Isolated Traffic Signal Optimization Considering Delay, Energy, … · 2021. 1. 5. · Isolated Traffic Signal Optimization Considering Delay, Energy, and Environmental Impacts Alvaro

Isolated Traffic Signal Optimization Considering Delay, Energy, and

Environmental Impacts

Alvaro Jesus Calle Laguna

Thesis submitted to the faculty of the Virginia Polytechnic Institute and State University in

partial fulfillment of the requirements for the degree of

Master of Science

In

Civil Engineering

Hesham A. Rakha, Chair

Jianhe Du

Bryan J. Katz

November 28th, 2016

Blacksburg, VA

Keywords: Traffic Signal Control Systems; Signal Optimization; Microsimulation; Fuel

Consumption Modeling; Greenhouse Gases Modeling




ABSTRACT

Traffic signal cycle lengths are traditionally optimized to minimize vehicle delay at intersections

using the Webster formulation. This thesis includes two studies that develop new formulations to

compute the optimum cycle length of isolated intersections, considering measures of

effectiveness such as vehicle delay, fuel consumption and tailpipe emissions. Additionally, both

studies validate the Webster model against simulated data. The microscopic simulation software,

INTEGRATION, was used to simulate two-phase and four-phase isolated intersections over a

range of cycle lengths, traffic demand levels, and signal timing lost times. Intersection delay, fuel

consumption levels, and emissions of hydrocarbon (HC), carbon monoxide (CO), oxides of

nitrogen (NOx), and carbon dioxide (CO2) were derived from the simulation software. The cycle

lengths that minimized the various measures of effectiveness were then used to develop the

proposed formulations. The first research effort entailed recalibrating the Webster model to the

simulated data to develop a new delay, fuel consumption, and emissions formulation. However,

an additional intercept was incorporated to the new formulations to enhance the Webster model.

The second research effort entailed updating the proposed model against four study intersections.

To account for the stochastic and random nature of traffic, the simulations were then run with

twenty random seeds per scenario. Both efforts noted its estimated cycle lengths to minimize fuel

consumption and emissions were longer than cycle lengths optimized for vehicle delay only.

Secondly, the simulation results manifested an overestimation in optimum cycle lengths derived

from the Webster model for high vehicle demands.




GENERAL AUDIENCE ABSTRACT

Traffic signal timings are traditionally designed to reduce vehicle congestion at an intersection.

This thesis is based on two studies that develop new formulations to compute the most efficient

signal cycle lengths of intersections, considering vehicle fuel consumption and tailpipe

emissions. Additionally, both studies validate the Webster model, a model that is traditionally

used in traffic signal design. Simulations were run to determine the intersection delay, fuel

consumption levels, and emissions of hydrocarbon (HC), carbon monoxide (CO), oxides of

nitrogen (NOx), and carbon dioxide (CO2) of the study intersections. To account for the random

nature of traffic, each simulation scenario was run twenty different times. The cycle lengths that

minimized the noted simulation outputs were then used to develop the proposed formulations.

The new formulations demonstrated its estimated cycle lengths to minimize fuel consumption

and emissions were longer than cycle lengths designed to minimize vehicle congestion.


from the Webster model for high vehicle traffic.

iv

ACKNOWLEDGEMENTS

To my late father, thank you for loving and caring for me throughout my childhood. He will

always be in my thoughts and prayers as I strive to keep making him proud. To my mother, thank

you for supporting me through every hardship after my father passed away. To my brother, thank

you for your morale support and encouragement in my academics. I would not be the person I

am today without the love and support from my family.

I would like to acknowledge my advisor, Dr. Hesham Rakha, for his mentorship, tolerance, and

most importantly, his friendship while completing my M.S. degree with a thesis in one year. His

continuous support and advices have helped develop my knowledge of the transportation field

and understand the importance of research.

I would like to thank Dr. Jianhe Du for providing oversight on this project as a committee

member. Her support in the literary review, microsimulation modeling, and statistical analysis

were helpful in the completion of my research.

I would also like to thank Dr. Bryan Katz for his friendship and mentorship during my

undergraduate and graduate studies at Virginia Tech. I truly appreciate his care for my academics

and future career.

Lastly, I must thank the MATS University Transportation Center, TranLIVE University Center,

and the Virginia Department of Transportation for funding this research thus allowing me to

obtain my M.S. degree.

v

ATTRIBUTIONS

Dr. Hesham Rakha, committee chair, and Dr. Jianhe Du, committee member, oversaw and

assisted with the data analysis in this research effort. Dr. Rakha provided guidance in the

development of microsimulation scenarios and models to be tested. Dr. Rakha also provided

guidance, edited and served as the corresponding author in the paper submissions to the

Transportation Research Board (TRB) and Transportation Research Part D: Transport and

Environment journal. Dr. Du assisted with the literature review, research results, and in peer

reviewing the writing presented in this thesis.

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TABLE OF CONTENTS

Abstract ........................................................................................................................................... ii

General Audience Abstract ............................................................................................................ iii

Acknowledgements ........................................................................................................................ iv

Attributions ..................................................................................................................................... v

Table of Contents ........................................................................................................................... vi

List of Figures .............................................................................................................................. viii

List of Tables ................................................................................................................................. ix

Chapter 1: Introduction ................................................................................................................... 1

1.1. Background .......................................................................................................................... 1

1.2. Thesis Objectives ................................................................................................................. 1

1.3. Thesis Organization ............................................................................................................. 2

1.4. References ............................................................................................................................ 2

Chapter 2: Optimizing Isolated Signal timing Considering Energy and Environmental Impacts .. 3

2.1. Abstract ................................................................................................................................ 3

2.2. Background of Research ...................................................................................................... 3

2.3. Methodology ........................................................................................................................ 6

2.4. Data Analysis and Results ................................................................................................... 9

2.4.1. Simulation Results ........................................................................................................ 9

2.4.2 Optimum Cycle Length Formulation ........................................................................... 16

2.5. Conclusions ........................................................................................................................ 20

2.6. Acknowledgements ............................................................................................................ 21

2.7. References .......................................................................................................................... 21

Chapter 3: Comprehensive Analysis On Signal Timing Optimization to Reduce Energy And

Environmental Impacts ................................................................................................................. 26

3.1. Abstract .............................................................................................................................. 26

vii

3.2. Introduction ........................................................................................................................ 26

3.3. Background of Research .................................................................................................... 28

3.4. Methodology ...................................................................................................................... 29

3.5. Data Analysis and Results ................................................................................................. 33

3.5.1. Simulation Results ...................................................................................................... 33

3.5.2. Optimum Cycle Length Formulations ........................................................................ 40

3.6. Conclusions ........................................................................................................................ 44

3.7. Acknowledgements ............................................................................................................ 45

3.8. References .......................................................................................................................... 45

Chapter 4: Implementing Multiple Random Seeds In Simulation Runs ....................................... 50

4.1. Data Analysis and Results ................................................................................................. 50

4.1.1 Simulation Results ....................................................................................................... 50

4.1.2. Hypothesis Testing for Simulation Results ................................................................. 57

4.1.3. Optimum Cycle Length Formulations ........................................................................ 60

4.2. References .......................................................................................................................... 64

Chapter 5: Conclusions and Recommendations For Further Research ........................................ 65

5.1. Conclusions ........................................................................................................................ 65

5.2. Recommendations for Future Research ............................................................................. 66

viii

LIST OF FIGURES

Figure 1. INTEGRATION Fuel Consumption Results ................................................................. 10

Figure 2. INTEGRATION Hydrocarbon Results ......................................................................... 11

Figure 3. INTEGRATION Carbon Monoxide Results ................................................................. 12

Figure 4. INTEGRATION Nitrogen Oxides Results .................................................................... 13

Figure 5. INTEGRATION Carbon Dioxide Results ..................................................................... 14

Figure 6. Optimum Cycle Length vs. 1/(1-Y) ............................................................................... 19

Figure 7. Phasing schemes ............................................................................................................ 32

Figure 8. Optimum Cycle Length vs. 1/(1-Y) ............................................................................... 43

Figure 9. Simulation Results of One Random Seed vs. Twenty Random Seeds .......................... 58

Figure 10. Optimum Cycle Length vs. 1/(1-Y) ............................................................................. 63

ix

LIST OF TABLES

Table 1. Simulation Experimental Design ...................................................................................... 8

Table 2. V/S Flow Ratios ................................................................................................................ 8

Table 3. Optimum Cycle Length (s) for Different Measures of Effectiveness (MOEs) ............... 15

Table 4. Regression Results for Model I ...................................................................................... 16

Table 5. Regression Results for Model II ..................................................................................... 18

Table 6. V/S Flow Ratios ............................................................................................................. 31

Table 7. Intersection 1 Optimum Cycle Length Results (s) – Part 1 ........................................... 34

Table 8. Intersection 1 Optimum Cycle Length Results (s) – Part 2 ........................................... 35

Table 9. Intersection 1 Optimum Cycle Length Results (s) – Part 3 ............................................ 36

Table 10. Intersection 2 Optimum Cycle Length Results (s) – Part 1 ......................................... 37



Table 13. Regression Results for Study Intersections .................................................................. 41

Table 14. Intersection 1 Optimum Cycle Length Results (s) – Part 1 .......................................... 51






Table 20. Two-Tail T-Test Results ............................................................................................... 59

Table 21. Regression Results for Study Intersections .................................................................. 61

1

CHAPTER 1: INTRODUCTION

The research presented in this thesis introduces a new signal timing optimization model

considering vehicle fuel consumption and tailpipe emissions at isolated intersections. This

chapter presents an introduction to the research conducted, objectives of the research, and the

layout of how the research is presented in this thesis.

1.1. Background

The traditional goal of optimizing traffic signal cycle length is minimizing vehicle delay and

increasing throughput at an intersection. The traditional method was designed by the British

researcher, Webster, who developed a formulation for the optimum cycle length that

approximates the necessary signal timings to minimize vehicle delay (1), as seen in Equation (1).

This formulation has been used in traffic analysis for years and is still one of the prevailing

methodologies to determine the optimum cycle length.

𝐶!"# = !.!!!!!!!

(1)

where, Copt is the cycle length that minimizes vehicle delay (s); L is the total lost time per cycle

(s); and Y is the sum of the critical group flow ratios based on the phasing scheme.

As transportation systems develop, traffic demand tends to increase. According to the

National Transportation Statistics, the total number of vehicles in the United States reached 260

million in 2014 (2). These vehicles account for nearly 70% of oil consumption in the United

States and have a large impact on the environment. According to the EPA, the transportation

sector in the United States produces approximately 26% of the country’s greenhouse gas (GHG)

emissions, making it the second largest source of emissions next to electricity (3). Thus, there is

an urgent need to make our transportation systems more environmentally sustainable.

1.2. Thesis Objectives

The objectives of this thesis are two-fold. First, it validates the Webster cycle length model

against simulated data from the INTEGRATION software. Second, it develops new formulations

to compute the optimum cycle length considering measures of effectiveness such as delay,

vehicle fuel consumption levels and tailpipe emissions. In developing the formulations, different

methods were considered to enhance the research results and model significance.

2

The application of this model is to produce better traffic signal timings when calibrated to

minimize vehicle delay, fuel consumption, and tailpipe emissions levels. The model can assist

traffic engineers and practitioners in the design of traffic signals.

1.3. Thesis Organization

This thesis is organized as follows. The first chapter presented an introduction to the subject

matter discussed in the following chapters. The second chapter is a paper that was accepted for

presentation at the 95th Annual Meeting of the Transportation Research Board (TRB) entitled,

“Optimizing Isolated Signal Timing Considering Energy and Environmental Impacts.” The third

chapter is a paper that was accepted for presentation at the 96th Annual Meeting of the

Transportation Research Board (TRB) entitled, “Comprehensive Analysis on Signal Timing

Optimization to Reduce Energy and Environmental Impacts.” This paper continues the work

presented in Chapter 2 by analyzing the fuel consumption and emissions yield at four isolated

intersections in Blacksburg and Christiansburg, Virginia, under 20 different vehicle demand

levels. The fourth chapter enhances the results presented in Chapter 3 by implementing 20

random seeds per scenario to the simulation runs and presents the final proposed model. The fifth

chapter presents the conclusions of the thesis and provides recommendations for future research.

1.4. References

1. Webster, F.V., Traffic Signal Settings. Road Research Technical Paper No. 39. 1958,

London: Her Majesty’s Stationery Office.

2. USDOT and BTS, National Transportation Statistics. 2015.

3. EPA, U.S. Greenhouse Gas Inventory Report: 1990-2014. 2014.

3

CHAPTER 2: OPTIMIZING ISOLATED SIGNAL TIMING CONSIDERING

ENERGY AND ENVIRONMENTAL IMPACTS

Based on A. Calle-Laguna, H. Rakha, and J. Du, “Optimizing Isolated Signal Timing

Considering Energy and Environmental Impacts,” Presented at the 95th Annual Meeting of the

Transportation Research Board and MATS UTC Annual Meeting, 2016.

