects of

bus stops. It seeks to take into account factors such as defined time periods, bus stop type,

green time, flow rate, dwell time, bus stop location, and turning proportion of vehicles

that would influence the overall intersection operation, and use those to calculate more

accurate estimated impacts as a result of the buses. Adjustment factors, based on derived

equations, take into account these factors and are later compared with simulation. This

section aims to explain the methods and procedures used while conducting the research.

Model Formulation

Because the HCM fails to distinguish between bus stop locations, new equations

are presented for both far-side bus stops and side street bus stops. Figure 2 illustrates the

difference between far-side and side-street bus stops with relation to the approaching

(28)

Direction of Traffic Flow

Side-Street Bus Stop

Far-Side Bus Stop

Figure 2. Diagram of Far-Side and Side Street Bus Stops

Far-Side Bus Stop

A far-side bus stop is located downstream of the intersection, with respect to the

approach direction of travel. This type of bus stop requires buses to first pass through the

intersection before making their stop. Because the space available between the stopped

bus and the intersection is often limited, only a certain number of vehicles traveling in the

same lane as the bus can queue behind the bus when it is stopped.

To calculate the effects of this bus stop, several of the analytical equations and

methods in Holt’s research (5) were used, with modifications, to account for the factors

that influence bus stop effect. Some of Holt’s equations are presented below and are

borrowed from his research.

Like the equations presented by Rodriquez-Seda and Benekohal, (3) the equations

for far-side bus stops are based upon when the bus arrives within the cycle. Unlike their

research, Holt only used three time periods within the cycle to analyze bus stop effect,

(29)

account for all occurrences of a bus stopping within a signal cycle and are determined by

when the bus crosses the stop bar. Only one of the three periods occurs within any one

phase. In order to utilize these time periods we assume that traffic can only move through

the intersection in the lane group of interest during a green phase (i.e., right-turns on red

are not allowed from a shared through-right lane).

The three time periods (P1, P2, and P3) correspond to three average vehicular

volumes (V1, V2, and V3) that occur as a result of a bus crossing the stop bar during those

times. The three time periods are described as follows:

¾ P1 – Full Blockage

Time period defined by a bus arriving early enough in a green phase that it will

depart during the same phase and vehicles will be able to be processed through

the stop bar at the end of the phase. Between the time that the storage behind the

bus is filled and the bus departs, a blockage of the stop bar is created that only

ends when the bus and queue behind it moves again.

¾ P2 – Partial Blockage

Time period during the middle of a green phase in which a bus arrives and blocks

the stop bar so that it does not clear in time to process more vehicles before the

green indication ends. Any vehicles queued in the storage area behind the bus will

be released once the bus moves, but this only creates available space during the

red indication. If buses arrive during this time period, vehicles are only blocked

for part of the time between when the bus crossed the stop bar and when the bus

and queue behind it begins to move again.

¾ P3 – No Blockage

Time period at the end of a phase in which the bus arrives late enough that the

storage behind the bus never fills completely. Buses arriving during this time

period depart during the red indication. When buses arrive during this period,

there is never a blockage of approaching vehicles at the intersection.

To calculate the volume V1, during the period P1, a number of factors have to be

considered about the nature of far-side bus stops. First is the maximum number of

(30)

need for adjustment, i.e., for stopping buses. This value is referred to as the ideal number

of vehicles. If an average vehicle headway (h) is assumed, this ideal number of vehicles

can be expressed as the effective green time (g) divided by the headway, or g/h.

This study considered the stop bar on the near side of the intersection approach to

be an integral part in the calculation of the saturation flow rate due to stopping buses. The

time between the bus crossing the stop bar and starting to move again after making a stop

is referred to as the bus blockage time (BT). This blockage time can be broken down into

the time required for the bus to pass the stop bar and come to a complete stop (Ts) plus

the dwell time (Dw) required to make the stop. For the purposes of this study, both Ts and

Dw were taken from the simulation. Figure 3 illustrates the time and space relationship

between the BT and its measurement locations.

Stop Bar

Direction of

Traffic Flow Bus Stop

Begi

n Measuring

BT

(Bus Crosse

s Stop

Ba

r)

Stop Measur

ing

BT

(Bus D

eparts

from Bus Sto

p)

BT

(Bus Blockage Time)

Figure 3. Diagram of Time and Space Relationship of BT

With an understanding of BT we can then determine how the bus blocks traffic

when making a stop. If we assume that there is only a one-lane approach when a bus

stops at a curb side bus stop (or a multilane approach at saturation flow during which lane

changes are not possible), it makes sense that the traffic is blocked behind the bus and

(31)

vehicle headway, the number of vehicles blocked by the bus can be calculated by

dividing the bus blockage time by saturation headway or BT/h.