2.1. Abstract

Traffic signal cycle lengths are typically computed to minimize the intersection vehicle delay

using the Webster formula. The objectives of this study are two-fold. First, it validates the

Webster formula against simulated data. Second, it develops new formulations to compute the

optimum cycle length considering other measures of effectiveness including vehicle fuel

consumption levels and tailpipe emissions. The microscopic simulation software,

INTEGRATION, is used to simulate a two-phase intersection over a range of cycle lengths,

traffic demand levels, and signal timing lost times. Intersection delay, fuel consumption levels,

and hydrocarbon (HC), carbon monoxide (CO), oxides of nitrogen (NOx), and carbon dioxide

(CO2) emissions were derived from the simulation model. The cycle lengths that minimized the

various measures of effectiveness were then used to develop the proposed models. The first

effort entailed re-calibrating the Webster model to the simulated data. The second effort entailed

enhancing the Webster model by incorporating an additional intercept term. The proposed model

is demonstrated to produce better traffic signal timings and is calibrated to minimize delay, fuel

consumption and CO2 emission levels. The model estimates produce shorter cycle lengths when

compared to the Webster model and also considers fuel consumption and Green House Gas

(GHG) emissions in the optimization procedure.

2.2. Background of Research

The traditional goal of optimizing traffic signal cycle length usually focuses on minimizing

vehicle delay and increasing throughput at the intersection. The classic method is designed by

the British researcher, Webster, who developed the optimum cycle length formulation that




4

𝐶!"# = !.!!!!!!!

(1)

Here, Copt is the cycle length that minimizes vehicle delay (s); L is the total lost time per

cycle (s); and Y is the sum of the critical group flow ratios based on the phasing scheme.

With the development of the transportation system traffic demand has increased rapidly.

According to the National Transportation Statistics, the total number of vehicles in the United

States reached 250 million in 2012 (2). These vehicles consume a large portion of the oil (nearly

70% of U.S oil consumption) and have a large impact on the environment. According to a report

by the United States Environmental Protection Agency (EPA), the transportation sector in the

United States accounts for approximately 26% of the country’s greenhouse emissions, making it

the second largest source of emissions next to electricity (3).

To alleviate the pollution problem generated by vehicles, numerous research efforts have

been conducted focusing on air pollution generated by the transportation system. These efforts

included the impact of vehicle acceleration/deceleration levels, vehicle characteristics, and route

choice effects on vehicle emissions (4-10). Eisele et al. (11) developed a method to determine the

carbon dioxide emissions and fuel consumption caused by congestion and found that 56 billion

pounds of additional CO2 were produced because of the lower speeds under congested

conditions.

As a key element in the urban transportation network, signal controlled intersections will

inevitably create speed variations and stops for some of the vehicles. At signalized intersections,

the traffic signals force vehicles to slow down, stop, and accelerate. Significant amounts of

emissions are generated due to the variations in vehicle speeds. Consequently, one effective

solution to decrease the emissions generated by vehicles is to optimize their trajectory passing

through an intersection. To accomplish this goal, one can carefully design the signal timings at

intersections such that the percentage of vehicles that can drive through intersections with only

necessarily minimum acceleration/deceleration and stops. Indeed, traffic signal optimization has

been a research topic of numerous previous studies. In previous research that aimed at

optimizing traffic signal timing, different objective functions are adopted. Some tried to

minimize delays, some focused on minimizing the number of vehicle stops and delay, and others

tried to maximize the throughput minus queue length (12-17). However, limited research has

focused on optimizing signal timing specifically for the purpose of minimizing emissions,

though previous research studied emissions related to intersections. Papson et al. used MOVES

5

to study the pollution at intersections and confirmed in their study that emissions are much less

sensitive to congestion than control delay. They concluded that by modifying control strategies at

intersections, vehicle emissions could be significantly reduced (18). Hallmark et al. (19) used a

Portable Emission Measurement System (PEMS) to study emissions along two parallel corridors

that had similar traffic demands and concluded that under congested conditions, roundabouts can

result in higher emissions. Signal controlled intersection and stop sign controlled intersections

both performed better in terms of pollution control. In the studies of Ahn et al. (4), they found

that at the intersection of a high-speed road with a low-speed road, an isolated roundabout does

not reduce vehicle fuel consumption compared to traffic signal or stop controlled intersections.

Pulter et al. (20) compared the results of their agent-based control mechanism at intersections

with a static signal control and concluded that their model can save up to 26% of fuel

consumption. Li et al. (21) created an index to evaluate the performance of signal timing in terms

of traffic quality and emissions and illustrated one example intersection in Nanjing, China. Lv

and Zhang (22) used VISSIM and MOVES jointly to quantify the effects of traffic signal

coordination on emissions and found that increased cycle length will generate longer delay but

not significantly more stops and emissions. Increased platoon ratio will help with the emission

reduction. Madireddy et al. integrated two simulation software, Quadstone Paramics and

VERSIT, to study the benefits of reducing speed limits in a residential area. They found that the

emission can be reduced by 25% if speed limits are lowered from 50 km/h to 30 km/h.

Specifically, the concluded that by using a coordinated signal control scheme, a reduction of

10% in emissions was achievable (23). Ma et al. (24) integrated VISSIM and SUMO to optimize

traffic signals. They found that there are apparent trade-offs between the goal of mobility and

sustainability. Li et al. (25) studied the emissions at isolated intersections and found that the goal

of decreasing delays at intersections and reducing emissions is not simply equivalent. Delays at

intersections will increase if the number of vehicle stops are reduced, which will help to decrease

the pollution at intersections. Liao, one of the few researchers conducting research on

optimization of signal timing plans for the purpose of decreasing emissions and fuel

consumption levels (26), considered fuel-based signal optimization based on a model composed

of a description of the fuel consumption and defined stochastic effects of vehicle movements

which consume excess fuel. She compared her model with the results using Webster’s model as

6

well as TRANSYT 7F and Synchro and found that her approach reduced fuel consumption levels

by up to 40%.

The research discussed above indicated that: 1) Emissions of vehicles might be reduced

with improved traffic control; 2) It is feasible to decrease the fuel consumption and emission

levels through optimizing traffic signal timing plans at intersections; 3) The optimum signal

timing for minimizing delays is not necessarily identical with the timing plans that aim at

minimizing pollutions. Modifying signal timing in terms of pollution control is not only possible

but also effective since no major construction of change of the infrastructure is needed. With the

advanced microscopic traffic simulation software and a better understanding of vehicle

dynamics, it is now possible to develop a formulation that seeks to move vehicles more fuel

efficient by minimizing emissions and fuel consumption levels at signalized intersections.

The goal of this research is to develop an analytic formulation to approximate an

optimum cycle length that minimizes the delay, energy consumption and hydrocarbon (HC),

carbon monoxide (CO), oxides of nitrogen (NOx), and carbon dioxide (CO2) at an isolated

intersection. At the same time, the research compares the traffic signal timing settings that

minimize delays and the optimum traffic timing recommendations made by Webster.

In terms of the paper organization, initially the project background is presented.

Subsequently, the methodology used in the study is described. The results from the simulation

are then analyzed, where the INTEGRATION results are presented. The optimum cycle length is

then investigated and regression models are fit to develop an analytical formulation to calculate

the optimum cycle length for various demand levels and lost times. The final section presents the

conclusions of the study.

2.3. Methodology

The majority of the research discussed in the literature review section integrated two simulation

software, namely: a microscopic traffic simulation software and an emission software (22-24).

They usually used vehicle trajectories generated by the simulation software as inputs to the

emission software. Alternatively, this study used INTEGRATION (27, 28), a microscopic traffic

simulation software that uses the VT-Micro fuel consumption and emission model to estimate

and output the fuel consumption and emission estimates directly without the need to post process

the data. The INTEGRATION software is a microscopic traffic assignment and simulation

software that was developed in the late 1980s and continues to be developed (29-31). It was

7

conceived as an integrated simulation and traffic assignment model and performs traffic

simulations by tracking the movement of individual vehicles every 1/10th of a second. This

allows detailed analysis of lane-changing movements and shock wave propagations. It also

permits considerable flexibility in representing spatial and temporal variations in traffic

conditions. In addition to estimating stops and delays (17, 32), the model can also estimate the

fuel consumed by individual vehicles and the emissions emitted (33, 34). Finally, the model also

estimates the expected number of vehicle crashes using a time-based crash prediction model

(35). The INTEGRATION software uses the Rakha-Pasumarthy-Adjerid (RPA) car-following

model to replicate vehicular longitudinal motion. The RPA model is composed of a steady-state

first-order model (fundamental diagram), collision avoidance constraints, and vehicle

acceleration constraints. The vehicle acceleration and collision avoidance constraints reverts the

model from a first-order to a second-order traffic stream model. This model requires four

parameters for calibration to local driver behavior. The INTEGRATION software incorporates a

variable power model that computes the vehicle’s tractive effort, aerodynamic, rolling, and

grade-resistance forces (36, 37). The INTEGRATION model has not only been validated against

standard traffic flow theory (17, 32, 38, 39), but also has been utilized for the evaluation of large-

scale real-life applications (40-42). The INTEGRATION lane-changing logic was described and

validated against field data in an earlier publication (43). Furthermore, Zhang and Rakha (44)

demonstrated the validity of the INTEGRATION software for estimating the capacity of

weaving sections by comparing to field observed weaving section capacities.

The following assumptions and scenarios were made in conducting the traffic simulations

in INTEGRATION:

• All vehicle movements were assumed to be straight through only to avoid the need to

consider permissive movements;

• Approach speeds were set at 56 km/h (35 mph) because this is typical of arterial road

facilities;

• The base saturation flow rates for all approaches were set at 1800 veh/h/lane;

• The jam density for all approaches was set at 167 veh/km/lane;

• The length of the approach links were assumed to be 1,000 meters so that queues did not

spillback beyond the entrance points;

• The lost time was controlled by varying the interphase times (yellow and all-red).

8

• The traffic demand was generated to be totally random (i.e. the inter-vehicle headways

followed a negative exponential distribution);

• Variability in driver car-following behavior was modeled considering a speed variability

coefficient of variation of 10 percent based on empirical observations (45, 46).

In conducting the analysis a series of traffic simulations were created to model a wide

range of cycle lengths, traffic demand levels, and lost times. Table 1 demonstrates the range of

parameters that were explored in the study resulting in a total of 1,224 simulation runs that were

executed (17×9×8).

Table 1. Simulation Experimental Design Parameters Values

Cycle Length (s) 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180 Total Lost Time (s) 6, 7, 8, 9, 10, 11, 12, 13, 14 Demand (veh/h) 360, 540, 720, 900, 1080, 1260, 1440, 1620

In order to determine how much green time should be allocated to each phase, the green

time was distributed in proportion to the critical phase y-ratios for the critical lane groups (47).

The results of each simulation run were then used to determine the optimum cycle length for all

measures of effectiveness (delay, fuel consumption and vehicle emissions). The following

summarizes the procedure adopted to conduct the analysis:

1. Create the input files and parameters.

a. Load the traffic demands in Table 2 for 1800 seconds and set the simulation time to

3600 seconds to ensure that all vehicles clear the network by the conclusion of the

simulation.

b. Vary the cycle length from 20 to 180 seconds in increments of 10 seconds.

c. Vary the lost time per phase from 3 to 7 seconds at increments of 0.5 seconds.

Table 2. V/S Flow Ratios Demand EB WB NB SB

1 0.1 0.1 0.1 0.1 2 0.2 0.2 0.1 0.1 3 0.2 0.2 0.2 0.2 4 0.3 0.3 0.2 0.2 5 0.3 0.3 0.3 0.3 6 0.4 0.4 0.3 0.3 7 0.6 0.6 0.2 0.2 8 0.7 0.7 0.2 0.2

2. Export the results of each simulation.

9

3. Create the following plots for each demand, with a series for each total lost time:

a. Fuel Consumption (liters) vs. Cycle Length (seconds)

b. HC (grams) vs. Cycle Length (seconds)

c. CO (grams) vs. Cycle Length (seconds)

d. NOx (grams) vs. Cycle Length (seconds)

e. CO2 (grams) vs. Cycle Length (seconds)

4. Identify the cycle length associated with the minimum delay, fuel consumed, HC, CO, NOx,

and CO2 values of each demand level. Identify the optimum cycle length for each total lost

time.

5. Perform a linear regression analysis to re-calibrate the Webster parameters and develop a

new optimum cycle length formulation. Details of the regression analysis will be described

in a later section in the paper.