When the bus is stopped at a far-side stop there are some spaces created behind

the stop, and until those spaces are filled, traffic can continue to flow past the stop bar

through the intersection. The number of vehicles able to fill the spaces behind the bus is

directly affected by the number of vehicles turning at the intersection approach in

question and the number of vehicles on the adjacent side street turning to follow the path

of the bus on the far-side segment. Vehicles turning off of the approaching segment in

question increase the number of vehicles able to transverse the intersection, while

vehicles turning onto the bus departure segment from a side street decrease the number of

vehicles able to transverse the intersection. Considering only the vehicles turning from

the approach of interest, the number of vehicles able to traverse the intersection after the

bus crosses the stop bar can be calculated by dividing the number of storage spaces

between the bus stop and the stop bar (ST) by the proportion of through vehicles in the

traffic stream (1-Prt) or ST/(1-Prt). Figure 4 shows a diagram of the stop bar location and

the storage space for a far-side bus stop with respect to the intersection and bus stop.

Stop Bar Bus Stop

Direction of Traffic Flow Storage Spaces

(ST)

Figure 4. Diagram of Stop Bar Location and Vehicle Storage Spaces For Far-Side

(32)

The equation ST/(1-Prt) is applicable to all proportions of vehicles turning right at

the intersection. The extreme cases for this calculation are when 0% vehicles turn right at

the intersection (Prt=0) and when 100% of vehicles turn right at the intersection (Prt=1).

Examining further, if Prt = 0 and a ST value of 4 is assumed, the number of vehicles able

to traverse the intersection after the bus crosses the stop bar is equal to 4 vehicles. This

means that if 0% of vehicles turn right at the intersection, only 4 vehicles can cross the

stop bar and be stored behind the bus after the bus has crossed the stop bar.

If the other extreme case of 100% of vehicles turning right at the intersection is

examined and again a ST value of 4 is assumed, the number of vehicles able to traverse

the intersection after the bus crosses the stop bar is undefined or infinite. This calculation

result is misleading however because an infinite value of vehicles crossing after the bus is

unreasonable. Recall that the equations intended for use in calculating the number of

vehicles able to traverse an intersection after a bus, taking into consideration the

proportion of right-turning vehicles in the traffic stream. Consider that when Prt=1, there

are no vehicles traveling straight through the intersection besides the bus, and under those

circumstances this calculation is no longer needed, and can be removed from all further

saturation flow rate calculations. This extreme case though is unrealistic in itself because

it is very unlikely that a situation would exist in which only the bus would travel straight

and every other vehicle would turn right at the intersection. For the purposes of this

analysis, this extreme case was not considered because it was very unlikely to occur.

There is also a reduction in vehicles able to cross the intersection due to an

assumed lost time and startup headway delay between buses finishing their stop and

when blocked vehicles start flowing again. The lost time is due to delayed reaction time

occurring when the traffic begins to move again after a bus stop. The startup headway

delay is caused by the time incurred when blocked vehicles regain vehicle headway after

starting to move. Because delays result from both the lost time and the startup headway,

they both effectively reduce the available time for vehicles to cross the intersection. The

number of vehicles unable to traverse the intersection due to this reduction can be

calculated by adding this lost time (L) to the average headway (h) and dividing their sum

(33)

Putting all the factors together results in a calculation for the number of vehicles

processed during time period one as:

h h L P ST h

BT h g V

rt + − − + − =

1

1 (6)

This formula for flow during P1 assumes a constant maximum number of vehicles

able to be processed during the first time period. This constant assumption arises because

vehicles can traverse through the intersection both before the bus blockage time and after

the bus departs from the bus stop. Because all of the blockage time occurs during the

green time, the bus blockage time is always the same. When the blockage time is

constant, the time available to traverse the intersection is also the same, resulting in a

constant number of vehicles able to traverse the intersection.