2.4. Data Analysis and Results

2.4.1. Simulation Results

This section presents the results of the INTEGRATION simulations and the development of the

optimum cycle length equation associated with minimizing delay, fuel consumption, and

emission levels. The variation of cycle lengths with an increase in vehicle demand was presented

for the fuel consumed and tailpipe emissions results of each simulation. Figure 1 to Figure 5

demonstrate the INTEGRATION simulation results. Table 3 lists the corresponding numeric

output of the simulations. One noteworthy observation from the results is that the Webster

optimum cycle lengths is not in accordance with the optimum cycle lengths for minimizing

tailpipe emissions. Typically, the Webster optimum cycle lengths are shorter than the optimum

cycle lengths identified by simulation when the volume is low. The discrepancy decreases when

the demand increases. This difference will be further explored in the next section.

10

Figure 1. INTEGRATION Fuel Consumption Results

(b) 540 veh/h (a) 360 veh/h

(c) 720 veh/h (d) 900 veh/h

(e) 1080 veh/h (f) 1260 veh/h

(g) 1440 veh/h (h) 1620 veh/h

11

Figure 2. INTEGRATION Hydrocarbon Results

(a) 360 veh/h (b) 540 veh/h

(c) 720 veh/h (d) 900 veh/h

(e) 1080 veh/h (f) 1260 veh/h

(g) 1440 veh/h (h) 1620 veh/h

12

Figure 3. INTEGRATION Carbon Monoxide Results

(a) 360 veh/h (b) 540 veh/h

(c) 720 veh/h (d) 900 veh/h

(e) 1080 veh/h (f) 1260 veh/h

(g) 1440 veh/h (h) 1620 veh/h

13

Figure 4. INTEGRATION Nitrogen Oxides Results

(a) 360 veh/h (b) 540 veh/h

(c) 720 veh/h (d) 900 veh/h

(e) 1080 veh/h (f) 1260 veh/h

(g) 1440 veh/h (h) 1620 veh/h

14

Figure 5. INTEGRATION Carbon Dioxide Results

(a) 360 veh/h (b) 540 veh/h

(c) 720 veh/h (d) 900 veh/h

(e) 1080 veh/h (f) 1260 veh/h

(g) 1440 veh/h (h) 1620 veh/h

15

Table 3. Optimum Cycle Length (s) for Different Measures of Effectiveness (MOEs)

Demand (veh/h)

Y W-‐C Delay Fuel CO2 CO HC NOx

360 0.2 18 22 32 32 172 172 172540 0.3 20 22 42 42 162 162 172720 0.4 23 22 52 32 162 162 162900 0.5 28 22 62 42 172 172 1721080 0.6 35 32 62 42 182 182 1821260 0.7 47 32 82 52 182 182 1821440 0.8 70 52 102 72 172 172 1721620 0.9 140 82 132 132 172 172 172360 0.2 19 22 42 32 172 172 172540 0.3 22 22 42 42 172 172 172720 0.4 26 22 52 52 162 162 162900 0.5 31 22 62 42 172 172 1721080 0.6 39 32 62 62 182 182 1821260 0.7 52 42 82 52 182 182 1821440 0.8 78 52 122 122 172 172 1721620 0.9 155 132 132 132 172 172 172360 0.2 21 22 42 42 172 172 172540 0.3 24 22 42 42 172 172 172720 0.4 28 22 62 32 162 162 162900 0.5 34 22 62 32 172 172 1721080 0.6 43 32 62 62 182 182 1821260 0.7 57 32 62 62 182 162 1821440 0.8 85 62 132 62 182 172 1721620 0.9 170 132 132 132 172 172 172360 0.2 23 22 42 42 172 172 172540 0.3 26 22 42 42 182 172 172720 0.4 31 22 52 52 162 162 162900 0.5 37 22 42 32 172 172 1721080 0.6 46 32 62 32 182 182 1821260 0.7 62 32 82 42 182 182 1821440 0.8 93 52 72 62 182 172 1721620 0.9 185 132 132 132 172 172 172360 0.2 25 22 42 42 172 172 172540 0.3 29 22 52 52 182 172 172720 0.4 33 22 62 32 182 162 162900 0.5 40 32 52 42 172 172 1721080 0.6 50 32 62 62 182 182 1821260 0.7 67 32 82 52 182 182 1821440 0.8 100 62 62 62 182 182 1721620 0.9 200 132 132 132 172 172 172360 0.2 27 22 62 62 172 172 172540 0.3 31 22 52 52 182 182 172720 0.4 36 22 52 32 182 182 162900 0.5 43 32 72 42 172 172 1721080 0.6 54 32 62 42 182 182 1821260 0.7 72 32 82 62 182 182 1821440 0.8 108 62 122 122 182 172 1721620 0.9 215 132 132 132 172 172 172360 0.2 29 22 62 62 172 172 172540 0.3 33 32 52 52 182 182 172720 0.4 38 32 52 32 162 162 162900 0.5 46 32 62 42 172 172 1721080 0.6 58 32 62 42 182 182 1821260 0.7 77 42 82 52 182 182 1821440 0.8 115 52 142 62 182 182 1721620 0.9 230 132 132 132 182 182 182360 0.2 31 22 62 42 172 172 172540 0.3 35 32 52 52 182 172 172720 0.4 41 32 42 42 172 172 172900 0.5 49 32 72 42 172 172 1721080 0.6 61 32 62 42 182 182 1821260 0.7 82 42 72 62 182 182 1821440 0.8 123 52 122 72 182 162 1621620 0.9 245 132 132 132 172 172 172360 0.2 33 22 62 52 172 172 172540 0.3 37 32 52 52 172 172 172720 0.4 43 32 42 42 162 162 162900 0.5 52 32 72 42 172 172 1721080 0.6 65 32 72 62 182 182 1821260 0.7 87 42 72 72 182 182 1821440 0.8 130 72 182 82 182 172 1721620 0.9 260 132 182 182 182 182 182

L=12s

L=13s

L=14s

L=6s

L=7s

L=8s

L=9s

L=10s

L=11s

16

2.4.2 Optimum Cycle Length Formulation

The optimum cycle lengths identified in the simulation for each scenario were used to calibrate

the Webster model. As can be seen in Figure 2 through Figure 5 and Table 3, the optimum cycle

length that minimizes the HC, CO, and NOx emissions are very similar to the maximum cycle

length. Consequently, cycle lengths should be maximized if the objective is to minimize HC, CO

and NOx emissions. To identify the optimum cycle length to minimize vehicle delays, fuel

consumption and CO2 emission levels three sets of model parameters are calibrated, respectively.

Two model formulations are considered. The first regression model (format I) sought to

develop a formulation that would be comparable with the Webster formulation and the 2010

HCM recommendation. Equation (1) is re-written in a more general form, as shown in Equation

(2) and then re-cast in Equation (3).

𝐶!"# = ∝!! ! !!!

(2)

𝐶!"# 1− 𝑌 = 𝛼𝐿 + 𝛽 (3)

Here Copt is the optimum cycle length in seconds; ∝ & 𝛽 are the model coefficients; L is

the total lost time per cycle in seconds; and Y is the sum of flow ratios for all critical lane groups.

Rearranging Equation (2), Equation (3) is cast where the lost time (L) is the independent

variable and the Copt×(1-Y) is the dependent variable. A linear regression analysis was conducted

on the simulated data using the formulation of Equation (3). Table 4 presents the estimated

model coefficients, the associated T-values, and the coefficient of determination (R2) for each

model. As can be seen from Table 4 that coefficient of determination for all three models is

extremely low, indicating a weak model prediction power. Equations (4) through (6) present the

developed models that minimize vehicle delay, fuel consumption and CO2 emissions.

Table 4. Regression Results for Model I MOE R2 Estimated 𝜶 T-Value for 𝜶 (Pr>|t|) Estimated 𝜷 T-Value for 𝜷 (Pr>|t|) Delay 0.1407 0.46 3.39 (<0.05) 9.5 6.80 (<0.05) Fuel 0.0487 0.76 1.89 (0.0624) 20 4.87 (<0.05) CO2 0.0236 0.53 1.3 (0.1977) 17 4.07 (<0.05)

𝐶!"#,!"#$% = !.!"!!!.!

!!! (4)

𝐶!"#,!"#$ = !"!!!

(5)

𝐶!"#,!"! = !"!!!

(6)

17

In an attempt to enhance the model, another model was developed by reformatting and

casting the model, as shown in Equation (7) (format II). In this model, there are two explanatory

variables, namely: L/(1-Y) and 1/(1-Y). In addition, an intercept term 𝛾 is introduced in the

equation. The 𝛾 parameter can be viewed as a minimum optimum cycle length. Table 5 lists

the estimated model coefficients, the associated T-value, and the coefficient of determination for

each model. As can be seen, the model explanatory power increases significantly with

coefficients of determination in excess of 0.5. Specifically, the optimum delay model has a

coefficient of determination of 0.95 with an intercept term that is very small (3.8 s),

demonstrating that the minimum cycle length is rather small. The optimum coefficients are 0.33

and 8.56, respectively, which are comparable to the Webster coefficients of 1.5 and 5.0,

respectively.

The intercept term in the proposed model is a significant addition because it represents a

minimum cycle length that is not included in the Webster optimum cycle length formulation. In

order to compare the results from Webster formulation (Equation (1)) with the results from the

proposed model (Equation (8)), one of the independent variables (1-Y)-1 was plotted against the

optimum cycle length, as illustrated in Figure 6. The figure shows the proposed model versus the

Webster model overlaid on the simulation results. As can be seen, when the demand is low, the

two models produce comparable optimum cycle length estimates. However, the difference

between the recommended optimum cycle lengths in the two methods increases as the traffic

demand increases. The results are compatible with a previous study by Chen et al., who sought to

improve Webster formulation using Synchro 5. They compared the optimum cycle length from

the Webster formation with the optimum cycle length generated by Synchro 5 under situations

when the traffic demand at an intersection is high and concluded that cycle lengths generated by

Webster formulation were approximately 40 seconds longer (48). In our case, this difference can

be as large as 150 seconds as the degree of saturation approaches 1.0.

In the case of the fuel consumption and CO2 emission optimum cycle lengths, the

intercept is much higher, 40s and 24s, respectively. The results demonstrate that the model

coefficients are significantly different depending on the measure of effectiveness that is being

minimized (delay, fuel consumption or CO2 emissions).

𝐶!"# = !!!!!

+ !!!!

+ 𝛾 (7)

18

Table 5. Regression Results for Model II MOE R2 Estimated

𝜶 T-Value 𝜶

(Pr>|t|) Estimated

𝜷 T-Value 𝜷

(Pr>|t|) Estimated

𝜸 T-Value 𝜸

(Pr>|t|) Delay 0.95 0.33 4.33 (<0.05) 8.56 10.38 (<0.05) 3.8 2.76 (<0.05) Fuel 0.54 0.82 3.27 (<0.05) 0.49 0.18 (0.8586) 40 8.83 (<0.05) CO2 0.85 0.27 1.97 (0.05) 8.45 5.65 (<0.05) 24 9.66 (<0.05)

𝐶!"#,!"#$% = !.!!!!!.!"

!!!+ 3.8 (8)

𝐶!"#,!"#$ = !.!"#!!!

+ 40 (9)

𝐶!"#,!"! = !.!"!!!.!"

!!!+ 24 (10)

19

Figure 6. Optimum Cycle Length vs. 1/(1-Y)

Total Lost Time – 8 sec Total Lost Time – 9 sec

Total Lost Time – 6 sec





20

2.5. Conclusions

The paper developed analytical models to compute the optimum cycle length that minimizes the

intersection delay, fuel consumption levels and GHG emissions using data generated using the

INTEGRATION microscopic traffic simulation software considering different demand levels,

cycle lengths, and lost times. Optimum cycle lengths were identified for each scenario for the

purpose of minimizing vehicle delay, fuel consumption levels, and emissions.

For minimizing HC, CO, and NOx emissions, longer cycle lengths are consistently

favored regardless of the demand levels and lost times. To identify the optimum cycle lengths to

minimize vehicle delays, the fuel consumption levels, and CO2 emissions two sets of regression

models were fit to the data. The first set of models entailed recalibrating the Webster optimum

cycle length formulation. Although the results from this model were comparable with the

Webster formulation, the regression results produced poor prediction power. Consequently, a

second set of models were proposed considering two explanatory variables, L(1-Y)-1 and (1-Y)-1,

and an intercept term, γ, in the formulation. The results demonstrated that the second set of

models provided a very strong explanatory power. This proposed model showed that:

1. Calibration of the Webster formulation to the INTEGRATION delay estimates

produced similar model parameters:

a. The minimum cycle length term is modest (3.8 seconds);

b. The model parameters, 0.33 and 8.56, are comparable with the parameters

used in the Webster formulation, 1.50 and 5.00.