Period one begins when the effective green time starts and doesn’t end until the

time when a bus moves past the stop bar such that a space is not created until the start of

the red time. Thus P1 can be expressed by the following boundary:

) (

0<P1 <gBTL+h (7)

A numerical example of the end of period one is shown by assuming a green time

of 50 sec, a bus blockage time of 25 seconds, a lost time of 2 seconds, and a vehicle

headway time of 2 seconds. The calculation is as follows:

s P of End

P of End

h L BT g P of End

21 1

) 2 2 ( 25 50 1

) ( 1

=

+ − − =

+ − − =

(8)

This example shows that 21 seconds after the start of the green time, period one

ends. At this point no more vehicles can cross the intersection without being stored

behind the bus and departing after the signal indication turns red.

The previous stated boundary of P1 assumes that g > BT + (L + h). If this

assumption is ever violated a full blockage of the traffic is never created and P1 does not

exist. In this case only P2 and P3 exist (as described below) and should be considered in

the estimation of fbb.

During the second time period (P2), buses stopping for passenger service will not

(34)

vehicles crossing through the intersection to be stored behind the bus until that space is

filled and will not allow any more vehicles to be processed through the intersection.

The number of vehicles allowed to traverse the intersection if the bus crosses the

stop bar in period two can be determined by first calculating the number of vehicles able

to cross the stop bar before the bus crosses the stop bar. This value can be represented by

dividing the time elapsed from the beginning of the green indication to when the bus

crosses the stop bar (BST) by the average vehicle headway (h) or BST/h.

By combining the number of vehicles able to traverse the intersection and fill up

available storage spaces vehicles (described previously as ST/(1-Prt)) with the number of

vehicles able to traverse the intersection before the blockage time (BST/h), we can

estimate the vehicles able to traverse the intersection when the bus crosses the stop bar

during period two as:

) 1 ( 2

rt P ST h

BST V

− +

= (9)

While this equation is the most accurate method to calculate the number of

vehicles processed as a result of buses stopping in this period, this equation is difficult to

use because very rarely is the time that the bus passes the stop bar known or able to be

measured. In its absence, the best estimation of the value V2 comes from taking an

average value of vehicles able to cross the intersection during the first time period, P1, and

the last time period, P3. During P3, as discussed later, a constant number of vehicles is

able to be processed. An alternate equation for calculating V2 is thus shown as:

2 3 1 2

V V

V = + (10)

This equation relies on the assertion that an average numbers of vehicles able to

be processed between the end of P1 and the beginning of P3 accurately reflects the number

of vehicles able to be processed during the second time period. This is true if a linear

relationship exists bridging the number of vehicles processed under P1 conditions to the

number of vehicles allowed in P3 conditions. Using equations 9 this relationship can be

illustrated by varying the time at which the bus crosses the stop bar, while holding all

other values constant and calculating the resulting V2 values. Assuming a headway time

(35)

varying the time that the bus crosses the stop bar (BST) between 10, 20, and 30 seconds

we obtain V2 values of 13, 18, and 23 seconds, respectively. A plot of the BST versus the

number of vehicles processed is shown in Figure 5. This figure shows that the number of

vehicles processed increases at the same rate as BST during period 2, thus verifying that

the relationship between the two is linear.

10 12 14 16 18 20 22 24

5 10 15 20 25 30 35

BST (seconds)

# o

f Veh

icl

es Pro

cessed

Figure 5. Linear Relationship Between BST and the Number of Vehicles Processed

This relationship can further be explained by examining how vehicles are blocked

during this time period. Buses crossing the stop bar at the beginning of period two will

cause the storage spaces available behind the bus to fill quickly, not allowing any more

flow through the intersection. Buses crossing the stop bar at the end of this period will

allow more flow through the intersection before the bus stops and blocks traffic. Because

of this difference in trips that can be processed during certain times of the phase, the

linear relationship is present. Figure 6 is another illustration of the linear relationship

between the vehicles able to be processed and the time when the bus crosses the stop bar

(36)

#

of Proc

ess

ed

Ve

hi

cl

es

Time

V1

End of P2 (g-(St*h)/(1-Pr)) End of P1

(g-BT-(L+h))

V3

End of Green Indication

V1=g/h-BT/h+St/(1-Pr)-(L+H)

V3=(g/h)

Start of Green Indication

Period 2

Figure 6. Diagram of Time Periods and Relationships

P2 begins when the bus passes the stop bar at some time greater than g-BT-(L+h),

and ends when the bus arrives so late in the phase that the storage behind it can no longer

be filled before the light turns red. We assume that all buses depart the bus stop during

the red phase and before the start of the next green phase. This assumption is different

than that made in the Rodriquez-Seda and Benekohal study (3), which assumes that some

of the buses do not depart until after the start of the next green time.