2. At lower demand levels, the modified proposed model generates a similar optimum

cycle length to the Webster formulation. However, as the demand increases, the

discrepancy increases significantly with the proposed model recommending shorter

cycle lengths when compared with the Webster method.

3. The cycle lengths for minimizing fuel consumption and CO2 emissions are longer

than the optimum cycle length to minimize vehicle delays.

4. A minimum cycle length threshold is required for the computation of the optimum

fuel consumption and CO2 cycle lengths.

The results from this study demonstrate that the optimum cycle length for delay is

significantly different from that for minimizing vehicle fuel consumption and emission levels.

The design of the traffic signal needs to be customized for different design purposes. If the goal

21

is to minimize fuel consumption and CO2 emission levels, a minimum cycle length threshold is

required. If the goal is to minimize vehicle delay, the optimum cycle length calculated using the

Webster method will typically overestimate the optimum cycle length.

This investigation was limited to using a two-phase signalized intersection and only eight

vehicle demand levels. Further studies should be conducted on three, four, and multiphase

simulations, along with different vehicle volumes, to determine if a more general formulation

exits.

2.6. Acknowledgements

This research effort was jointly sponsored by the MATS University Transportation Center, the

TranLIVE Transportation Center, and the Virginia Department of Transportation (VDOT).

2.7. References





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25

43. Rakha, H. and Y.H. Zhang, INTEGRATION 2.30 framework for modeling lane-changing

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weaving, merge, and diverge sections. Journal of transportation engineering, 2006.

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26

CHAPTER 3: COMPREHENSIVE ANALYSIS ON SIGNAL TIMING

OPTIMIZATION TO REDUCE ENERGY AND ENVIRONMENTAL

IMPACTS

Based on A. Calle-Laguna, H. Rakha, J. Du, “Comprehensive Analysis on Signal Timing

Optimization to Reduce Energy and Environmental Impacts,” approved for presentation at the

96th Annual Meeting of the Transportation Research Board, 2017.

3.1. Abstract

Traffic signal cycle lengths are traditionally optimized to minimize vehicle delay at intersections

using the Webster formulation. This study continues previous work to develop new formulations

to compute the optimum cycle length, considering measures of effectiveness such as vehicle fuel

consumption and tailpipe emissions. Additionally, it validates the Webster model against

simulated data. The microscopic simulation software, INTEGRATION, was used to simulate

two-phase and four-phase isolated intersections over a range of cycle lengths, traffic demand

levels, and signal timing lost times. Intersection delay, fuel consumption levels, and emissions of

hydrocarbon (HC), carbon monoxide (CO), oxides of nitrogen (NOx), and carbon dioxide (CO2)

were derived from the simulation software. The cycle lengths that minimized the various

measures of effectiveness were then used to develop the proposed formulations. The first effort

entailed enhancing the Webster model by incorporating an additional intercept to the new

formulations. The second effort entailed recalibrating the Webster model to the simulated data to

develop an updated delay formulation. The proposed model produced better traffic signal timings

and was calibrated against four study intersections to minimize delay, fuel consumption, and

emission levels. The proposed model considers fuel consumption and greenhouse gas emissions,

and its estimated cycle lengths were longer than cycle lengths optimized for vehicle delay only.


from the Webster model for high vehicle demands.

3.2. Introduction

The traditional goal of optimizing traffic signal cycle length is minimizing vehicle delay and

increasing throughput at an intersection. The traditional method was designed by the British

researcher, Webster, who developed a formulation for the optimum cycle length that


27



𝐶!"# = !.!!!!!!!

(1)

where, Copt is the cycle length that minimizes vehicle delay (s); L is the total lost time per cycle

(s); and Y is the sum of the critical group flow ratios based on the phasing scheme.

As transportation systems develop, traffic demand tends to increase. According to the National

Transportation Statistics, the total number of vehicles in the United States reached 260 million in

2014 (2). These vehicles account for nearly 70% of oil consumption in the United States and

have a large impact on the environment. According to the EPA, the transportation sector in the

United States produces approximately 26% of the country’s greenhouse gas (GHG) emissions,

making it the second largest source of emissions next to electricity (3). Thus, there is an urgent

need to make our transportation systems more environmentally sustainable.

Previous research conducted by the authors (4) recalibrated the Webster model for one

isolated intersection. We developed new formulations to optimize the traffic signal timings to

reduce the intersection’s environmental impact. This paper continues that research by analyzing

the fuel consumption and emission yield at four isolated intersections in Blacksburg and

Christiansburg, Virginia, under 20 different vehicle demand levels. Our goal was to develop

updated analytic formulations to approximate an optimum cycle length that minimizes the delay,

fuel consumption, and total emissions at an isolated intersection. Microsimulation was used to

generate various measures of effectiveness (MOEs), including hydrocarbon (HC), carbon

monoxide (CO), nitrous oxide (NOx), and carbon dioxide (CO2). In addition, we updated the

recalibrated Webster formulation by comparing the traffic signal timing settings that minimize

delays with the optimum traffic timing recommendations made by Webster. The optimum cycle

length is investigated and regression models are fit to develop analytical formulations that

estimate the optimum cycle lengths for various demand levels and lost times.

This paper is organized as follows. The project background is first presented.

Subsequently, the methodology used in the study is described. The results from the simulations

are then analyzed and presented. The final section presents the conclusions of the study.

28

3.3. Background of Research

Numerous research efforts have been conducted focusing on air pollution generated by

transportation systems. These efforts included the impact of vehicle acceleration and deceleration

levels, vehicle characteristics, and route choice on vehicle emissions (5-11). Eisele et al. (12)

developed a method to determine the carbon dioxide emissions and fuel consumption caused by

congestion and found that 56 billion pounds of additional CO2 were produced because of the

lower speeds under congested conditions.

As a key element in the urban transportation network, signal-controlled intersections

inevitably create speed variations and stops for most vehicles. Frey et al. (13) confirmed that the

speed variations and stops cause variability in on-road emissions in an effort that conducted

experiments to evaluate pollution prevention strategies for on-road vehicles. Chen and Yu

furthered this research by analyzing the relationship between instantaneous emissions and fuel

consumption rates and instantaneous speed and acceleration using the VISSIM microsimulation

software (14). Rakha and Ding noted that vehicle fuel consumption rates are sensitive to stops,

especially aggressive acceleration rates after the stops (15). At signalized intersections, traffic

signals force vehicles to slow down, stop, and accelerate. Significant amounts of emissions are

generated due to the variations in vehicle speeds. One effective solution to decrease the

emissions generated by vehicles is to optimize their trajectory passing through an intersection.

To accomplish this goal, one can carefully design the signal timings at intersections so that the

percentage of vehicles that can drive through intersections will do so with minimum acceleration

or deceleration and stops.

Indeed, traffic signal optimization has been a research topic of numerous previous

studies. In previous research that aimed at optimizing traffic signal timing, different objective

functions were considered. Some tried to minimize delays, some focused on minimizing the

number of vehicle stops and delay, and others tried to maximize the throughput minus queue

length (16-21). Moreover, research has been conducted on the relation of emissions to

intersections. Papson et al. used MOVES to study the pollution at intersections and confirmed

that emissions are less sensitive to congestion than control delay. They concluded that by

modifying control strategies at intersections, vehicle emissions could be significantly reduced

(22). Pulter et al. (23) compared the results of their agent-based control mechanism at

intersections with a static signal control and concluded that their model can save up to 26% of

29

fuel consumption. Li et al. (24) created an index to evaluate the performance of signal timing in

terms of traffic quality and emissions and illustrated one study intersection in Nanjing, China. Lv

and Zhang (25) used VISSIM and MOVES to quantify the effects of traffic signal coordination

on emissions and found that increased cycle length will generate longer delay but not

significantly more stops and emissions. Increased platoon ratio will help with emission

reduction. Madireddy et al. (26) concluded that by using a coordinated signal control scheme, a

reduction of 10% in emissions was achievable. Li et al. (27) studied the emissions at isolated

intersections and found that the goals of decreasing delays and reducing emissions at

intersections are not simply equivalent. Delays at intersections will increase if the number of

vehicle stops is reduced, which will help to decrease the pollution at intersections. Liao, one of

the few researchers that investigated optimization of signal timing plans for the purpose of

decreasing emissions and fuel consumption levels (28), considered fuel-based signal

optimization based on a model composed of a description of the fuel consumption and defined

stochastic effects of vehicle movements which consume excess fuel. She compared her model

with the results using Webster’s model as well as TRANSYT 7F and Synchro. Her approach

reduced fuel consumption levels by up to 40%.

The research discussed above indicated the following:

1) Emissions of vehicles might be reduced with improved traffic control.

2) It is feasible to decrease the fuel consumption and emission levels through optimizing traffic

signal timing plans at intersections.

3) The optimum signal timing for minimizing delays is not necessarily identical with the timing

plans that aim at minimizing fuel consumption and emissions.

4) Modifying signal timing in terms of fuel consumption and emissions control is not only

possible but also effective since no major construction or change of the infrastructure is

needed.

3.4. Methodology

The majority of the research discussed in the background section integrated microscopic traffic

simulation software and emission software (23-27). Vehicle trajectories generated by the

simulation software were used as inputs to the emission software. Alternatively, this study used

INTEGRATION (29, 30), a microscopic traffic simulation software that embedded the VT-

Micro fuel consumption and emission model in the traffic simulation to estimate and output the

30

fuel consumption and emission estimates directly without the need to post-process the data.

INTEGRATION is a microscopic traffic assignment and simulation software that was developed

in the late 1980s and continues to be developed (31-33). It was conceived as an integrated

simulation and traffic assignment model and performs traffic simulations by tracking the

movement of individual vehicles every 1/10th of a second. This allows detailed analysis of lane-

changing movements and shock wave propagations. It also permits considerable flexibility in

representing spatial and temporal variations in traffic conditions. In addition to estimating stops

and delays (21, 34), the model can also estimate the fuel consumed by individual vehicles and

the emissions emitted (35, 36). The INTEGRATION software uses the Rakha-Pasumarthy-

Adjerid (RPA) car-following model to replicate vehicular longitudinal motion. The RPA model

is composed of a steady-state first-order model (fundamental diagram), collision avoidance

constraints, and vehicle acceleration constraints. The vehicle acceleration and collision

avoidance constraints revert the model from a first-order to a second-order traffic stream model.

This model requires four parameters for calibration to local driver behavior. INTEGRATION

incorporates a variable power model that computes the vehicle’s tractive effort and aerodynamic,

rolling, and grade-resistance forces (38, 39). The INTEGRATION model has not only been

validated against standard traffic flow theory (21, 34, 40, 41), but also has been utilized for the

evaluation of large-scale real-life applications (42-44).

The following assumptions and scenarios were made in conducting the INTEGRATION

traffic simulations:

• At the study intersections, the vehicle demand distribution consisted of 60% through

traffic, 20% left-turning traffic, and 20% right-turning traffic.

• The base saturation flow rates for all approaches were set at 1,800 vehicles per hour per

lane (vphpl);

• The jam density for all approaches was set at 167 veh/km/lane;

• The length of the approach links was assumed to be 1,000 meters so that queues did not

spill back beyond the entrance points;

• The lost time was controlled by the yellow and all-red timings.

• The traffic demand was generated to be totally random (i.e., the inter-vehicle headways

followed a negative exponential distribution);

31

• Variability in driver car-following behavior was modeled considering a speed variability

coefficient of variation of 10% based on empirical observations (47, 48).

The simulations were created to model the traffic at the following isolated intersections in

Blacksburg and Christiansburg, Virginia:

1) North Main Street and Roanoke Street

2) Prices Fork Road and Stanger Street/Toms Creek Road

3) Patrick Henry Drive and Toms Creek Drive/University City Boulevard

4) North Franklin Street and Laurel Street

The existing roadway geometry and lane configurations of each intersection were used.

Table 6 defines the volume/saturation (v/s) ratios by approach for each demand level that were

applied to determine the vehicle volumes of the simulated intersections.

Table 6. V/S Flow Ratios Demand EB WB NB SB 1 0.1 0.1 0.1 0.1 2 0.2 0.2 0.1 0.1 3 0.2 0.2 0.2 0.2 4 0.3 0.3 0.1 0.1 5 0.3 0.3 0.2 0.2 6 0.3 0.3 0.3 0.3 7 0.4 0.4 0.1 0.1 8 0.4 0.4 0.2 0.2 9 0.4 0.4 0.3 0.3 10 0.4 0.4 0.4 0.4 11 0.5 0.5 0.1 0.1 12 0.5 0.5 0.2 0.2 13 0.5 0.5 0.3 0.3 14 0.5 0.5 0.4 0.4 15 0.6 0.6 0.1 0.1 16 0.6 0.6 0.2 0.2 17 0.6 0.6 0.3 0.3 18 0.7 0.7 0.1 0.1 19 0.7 0.7 0.2 0.2 20 0.8 0.8 0.1 0.1

In order to determine how much green time should be allocated to each phase, the green

time was distributed in proportion to the critical phase Y-ratios for the critical lane groups (49).

A 30-s cycle length was selected as the lower limit to model minimum green timings appropriate

for pedestrian crossings. A 180-s cycle length was selected as the maximum limit to model the

maximum timing accepted by drivers. The results of the simulations were then used to determine

32

the optimum cycle length for all measures of effectiveness (delay, fuel consumption, and vehicle

emissions). The following summarizes the procedure adopted to conduct the analysis:

1. Create the input files and parameters.

a. Determine the turning movement counts using the traffic demands in Table 6 and

assumed approach distributions.

b. Determine which demands require a protected left turn phase. Adjust the base

saturation flow rate of each demand using the methodologies presented in the

latest edition of the Highway Capacity Manual (HCM) (50).

c. Calculate the v/s ratios per travel lane, critical Y-ratios, and effective green times

per phase.

d. Vary the cycle length from 30 to 180 s in increments of 10 s. Vary the lost time

per phase from 3 to 7 s in an increments of 0.5 s.

e. Apply the phasing schemes shown in Figure 7.

Figure 7. Phasing schemes

f. Load the vehicle demands for 1,800 s and input the calculated signal timings. Set

the simulation time to 3,600 s to ensure that all vehicles clear the network by the

conclusion of the simulation.

33

i. Input the existing roadway geometry, lane configurations, and posted

speed limit of the intersection.

ii. For Intersections 1 and 3, operate demands 1 through 6 with two phases

and demands 7 through 20 with four phases.

2. Export the results of each simulation. Add the hydrocarbon (HC), carbon monoxide

(CO), nitrous oxide (NOx), and carbon dioxide (CO2) results to obtain the total

emissions.

3. Identify the cycle length for each critical Y-ratio associated with the minimum delay, fuel

consumed, and total emissions of each demand level. Identify the optimum cycle length

for each total lost time.

4. Perform a linear regression analysis to recalibrate the Webster parameters and develop

new optimum cycle length formulations.

5. Follow the same steps described above for the other study intersections.


3.5.1. Simulation Results

Intersections 1) and 3) were simulated with two phases for the first 6 demand levels and four

phases for demands 7 through 20. Intersections 2) and 4) were simulated as four-phase

intersections only, based on demand levels and existing roadway geometry. Table 7 through

Table 9 list the numeric simulation results corresponding to Intersection 1). Intersections 1) and

3) had similar results since the roadway geometry, lane configuration, and phasing schemes were

the same. Table 10 to Table 12 list the numeric simulation results corresponding to Intersection

2). The simulation results for Intersection 2) and 4) were found to have similar trends. The

simulation results in this paper advanced from those presented in previous work of the authors

(4) in that exclusive left-turn movements were added. The simulation results are consistent with

the conclusions from the recent literature (4, 25-28) that the Webster optimum cycle lengths are

not in accordance with the optimum cycle lengths for minimizing fuel consumption and tailpipe

emissions. This suggest that the results presented in Table 7 through Table 12, which will be use

for the regression modeling in the next section, are more appropriate to determining new

optimum cycle length formulations associated with minimizing delay, fuel consumption, and

emission levels.

34

Table 7. Intersection 1 Optimum Cycle Length Results (s) – Part 1

Y(Σ critical v/s)

1 0.16 17 30 36 372 0.24 18 30 37 353 0.32 21 30 57 524 0.32 21 30 57 525 0.40 23 30 44 406 0.48 27 30 38 377 0.49 45 57 94 938 0.58 55 70 89 869 0.68 72 88 125 11810 0.78 102 98 130 12611 0.58 55 70 89 8612 0.68 72 88 125 11813 0.78 103 98 130 12614 0.87 181 180 180 18015 0.68 72 88 125 11816 0.78 103 98 130 12617 0.87 182 180 180 18018 0.78 103 98 130 12619 0.87 181 180 180 18020 0.87 182 180 180 1801 0.16 18 31 36 392 0.24 20 30 37 353 0.32 23 30 57 534 0.32 23 30 57 535 0.40 26 30 46 416 0.48 30 30 39 37

7 0.49 50 64 96 95

8 0.58 62 72 92 929 0.68 81 90 130 12110 0.78 116 100 133 12711 0.58 62 72 92 9212 0.68 81 90 130 12113 0.78 116 100 133 12714 0.87 204 180 180 18015 0.68 81 90 130 12116 0.78 116 100 133 12717 0.87 206 180 180 18018 0.78 116 100 133 12719 0.87 204 180 180 18020 0.87 206 180 180 1801 0.16 20 33 52 432 0.24 22 34 35 353 0.32 25 30 55 534 0.32 25 30 55 535 0.40 28 30 47 426 0.48 33 30 39 377 0.49 56 67 97 968 0.58 69 80 92 929 0.68 90 92 135 12410 0.78 129 105 136 13211 0.58 69 80 92 9212 0.68 90 92 135 12413 0.78 130 105 136 13214 0.87 228 180 180 18015 0.68 90 92 135 12416 0.78 130 105 136 13217 0.87 209 180 180 18018 0.78 130 105 136 13219 0.87 228 180 180 18020 0.87 229 180 180 180

Total Emissions

Demand Webster-Cobbe Delay FuelL

= 6 s

L = 1

2 sL

= 7 s

L = 1

4 sL

= 8 s

L = 1

6 s

35


Y(Σ critical v/s)

1 0.16 22 36 54 482 0.24 24 39 40 393 0.32 27 30 55 534 0.32 27 30 55 535 0.40 31 30 52 476 0.48 36 30 42 407 0.49 62 73 97 968 0.58 76 82 110 1069 0.68 100 95 135 12410 0.78 131 112 143 13811 0.58 77 82 110 10612 0.68 100 95 135 12413 0.78 143 112 143 13814 0.87 252 180 180 18015 0.68 100 95 135 12416 0.78 143 112 143 13817 0.87 253 180 180 18018 0.78 143 112 143 13819 0.87 252 180 180 18020 0.87 253 180 180 1801 0.16 24 39 60 482 0.24 26 40 38 483 0.32 29 30 61 574 0.32 29 30 61 575 0.40 33 30 53 536 0.48 38 30 42 407 0.49 68 83 105 1058 0.58 84 90 115 1159 0.68 109 103 136 12610 0.78 156 122 145 14011 0.58 84 90 115 11512 0.68 109 103 136 12613 0.78 156 122 145 14014 0.87 275 180 180 18015 0.68 109 103 136 12616 0.78 156 122 145 14017 0.87 276 180 180 18018 0.78 156 122 145 14019 0.87 275 180 180 18020 0.87 276 180 180 1801 0.16 26 41 60 522 0.24 28 40 50 513 0.32 32 30 62 584 0.32 32 30 62 585 0.40 36 30 48 506 0.48 41 40 45 377 0.49 74 86 125 1248 0.58 90 93 121 1209 0.68 118 103 137 13010 0.78 169 128 147 14011 0.58 91 93 121 12012 0.68 118 103 137 13013 0.78 170 128 147 14014 0.87 299 180 180 18015 0.68 119 103 137 13016 0.78 170 128 147 14017 0.87 300 180 180 18018 0.78 170 128 147 14019 0.87 299 180 180 18020 0.87 300 180 180 180

L = 9

sL

=18 s

L = 1

0 sL

= 20 s

L = 1

1 sL

= 22 s

Demand Webster-Cobbe Delay Fuel Total Emissions

36


Y(Σ critical v/s)

1 0.16 27 38 62 542 0.24 30 36 53 573 0.32 34 30 64 594 0.32 34 30 64 595 0.40 38 30 48 506 0.48 44 43 50 427 0.49 80 88 125 1258 0.58 98 104 121 1209 0.68 128 115 140 13610 0.78 183 129 147 14211 0.58 98 104 121 12012 0.68 128 115 140 13613 0.78 183 129 147 14214 0.87 322 180 180 18015 0.68 128 115 140 13616 0.78 183 129 147 14217 0.87 324 180 180 18018 0.78 183 129 147 14219 0.87 322 180 180 18020 0.87 324 180 180 1801 0.16 29 34 55 462 0.24 32 37 56 603 0.32 36 30 65 614 0.32 36 30 65 615 0.40 41 37 54 546 0.48 47 47 53 467 0.49 85 92 128 1268 0.58 105 110 132 1289 0.68 137 120 147 14010 0.78 196 130 150 14511 0.58 105 110 132 12812 0.68 137 120 147 14013 0.78 197 130 150 14514 0.87 346 180 180 18015 0.68 137 120 147 14016 0.78 197 130 150 14517 0.87 347 180 180 18018 0.78 197 130 150 14519 0.87 346 180 180 18020 0.87 347 180 180 1801 0.16 31 38 58 502 0.24 34 36 59 613 0.32 38 40 65 614 0.32 38 40 65 615 0.40 44 41 55 556 0.48 50 52 55 477 0.49 91 93 135 1318 0.58 112 118 136 1369 0.68 146 126 155 14710 0.78 209 130 150 14711 0.58 113 118 136 13612 0.68 146 126 155 14713 0.78 210 130 150 14714 0.87 369 180 180 18015 0.68 147 126 155 14716 0.78 210 130 150 14717 0.87 371 180 180 18018 0.78 210 130 150 14719 0.87 370 180 180 18020 0.87 371 180 180 180

L = 1

2 sL

= 24 s

L = 1

3 sL

= 26 s

L = 1

4 sL

=28 s


37


Y(Σ critical v/s)

1 0.13 27 30 74 722 0.19 28 34 86 853 0.27 31 41 70 674 0.27 31 41 70 675 0.33 34 43 72 726 0.40 38 45 75 727 0.31 33 50 95 948 0.38 37 52 90 749 0.46 43 61 84 8310 0.55 51 76 140 13411 0.36 36 60 80 8012 0.44 41 60 75 7313 0.52 48 68 78 7814 0.59 56 70 78 7815 0.42 40 56 93 9016 0.50 46 65 80 8017 0.57 54 69 78 7618 0.48 44 65 118 11519 0.55 51 76 140 13420 0.55 51 76 140 1341 0.13 30 30 83 852 0.19 32 37 86 863 0.27 36 42 72 704 0.27 36 42 72 705 0.33 39 45 75 736 0.40 43 50 77 727 0.31 37 51 96 928 0.38 42 55 95 769 0.46 48 61 86 8010 0.55 58 76 141 13511 0.36 41 61 88 8312 0.44 46 64 96 9013 0.52 54 70 98 9814 0.59 64 75 101 10015 0.42 45 60 116 11916 0.50 52 66 94 10017 0.57 61 70 100 9818 0.48 50 74 136 13619 0.55 58 76 141 13520 0.55 58 76 141 1351 0.13 34 30 85 872 0.19 36 38 86 933 0.27 40 52 80 804 0.27 40 52 80 805 0.33 43 58 85 836 0.40 49 60 90 867 0.31 42 53 112 1108 0.38 47 56 90 869 0.46 54 66 92 9210 0.55 65 79 145 13611 0.36 45 65 100 9612 0.44 52 69 103 9713 0.52 60 76 106 10614 0.59 71 78 114 11515 0.42 50 63 124 12516 0.50 58 70 101 10017 0.57 68 76 101 10218 0.48 55 76 142 14319 0.55 65 79 145 13620 0.55 65 79 145 136

L = 1

2 sL

= 14 s

L = 1

6 sDemand Webster-Cobbe Delay Fuel Total Emissions

38


Y(Σ critical v/s)

1 0.13 37 35 86 882 0.19 40 42 86 883 0.27 44 49 82 804 0.27 44 49 82 805 0.33 47 52 83 836 0.40 54 63 90 867 0.31 46 54 115 1128 0.38 52 60 92 879 0.46 59 67 94 9210 0.55 72 80 147 13911 0.36 50 66 110 10612 0.44 57 73 106 10313 0.52 66 77 109 10714 0.59 79 82 119 11615 0.42 55 65 124 12516 0.50 64 76 104 10417 0.57 75 80 116 11618 0.48 61 79 143 14219 0.55 72 80 147 13920 0.55 72 80 147 1391 0.13 40 38 90 902 0.19 43 46 88 883 0.27 48 53 86 884 0.27 48 53 86 885 0.33 52 62 85 846 0.40 59 68 91 887 0.31 50 56 117 1158 0.38 57 62 96 939 0.46 65 69 97 9510 0.55 78 83 155 14411 0.36 55 68 113 11012 0.44 62 75 108 11013 0.52 72 78 113 11014 0.59 86 88 130 12815 0.42 60 68 126 12716 0.50 69 80 110 10717 0.57 82 84 123 11718 0.48 67 82 150 15019 0.55 78 83 155 14420 0.55 78 83 155 1441 0.13 44 44 92 922 0.19 47 52 92 1003 0.27 52 58 88 904 0.27 52 58 88 905 0.33 56 66 88 866 0.40 64 73 95 947 0.31 55 63 120 1198 0.38 61 70 110 1109 0.46 70 77 110 11010 0.55 85 88 158 15011 0.36 60 72 115 11212 0.44 68 80 120 11513 0.52 79 83 116 11614 0.59 93 93 135 13315 0.42 65 72 126 12716 0.50 75 82 120 11817 0.57 89 90 128 12518 0.48 73 85 150 15219 0.55 85 88 158 15020 0.55 85 88 158 150