This second period end time can be expressed as the amount of green time (g)

reduced by the amount of time required to fill up all of the storage spaces or St(h)/(1-Prt).

The numerator of this term takes into account that the storage can only be filled as fast as

the average headway (h) allows the vehicles to arrive by multiplying the storage spaces

(St) by the average headway (h). The denominator term (1- Prt) accounts for the number

of vehicles traveling straight through the intersection by subtracting the proportion of

vehicles turning right from the overall flow. Combined, the two terms calculate the time

it takes for the storage behind the bus to fill, taking into account an adjustment for

vehicles turning at the intersection.

With an understanding of the beginning and ending of time P2, the boundaries of

the time period can be expressed by:

(37)

Upper Limit P2:

rt P

h St g

− ⋅ −

1 (12)

If the difference in upper and lower limits of P2 is taken, the formula for calculating the

length of P2 can then be derived as follows:

(

)

rt rt

P h St h L BT P of Length

h L BT g P

h St g P of Length

− ⋅ − + + =

+ − − − −

⋅ − =

1 ) (

) ( 1

2 2

(13)

The P2 limits make two assumptions. The first is that g>(St(h))/(1-Prt) and the

second is that (BT+L+h)>(St(h))/(1-Prt). If either of these assumptions is violated, it

means that the storage behind the bus never completely fills. In other words, vehicles can

always be processed through the intersection and no decrease in saturation flow rate

occurs. In either of these cases, because the storage never fills, no adjustment to

saturation flow rate is needed.

During time period three (P3), the buses arrive at the stop bar and stop so late in

the green phase the available storage spaces behind the bus are never filled before the

signal turns red. Because the spaces behind the bus are never filled, the length of P3 is

directly related to the amount of time needed to fill the storage spaces behind the bus.

The third time period can therefore be calculated as:

rt P

h St P

− ⋅ =

1

3 (14)

During this time period the number of vehicles able to be processed is the same

number that would be processed assuming no bus stop took place and the traffic flow

continued through the intersection uninterrupted. The maximum number of vehicles able

to be processed when the bus crosses the stop bar during this time period is equal to the

ideal flow rate g/h and is shown as:

h g

V3 = (15)

A diagram showing the relationship of the time periods versus the maximum

amount of vehicles able to be processed was shown previously in Figure 6. With all three

time periods defined and equations for calculating length and number of vehicles derived,

(38)

estimated as the weighted average of the three time period lengths and their volumes, and

is defined as:

g P V P V P V

Vt = 1⋅ 1+ 2⋅ 2+ 3⋅ 3

(16)

This equation assumes that the bus arrives at a random time during the phase with

an equal probability of stopping during either one of the time periods.

An example of the equation applied is shown below, which assumes an approach

with a 50-second effective green time, a vehicle headway time of 2 seconds, a startup lost

time of 2 seconds, 50% of the vehicles turning right, a bus blockage time of 25 seconds,

and a storage space behind the bus of 4 vehicles.

(

)

(

)

(

) ( ) (

) ( ) ( ) ( )

[

]

bus stopping a with cycle per vehicles average V V V P h St h g P h St h l BT h g h h l P St h BT h g h l BT g h h l P St h BT h g g V t t t rt rt rt rt t 4 . 21 16 25 13 8 . 21 21 5 . 18 50 1 5 . 1 2 4 2 50 2 2 5 . 1 2 4 25 2 2 2 2 5 . 1 4 2 25 2 50 2 ) 2 2 ( 25 50 2 2 2 5 . 1 4 2 25 2 50 50 1 1 1 2 1 ) ( 1 1 = ⋅ + ⋅ + ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⋅ ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + − ⋅ − ⋅ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + − + − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + − − ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − + − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⋅ ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − ⋅ − + + ⋅ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ + + − + − + + − − ⋅ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + − + − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ =

Side-Street Bus Stops

A side-street bus stop is located on a side-street with respect to the approach

travel lane on an intersection. To access the bus stop from the approach being studied, the

bus must turn right at the intersection. This bus stop allows vehicles to queue behind the

Figure

Figure 1. Diagram of Near-Side and Far-Side Bus Stops
Figure 2. Diagram of Far-Side and Side Street Bus Stops
Figure 5. Linear Relationship Between BST and the Number of Vehicles Processed
Table 1: Far-Side Bus Stop Case Descriptions for Calibration
+7

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