L = 1

8 sL

= 20 s

L = 2


39


Y(Σ critical v/s)

1 0.13 47 50 100 952 0.19 51 56 95 973 0.27 56 60 100 1004 0.27 56 60 100 1005 0.33 61 69 95 926 0.40 69 75 108 1027 0.31 59 65 120 1238 0.38 66 73 114 1189 0.46 76 80 116 11610 0.55 92 95 160 15711 0.36 64 72 117 11512 0.44 73 80 122 12013 0.52 85 86 118 11814 0.59 101 102 140 13515 0.42 71 75 130 13016 0.50 81 84 128 12517 0.57 96 96 138 13418 0.48 78 85 158 15219 0.55 92 95 160 15720 0.55 92 95 160 1571 0.13 51 58 100 1002 0.19 54 60 106 1023 0.27 60 65 105 1054 0.27 60 65 105 1055 0.33 65 77 108 1006 0.40 74 79 116 1117 0.31 63 78 130 1308 0.38 71 75 116 1189 0.46 81 85 120 12010 0.55 98 100 164 16211 0.36 69 73 122 12012 0.44 78 84 127 12413 0.52 91 92 140 12714 0.59 108 107 146 14015 0.42 76 80 130 13316 0.50 87 90 135 13017 0.57 103 100 140 14018 0.48 84 88 160 15719 0.55 98 100 164 16220 0.55 98 100 164 1621 0.13 54 60 110 1102 0.19 58 64 112 1123 0.27 64 80 120 1204 0.27 64 80 120 1205 0.33 70 84 115 1156 0.40 79 90 120 1227 0.31 68 80 140 1408 0.38 76 85 128 1249 0.46 87 88 130 13010 0.55 105 110 170 16711 0.36 74 88 136 13312 0.44 84 100 130 12813 0.52 97 95 140 14014 0.59 115 120 150 14615 0.42 81 110 132 14016 0.50 93 112 140 14017 0.57 110 118 150 15018 0.48 90 90 166 16019 0.55 105 110 170 16720 0.55 105 110 170 167

L = 2

4 sL

= 26 s

L = 2


40

3.5.2. Optimum Cycle Length Formulations

The optimum cycle lengths identified in the simulation for each scenario were used to recalibrate

the Webster model. As can be seen from Table 7 through Table 12 the optimum cycle lengths

that minimize fuel consumption and total emissions are greater than the optimum cycle lengths

that minimize vehicle delay. To identify the optimum cycle length to minimize vehicle delays,

fuel consumption, and emission levels, three sets of model parameters were calibrated,

respectively. Equation (2) shows the linear regression model used to develop new optimum cycle

length formulations for each study intersection.

𝐶!"# = !!!!!

+ !!!!

+ 𝛾 (2)

where Copt is the optimum cycle length in seconds; ∝ and 𝛽 are the model coefficients; L is the

total lost time per cycle in seconds; Y is the sum of flow ratios for all critical lane groups; and 𝛾

is an intercept that can be viewed as the minimum cycle length. Table 13 lists the estimated

model coefficients, the associated T-value, and the coefficient of determination for each

formulation.

41

Table 13. Regression Results for Study Intersections MOE R2 Estimated

𝜶 T-Value 𝜶 (Pr>|t|)

Estimated 𝜷

T-Value 𝜷 (Pr>|t|)

Estimated 𝜸

T-Value 𝜸 (Pr>|t|)

Inte

rsec

tion

1 Delay 0.90 1.14 11.76 (<0.05) 0.37 0.14 (0.89) 21.59 6.21

(<0.05)

Fuel 0.82 1.23 8.10 (<0.05) 1.76 0.41 (0.68) 37.01 6.79

(<0.05)

Emissions 0.81 1.24 8.34 (<0.05) 0.24 0.06 (0.95) 36.40 6.79

(<0.05)

Inte

rsec

tion

2 Delay 0.91 1.15 26.65 (<0.05) 12.69 9.19

(<0.05) 7.58 3.86 (<0.05)

Fuel 0.66 1.47 12.13 (<0.05) 13.68 3.58

(<0.05) 37.45 6.80 (<0.05)

Emissions 0.66 1.51 12.92 (<0.05) 9.37 2.50

(<0.05) 41.40 7.70 (<0.05)

Inte

rsec

tion

3 Delay 0.92 1.09 13.15 (<0.05) 0.17 0.07 (0.94) 27.03 9.09

(<0.05)

Fuel 0.84 1.07 8.93 (<0.05) 1.21 0.36 (0.72) 52.88 12.31

(<0.05)

Emissions 0.84 1.04 8.86 (<0.05) 0.89 0.27 (0.79) 52.96 12.60

(<0.05)

Inte

rsec

tion

4 Delay 0.92 1.12 25.61 (<0.05) 2.19 1.96 (0.05) 21.25 14.25

(<0.05)

Fuel 0.93 0.98 30.37 (<0.05) -0.13 -0.16 (0.88) 54.75 49.91

(<0.05)

Emissions 0.93 1.00 29.65 (<0.05) -0.20 -0.24 (0.81) 54.20 47.68

(<0.05)

As seen in Table 13, the model prediction power is high for each intersection, with

coefficients of determination in excess of 0.8 in majority of the cases. In the Intersection 1)

results, the 𝛽 coefficients were low and not significant. In Intersection 2), all coefficients were

significant, but the fuel and emissions model had less prediction power than the fuel and

emissions model of Intersection 1). The regression results of Intersections 3) and 4) had high

prediction power but each model did not have a significant 𝛽 coefficient. Equations (3) through

(5) present the developed formulations that minimize vehicle delay, fuel consumption, and total

emissions. These formulations represent the significant model with highest prediction power

from the regression results of the study intersections. It should be noted that the fuel and

emissions formulations are similar.

𝐶!"#,!"#$% =

!.!"!!!.!"!!!

+ 21 (3)

𝐶!"#,!"#$ = !.!"!!!!

+ 55 (4)

42

𝐶!"#,!"#$$#%&$ = !

!!!+ 54 (5)

In order to compare the results of the proposed formulations to the results of each study

intersection, one of the independent variables (1-Y)-1 was plotted against optimum cycle length.

Also, the results of the Webster formulation (generated using Equation (1)) were plotted in the

same figure. Figure 8 shows the calibration of the proposed formulations against the Webster

formulation and simulation results of each study intersection. For the purposes of this analysis, a

total lost time of 20 s was used.

When the demand is low, the proposed models have comparable optimum cycle length

estimates for minimizing delays as the length estimated by Webster. However, the difference

between the recommended optimum cycle lengths in the Webster and proposed models with the

simulation results increases as the traffic demand increases. This supports the results of the

previous study by the authors (4) and a study by Cheng et al. (51). Cheng et al. compared the

Webster optimum cycle lengths with the optimum cycle length generated by Synchro 5 and

concluded that the Webster cycle lengths were approximately 40 s longer when the traffic

demand at an intersection is high (51). In our case, the difference was observed to be as large as

60 s as the degree of saturation approached 1.0. Optimum cycle lengths to minimize fuel

consumption and emissions are similar to each other. Both have a much larger intercept value,

indicating a longer minimum cycle length threshold.

43

(a) Vehicle Delay

(b) Fuel Consumption

(c) GHG Emissions Figure 8. Optimum Cycle Length vs. 1/(1-Y)

44

3.6. Conclusions

This paper developed analytical models to estimate the optimum cycle length that minimizes the

intersection delay, fuel consumption levels, and greenhouse gas emissions. It furthered a

previous study conducted by the authors, which analyzed one synthetic isolated intersection with

one lane from each approaching direction and a signal plan with two phases. In this paper, four

real intersections with realistic lane configurations and real speed limits settings in the area of

Blacksburg, Virginia, were used in the simulation analysis. Left-turn protected phases were

introduced based on the demand level and recommendation by the HCM. The INTEGRATION

microscopic traffic simulation software was used to generate the noted MOEs at four study

intersections under different demand levels, cycle lengths, and signal lost times. For each study

intersection, optimum cycle lengths were then identified for each traffic demand scenario with

the purpose of minimizing intersection delay, fuel consumption levels, and total emissions.

To identify the optimum cycle lengths that minimize vehicle delay, fuel consumption

levels, and total emissions levels, a regression model was fit to the simulation data. The results

are compatible with a previous study by the authors in terms of optimum cycle lengths. For

minimizing fuel consumption and GHG emissions, longer cycle lengths are consistently favored

in comparison to the optimum cycle lengths to minimize vehicle delay. The results demonstrate

that the model coefficients are significantly different depending on the MOE being minimized.

The fuel consumption and emissions formulations were very similar. Compared to the optimum

cycle lengths to minimize delays, these two formulations required a longer minimum cycle

length threshold.

This study demonstrated that the proposed delay formulation was comparable to the

Webster formulation when the demand is low. However, minimizing vehicle delay using the

Webster method will typically overestimate the optimum cycle length at high traffic demand

levels. The design of the traffic signal needs to be balanced and optimized for different purposes.

The four intersections selected in this study demonstrate slightly different results in

fitting the models. The factors that caused such variations need to be further investigated. This

paper was limited to investigating isolated intersections. Future research will include

investigating arterial networks and actuated signal timings.

45

3.7. Acknowledgements

This research effort was jointly sponsored by the MATS University Transportation Center, the

TranLIVE University Center, and the Virginia Department of Transportation (VDOT).

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INTEGRATION Steady-state Car-following Behavior. Transportation Research Part A:

Policy and Practice, 2003. 37: p. 1-27.

41. Rakha, H. and B. Crowther, Comparison of Greenshields, Pipes, and Van Aerde Car-

following and Traffic Stream Models. Transportation Research Record, 2002. 1802: p.

248-262.

42. Rakha, H., An Evaluation of the Benefits of User and System Optimised Route Guidance

Strategies. 1990, Queen's University, Kingston.

43. Rakha, H., et al., Construction and calibration of a large-scale microsimulation model of

the Salt Lake area. Transportation Research Record, 1998. 1644: p. 93-102.

44. Rakha, H., et al., Evaluating Alternative Truck Management Strategies Along Interstate

81. Transportation Research Record: Journal of the Transportation Research Board, 2005.

1925: p. 76-86.

45. Rakha, H. and Y.H. Zhang, INTEGRATION 2.30 framework for modeling lane-changing

behavior in weaving sections. Traffic Flow Theory and Highway Capacity and Quality of

Services 2004, 2004(1883): p. 140-149.

49

46. Rakha, H. and Y. Zhang, Analytical procedures for estimating capacity of freeway

weaving, merge, and diverge sections. Journal of transportation engineering, 2006.

132(8): p. 618-628.

47. Farzaneh, M. and H. Rakha, Impact of differences in driver desired speed on steady-state


Research Board, 2006. 1965: p. 142-151.

48. Farzaneh, M. and H. Rakha, Impact of differences in driver-desired speed on steady-state


Research Board, 2006. 1965(1): p. 142-151.

49. Mannering, F. and S. Washburn, Principles of Highway Engineering and Traffic Anlysis,

ed. 5. 2013, New York: Wiley.

50. HCM 2010 - Highway Capacity Manual. Transportation Research Board of the National

Academies. Washington D.C., 2010.


Based on HCM 2000, in Annual Meeting of the Transportation Research Board. 2003:

Washington D.C.

50

CHAPTER 4: IMPLEMENTING MULTIPLE RANDOM SEEDS IN

SIMULATION RUNS

Based on A. Calle-Laguna, H. Rakha, J. Du’s update to “Comprehensive Analysis on Signal

Timing Optimization to Reduce Energy and Environmental Impacts,” submitted to the

Transportation Research Part D: Transportation and Environment – An International Journal.


4.1.1 Simulation Results

Intersections 1) and 3) were simulated with two phases for the first 6 demand levels and four

phases for demands 7 through 20. Intersections 2) and 4) were simulated as four-phase

intersections only, based on demand levels and existing roadway geometry. For all intersection

simulations, twenty random seeds per scenario were run to account for the stochastic nature of

traffic. The results of each seed simulation were then averaged to obtain the final simulation

results. The difference between simulating with one random seed and twenty different random

seeds will be discussed in the next section.

Table 14 through Table 16 list the numeric simulation results corresponding to

Intersection 1). Intersections 1) and 3) had similar results since the roadways geometry, lane

configuration, and phasing schemes were the same. Table 17 through Table 19 list the numeric

simulation results corresponding to Intersection 2). The simulation results for Intersection 2) and

4) were found to have similar trends. The simulation results in this paper advanced those

presented in the previous work of the authors (1) in that exclusive left-turn movements were

added. The simulation results are consistent with the conclusions from the recent literature (1, 2-

5) that the Webster optimum cycle lengths are not in accordance with the optimum cycle lengths

for minimizing fuel consumption and tailpipe emissions. This suggest that the results presented

in Table 14 through Table 19 are more appropriate to determining new optimum cycle length

formulations associated with minimizing delay, fuel consumption, and emission levels.

51


Y(Σ critical v/s)

1 0.16 17 30 55 542 0.24 18 30 56 553 0.32 21 30 71 674 0.32 21 30 71 675 0.40 23 30 60 586 0.48 27 30 58 547 0.49 45 54 94 938 0.58 55 65 92 909 0.68 72 81 122 11810 0.78 102 102 130 12711 0.58 55 65 93 9012 0.68 72 81 122 11813 0.78 103 102 130 12714 0.87 181 180 180 18015 0.68 72 81 122 11816 0.78 103 102 130 12717 0.87 182 180 180 18018 0.78 103 102 130 12719 0.87 181 180 180 18020 0.87 182 180 180 1801 0.16 18 31 56 572 0.24 20 30 60 603 0.32 23 30 71 694 0.32 23 30 71 695 0.40 26 30 61 576 0.48 30 30 59 54

7 0.49 50 64 97 97

8 0.58 62 69 96 959 0.68 81 88 126 12310 0.78 116 105 132 12911 0.58 62 69 96 9512 0.68 81 88 126 12313 0.78 116 105 132 12914 0.87 204 180 180 18015 0.68 81 88 126 12316 0.78 116 105 132 12917 0.87 206 180 180 18018 0.78 116 105 132 12919 0.87 204 180 180 18020 0.87 206 180 180 1801 0.16 20 32 70 642 0.24 22 32 61 613 0.32 25 30 71 694 0.32 25 30 71 695 0.40 28 30 62 586 0.48 33 30 60 557 0.49 56 64 101 998 0.58 69 78 96 969 0.68 90 92 130 12510 0.78 129 112 134 13111 0.58 69 78 96 9612 0.68 90 92 130 12513 0.78 130 112 134 13114 0.87 228 180 180 18015 0.68 90 92 130 12516 0.78 130 112 134 13117 0.87 209 180 180 18018 0.78 130 112 134 13119 0.87 228 180 180 18020 0.87 229 180 180 180

L = 1

4 sL

= 8 s

L = 1

6 sL

= 6 s

L = 1

2 sL

= 7 s


52


Y(Σ critical v/s)

1 0.16 22 33 72 672 0.24 24 35 66 673 0.32 27 30 75 744 0.32 27 30 75 745 0.40 31 30 66 636 0.48 36 30 62 577 0.49 62 70 104 1038 0.58 76 82 112 1109 0.68 100 95 132 12610 0.78 131 116 142 13811 0.58 77 82 112 11012 0.68 100 95 132 12613 0.78 143 116 142 13814 0.87 252 180 180 18015 0.68 100 95 132 12616 0.78 143 116 142 13817 0.87 253 180 180 18018 0.78 143 116 142 13819 0.87 252 180 180 18020 0.87 253 180 180 1801 0.16 24 35 76 692 0.24 26 35 66 713 0.32 29 30 79 784 0.32 29 30 79 785 0.40 33 30 68 676 0.48 38 30 62 597 0.49 68 77 108 1088 0.58 84 88 118 1189 0.68 109 102 135 12810 0.78 156 123 145 14111 0.58 84 88 118 11812 0.68 109 102 135 12813 0.78 156 123 145 14114 0.87 275 180 180 18015 0.68 109 102 135 12816 0.78 156 123 145 14117 0.87 276 180 180 18018 0.78 156 123 145 14119 0.87 275 180 180 18020 0.87 276 180 180 1801 0.16 26 36 77 732 0.24 28 35 73 743 0.32 32 30 80 784 0.32 32 30 80 785 0.40 36 30 65 666 0.48 41 35 65 597 0.49 74 80 123 1218 0.58 90 92 122 1209 0.68 118 104 139 13310 0.78 169 129 149 14511 0.58 91 92 122 12012 0.68 118 104 139 13313 0.78 170 129 149 14514 0.87 299 180 180 18015 0.68 119 104 139 13316 0.78 170 129 149 14517 0.87 300 180 180 18018 0.78 170 129 149 14519 0.87 299 180 180 18020 0.87 300 180 180 180

Total EmissionsDemand Webster-Cobbe Delay FuelL

= 9 s

L =1

8 sL

= 10 s

L = 2

0 sL

= 11 s

L = 2

2 s

53


Y(Σ critical v/s)

1 0.16 27 34 79 742 0.24 30 33 76 773 0.32 34 30 82 804 0.32 34 30 82 805 0.40 38 32 67 676 0.48 44 41 69 627 0.49 80 84 125 1248 0.58 98 102 125 1229 0.68 128 113 140 13810 0.78 183 131 149 14611 0.58 98 102 125 12212 0.68 128 113 140 13813 0.78 183 131 149 14614 0.87 322 180 180 18015 0.68 128 113 140 13816 0.78 183 131 149 14617 0.87 324 180 180 18018 0.78 183 131 149 14619 0.87 322 180 180 18020 0.87 324 180 180 1801 0.16 29 32 78 732 0.24 32 34 80 793 0.32 36 30 86 824 0.32 36 30 86 825 0.40 41 38 71 726 0.48 47 45 70 667 0.49 85 91 128 1268 0.58 105 110 131 1299 0.68 137 119 147 14310 0.78 196 133 155 15311 0.58 105 110 131 12912 0.68 137 119 147 14313 0.78 197 133 155 15314 0.87 346 180 180 18015 0.68 137 119 147 14316 0.78 197 133 155 15317 0.87 347 180 180 18018 0.78 197 133 155 15319 0.87 346 180 180 18020 0.87 347 180 180 1801 0.16 31 34 81 752 0.24 34 33 82 843 0.32 38 38 88 864 0.32 38 38 88 865 0.40 44 41 73 736 0.48 50 49 72 687 0.49 91 94 135 1318 0.58 112 117 138 1389 0.68 146 123 153 14910 0.78 209 133 160 15911 0.58 113 117 138 13812 0.68 146 123 153 14913 0.78 210 133 160 15914 0.87 369 180 180 18015 0.68 147 123 153 14916 0.78 210 133 160 15917 0.87 371 180 180 18018 0.78 210 133 160 15919 0.87 370 180 180 18020 0.87 371 180 180 180

Total EmissionsDemand Webster-Cobbe Delay FuelL

= 12 s

L = 2

4 sL

= 13 s

L = 2

6 sL

= 14 s

L =2

8 s

54


Y(Σ critical v/s)

1 0.13 27 30 80 782 0.19 28 32 88 883 0.27 31 38 81 784 0.27 31 38 81 785 0.33 34 40 81 816 0.40 38 43 78 747 0.31 33 43 102 998 0.38 37 46 90 799 0.46 43 53 84 8210 0.55 51 68 125 12211 0.36 36 50 87 8612 0.44 41 53 78 7713 0.52 48 63 82 8214 0.59 56 70 83 8415 0.42 40 53 99 9716 0.50 46 61 80 8017 0.57 54 69 82 8118 0.48 44 58 118 11519 0.55 51 68 125 12220 0.55 51 68 125 1221 0.13 30 30 86 852 0.19 32 36 89 883 0.27 36 42 84 824 0.27 36 42 84 825 0.33 39 44 87 846 0.40 43 48 82 767 0.31 37 46 103 1018 0.38 42 49 94 829 0.46 48 56 86 8210 0.55 58 71 131 12811 0.36 41 52 92 8912 0.44 46 56 93 9013 0.52 54 65 97 9714 0.59 64 74 101 9915 0.42 45 57 113 11516 0.50 52 63 92 9517 0.57 61 70 96 9418 0.48 50 65 128 13019 0.55 58 71 131 12820 0.55 58 71 131 1281 0.13 34 30 88 892 0.19 36 39 91 953 0.27 40 50 89 894 0.27 40 50 89 895 0.33 43 53 93 926 0.40 49 55 90 887 0.31 42 48 116 1158 0.38 47 53 92 889 0.46 54 63 93 9310 0.55 65 75 138 13311 0.36 45 55 100 9812 0.44 52 63 102 9913 0.52 60 70 108 10814 0.59 71 77 117 11815 0.42 50 61 119 11816 0.50 58 66 100 9917 0.57 68 75 101 10118 0.48 55 67 135 13419 0.55 65 75 138 13320 0.55 65 75 138 133

L = 1

2 sL

= 14 s

L = 1


55


Y(Σ critical v/s)

1 0.13 37 36 90 902 0.19 40 42 92 933 0.27 44 50 91 904 0.27 44 50 91 905 0.33 47 52 93 926 0.40 54 62 93 907 0.31 46 53 119 1188 0.38 52 58 94 919 0.46 59 65 99 9810 0.55 72 80 139 13711 0.36 50 60 107 10312 0.44 57 67 107 10613 0.52 66 74 111 11114 0.59 79 82 123 12015 0.42 55 63 120 12016 0.50 64 72 110 11017 0.57 75 82 112 11318 0.48 61 72 136 13519 0.55 72 80 139 13720 0.55 72 80 139 1371 0.13 40 39 93 922 0.19 43 46 93 933 0.27 48 54 95 954 0.27 48 54 95 955 0.33 52 59 96 956 0.40 59 65 96 947 0.31 50 55 121 1198 0.38 57 62 98 979 0.46 65 68 104 10310 0.55 78 84 148 14211 0.36 55 64 112 11012 0.44 62 70 109 11013 0.52 72 79 117 11314 0.59 86 89 130 12915 0.42 60 66 122 12416 0.50 69 75 114 11317 0.57 82 86 118 11718 0.48 67 77 140 13919 0.55 78 84 148 14220 0.55 78 84 148 1421 0.13 44 44 95 952 0.19 47 51 96 1003 0.27 52 58 99 1004 0.27 52 58 99 1005 0.33 56 63 101 996 0.40 64 72 105 1057 0.31 55 63 125 1228 0.38 61 67 111 1129 0.46 70 75 115 11410 0.55 85 89 154 15011 0.36 60 68 115 11212 0.44 68 76 119 11713 0.52 79 83 118 11914 0.59 93 94 138 13715 0.42 65 72 128 12916 0.50 75 81 120 12017 0.57 89 91 131 13018 0.48 73 80 145 14519 0.55 85 89 154 15020 0.55 85 89 154 150

Total EmissionsL

= 18 s

L = 2

0 sL

= 22 s

Demand Webster-Cobbe Delay Fuel

56


Y(Σ critical v/s)

1 0.13 47 50 100 982 0.19 51 56 99 1003 0.27 56 60 105 1054 0.27 56 60 105 1055 0.33 61 68 106 1046 0.40 69 75 114 1117 0.31 59 64 127 1268 0.38 66 72 114 1179 0.46 76 80 118 11810 0.55 92 95 160 15911 0.36 64 70 117 11512 0.44 73 79 123 12013 0.52 85 88 124 12414 0.59 101 101 142 14015 0.42 71 76 132 13016 0.50 81 85 128 12617 0.57 96 96 139 13718 0.48 78 84 151 14919 0.55 92 95 160 15920 0.55 92 95 160 1591 0.13 51 57 105 1032 0.19 54 59 110 1083 0.27 60 68 112 1124 0.27 60 68 112 1125 0.33 65 75 114 1106 0.40 74 79 120 1197 0.31 63 73 133 1308 0.38 71 75 119 1199 0.46 81 86 125 12510 0.55 98 100 164 16311 0.36 69 72 123 12212 0.44 78 83 128 12713 0.52 91 93 141 13414 0.59 108 109 148 14515 0.42 76 81 135 13716 0.50 87 90 135 13217 0.57 103 101 144 14318 0.48 84 89 152 15119 0.55 98 100 164 16320 0.55 98 100 164 1631 0.13 54 60 113 1102 0.19 58 63 115 1153 0.27 64 77 122 1224 0.27 64 77 122 1225 0.33 70 82 122 1216 0.40 79 87 125 1267 0.31 68 78 140 1408 0.38 76 83 128 1259 0.46 87 89 133 13210 0.55 105 110 172 16911 0.36 74 84 132 13112 0.44 84 95 132 13013 0.52 97 98 143 14314 0.59 115 120 152 15115 0.42 81 98 138 14216 0.50 93 103 139 13917 0.57 110 115 150 15018 0.48 90 90 157 15319 0.55 105 110 172 16920 0.55 105 110 172 169

Total EmissionsL

= 24 s

L = 2

6 sL

= 28 s

Demand Webster-Cobbe Delay Fuel

57

4.1.2. Hypothesis Testing for Simulation Results

In a microsimulation software such as INTEGRATION, different seed values are used to

investigate the stochastic nature of traffic. Running simulation scenarios with different seeds

results in different, but similar, measure of effectiveness outcomes. Previous work conducted by

the authors (1) did not consider multiple simulation runs of each scenario under different random

seeds. To improve the simulation results, twenty random seeds per simulation scenario were run.

The simulation results of the individual measures of effectiveness from the first random seed

were observed to compare with the average results of the twenty random seeds. Figure 9 shows

the distinction between the simulation results from the first random seed and the average results

of the twenty random seeds. For the purpose of this example, the results from intersection 4),

demand 4, and a total lost time of 18 seconds were used.

A two-tailed t-test assuming unequal variances was conducted to compare the simulation

results. For this test, the following data is defined:

• Null Hypothesis (H0): 𝜇! − 𝜇! = 0

• Alternative Hypothesis (Ha): 𝜇! − 𝜇! ≠ 0

• Significance Level (∝): 95%

where, 𝜇! is the mean of the simulation results from the first random seed and 𝜇! is the mean of

the simulation results of the twenty random seeds. Table 20 shows the results of the hypothesis

test, organized by each intersection, measure of effectiveness, and phasing scheme.

As seen in Table 20, the p-values for Intersections 1) and 2) are less than 0.05. This

indicates that there is a significant difference between the simulation results from one seed

versus twenty seeds for Intersections 1) and 2). However, since the p-values for Intersection 3)

and 4) are greater than 0.05, the simulation results from the different hypothesis testing scenarios

are not significantly different.

58

Figure 9. Simulation Results of One Random Seed vs. Twenty Random Seeds

59

Table 20. Two-Tail T-Test Results MOE Mean of One Random

Seed (𝝁𝟏) Mean of Twenty Random

Seeds (𝝁𝟐) T-Value (p-value)

Inte

rsec

tion

1

2 phases Delay 21.24 19.35 6.702 (<0.05) Fuel 0.192 0.188 25.231 (<0.05) Emissions 444.51 435.87 27.143(<0.05)

4 phases Delay 84.88 80.14 2.009 (<0.05) Fuel 0.224 0.222 2.137 (<0.05) Emissions 519.86 514.12 2.143 (<0.05)

Inte

rsec

tion

2

4 phases

Delay 34.73 21.34 25.600 (<0.05)

Fuel 0.203 0.197 24.022 (<0.05)

Emissions 469.62 455.06 24.278 (<0.05)

Inte

rsec

tion

3

2 phases Delay 21.57 21.35 0.789 (0.43) Fuel 0.194 0.194 1.777 (0.08) Emissions 450.49 450.03 1.624 (0.10)

4 phases Delay 82.82 82.24 0.261 (0.79) Fuel 0.227 0.226 0.267 (0.79) Emissions 525.42 524.78 0.265 (0.79)

Inte

rsec

tion

4

4 phases

Delay 45.51 45.10 0.583 (0.56)

Fuel 0.237 0.236 0.666 (0.51)

Emissions 544.90 544.18 0.619 (0.54)

60

4.1.3. Optimum Cycle Length Formulations

The optimum cycle lengths identified in the simulation for each scenario were used to recalibrate

the Webster model. As can be seen from Table 14 through Table 19 and Figure 9, the optimum

cycle lengths that minimize fuel consumption and total emissions are greater than the optimum

cycle lengths that minimize vehicle delay. To identify the optimum cycle length to minimize

vehicle delays, fuel consumption, and emission levels, three sets of model parameters were

calibrated, respectively. Equation (1) shows the linear regression model used to develop new

optimum cycle length formulations for each study intersection.

𝐶!"# = !!!!!

+ !!!!

+ 𝛾 (1)

where Copt is the optimum cycle length in seconds; ∝ and 𝛽 are the model coefficients; L is the

total lost time per cycle in seconds; Y is the sum of flow ratios for all critical lane groups; and 𝛾

is an intercept that can be viewed as the minimum cycle length. Table 21 lists the estimated

model coefficients, the associated T-value, and the coefficient of determination for each

formulation.

61

Table 21. Regression Results for Study Intersections MOE R2 Estimated

𝜶 T-Value 𝜶 (Pr>|t|)

Estimated 𝜷

T-Value 𝜷 (Pr>|t|)

Estimated 𝜸

T-Value 𝜸 (Pr>|t|)

Inte

rsec

tion

1 Delay 0.92 0.87 14.72 (<0.05) 6.74 4.14

(<0.05) 16.97 6.87 (<0.05)

Fuel 0.87 0.79 12.37 (<0.05) 4.00 2.27

(<0.05) 60.44 22.60 (<0.05)

Emissions 0.87 0.81 12.88 (<0.05) 3.18 1.84 (0.07) 59.12 22.56

(<0.05)

Inte

rsec

tion

2 Delay 0.97 1.29 48.08 (<0.05) 10.13 11.83

(<0.05) 5.30 4.35 (<0.05)

Fuel 0.73 1.55 16.28 (<0.05) 4.33 1.43 (0.16) 52.88 12.23

(<0.05)

Emissions 0.74 1.58 16.97 (<0.05) 2.67 0.90 (0.37) 53.29 12.60

(<0.05)

Inte

rsec

tion

3 Delay 0.95 0.93 20.27 (<0.05) 4.80 3.81

(<0.05) 23.28 12.21 (<0.05)

Fuel 0.90 0.88 14.23 (<0.05) 4.57 2.68

(<0.05) 53.15 20.51 (<0.05)

Emissions 0.90 0.88 14.45 (<0.05) 4.11 2.46

(<0.05) 52.84 20.77 (<0.05)

Inte

rsec

tion

4 Delay 0.93 1.14 27.97 (<0.05) 2.51 2.42

(<0.05) 20.59 14.89 (<0.05)

Fuel 0.95 1.00 36.87 (<0.05) -0.13 -0.20 (0.84) 55.65 61.26

(<0.05)

Emissions 0.95 1.00 35.99 (<0.05) -0.26 -0.37 (0.71) 55.25 59.08

(<0.05)

As seen in Table 21, the model prediction power is high for each intersection, with

coefficients of determination in excess of 0.8 in majority of the cases. In the Intersection 1)

results, the 𝛽 coefficient for the emissions model was low and not significant. In Intersection 2),

the 𝛽 coefficient for the fuel and emissions model were not significant, and had less prediction

power than the fuel and emissions model of Intersection 1). The regression results of

Intersections 3) and 4) had high prediction power and only Intersection 4) had non-significant

fuel and emissions model. Equations (2) through (4) present the developed formulations that

minimize vehicle delay, fuel consumption, and total emissions. These formulations represent the

significant model with highest prediction power from the regression results of the study

intersections. It should be noted that the fuel and emissions formulations are similar.

𝐶!"#,!"#$% =

!.!"!!!.!"!!!

+ 21 (2)

𝐶!"#,!"#$ = !

!!!+ 56 (3)

62

𝐶!"#,!"#$$#%&$ = !

!!!+ 55 (4)

In order to compare the results of the proposed formulations to the results of each study

intersection, one of the independent variables (1-Y)-1 was plotted against optimum cycle length.

Also, the results of the Webster formulation were plotted in the same figure. Figure 10 shows the

calibration of the proposed formulations against the Webster formulation and simulation results

of each study intersection. For the purposes of this analysis, a total lost time of 20 s was used.

When the demand is low, the proposed models have comparable optimum cycle length

estimates for minimizing delays as the length estimated by Webster. However, the difference

between the recommended optimum cycle lengths in the Webster and proposed models with the

simulation results increases as the traffic demand increases. This supports the results of the

previous study by the authors (1) and a study by Cheng et al. (6). Cheng et al. compared the

Webster optimum cycle lengths with the optimum cycle length generated by Synchro 5 and

concluded that the Webster cycle lengths were approximately 40 s longer when the traffic

demand at an intersection is high (6). In our case, the difference was observed to be as large as

60 s as the degree of saturation approached 1.0. Optimum cycle lengths to minimize fuel

consumption and emissions are similar to each other. Both have a much larger intercept value,

indicating a longer minimum cycle length threshold.

63

(a) Vehicle Delay

(b) Fuel Consumption

(c) GHG Emissions Figure 10. Optimum Cycle Length vs. 1/(1-Y)

64

4.2. References

1. Calle-Laguna, A., H. Rakha, and J. Du, Optimizing Isolated Traffic Signal Timing

Considering Energy and Environmental Impacts. Presented at the 95th Annual Meeting of

the Transportation Research Board, Washington D.C., 2016.



3. Madireddy, M., et al., Assessment of the Impact of Speed Limit Reduction on Traffic





Environment, 2011. 16(5): p. 409-414.




Based on HCM 2000, in Annual Meeting of the Transportation Research Board. 2003:

Washington D.C.

65

CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER

RESEARCH

5.1. Conclusions

This thesis developed analytical models to estimate the optimum cycle length that minimizes the

intersection delay, fuel consumption levels, and greenhouse gas emissions. It included two

studies conducted by the author and committee members. The first study analyzed one synthetic

isolated intersection with one lane from each approaching direction and a signal plan with two

phases. In second study, four real intersections with realistic lane configurations and real speed

limits settings in the area of Blacksburg, Virginia, were used in the simulation analysis. Left-turn

protected phases were introduced based on the demand level and recommendation by the

Highway Capacity Manual (HCM). The INTEGRATION microscopic traffic simulation

software was used to generate the noted measures of effectiveness (MOEs) at four study

intersections under different demand levels, cycle lengths, and signal lost times. The

INTEGRATION results were then enhanced by implementing 20 random seeds per simulation

scenario. For each study intersection, optimum cycle lengths were then identified for each traffic

demand scenario with the purpose of minimizing intersection delay, fuel consumption levels, and

total emissions.

To identify the optimum cycle lengths that minimize vehicle delay, fuel consumption

levels, and total emissions levels, a regression model was fit to the simulation data. The results

are compatible with the first study by the authors in terms of optimum cycle lengths. For

minimizing fuel consumption and Green House Gas (GHG) emissions, longer cycle lengths are

consistently favored in comparison to the optimum cycle lengths to minimize vehicle delay. The

results demonstrate that the model coefficients are significantly different depending on the MOE

being minimized. The fuel consumption and emissions formulations were similar. Compared to

the optimum cycle lengths to minimize delays, these two formulations required a longer

minimum cycle length threshold. Equations (1) to (3) show the overall proposed formulations

presented in this thesis.

𝐶!"#,!"#$% = !.!!!!.!!!!

+ 20 (1)

𝐶!"#,!"#$ = !

!!!+ 55 (2)

𝐶!"#,!"#$$#%&$ = !

!!!+ 55 (3)

66

Implementing twenty random seeds in the simulation runs, in comparison to only one

random seed, was shown to produce better regression results. When implementing one random

seed per simulation run, several model coefficients for each intersection formulation were not

significant. When implementing twenty random seeds per simulation run, the majority of the

model coefficients were significant. Also, each proposed overall formulations had a higher

prediction power in comparison to the formulations under one seed per simulation run.

This thesis demonstrated that the proposed delay formulation was comparable to the

Webster formulation when the demand is low. However, minimizing vehicle delay using the

Webster method will typically overestimate the optimum cycle length at high traffic demand

levels. The design of the traffic signal needs to be balanced and optimized for different purposes.

5.2. Recommendations for Future Research

This thesis developed a model for estimating the optimum cycle lengths to minimize delay, fuel

consumption, and GHG emissions at isolated intersections. However, more work can be done to

enhance and validate the model. It is recommended that the following research activities be

pursued:

• The four study intersections selected in this thesis demonstrate slightly different results in

fitting the models. The factors that caused such variations need to be further investigated.

• The model should be calibrated against existing vehicle demands at the four study

intersections, or vehicle demands from other urban isolated intersections.

• This research was limited to investigating isolated intersections. Future research should

investigate arterial networks and actuated signal timings using the NEMA phasing

scheme.

• In investigating arterial networks, optimum offsets should also be a parameter to

consider.

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