Modeling Drivers’ Acceleration and Lane Changing Behavior by Kazi Iftekhar Ahmed B. Sc. Eng. (Civil) Bangladesh Univ. of Eng. and Technology (BUET), Dhaka, Bangladesh (1991) M.S. in Transportation Massachusetts Institute of Technology, Cambridge, MA (1996) Submitted to the Department of Civil and Environmental Engineering in partial ful(cid:12)llment of the requirements for the degree of Doctor of Science in Transportation Systems and Decision Sciences at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY February 1999 c Massachusetts Institute of Technology 1999. All rights reserved. (cid:13) Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Department of Civil and Environmental Engineering January 8, 1999 Certi(cid:12)ed by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Moshe E. Ben-Akiva Professor of Civil and Environmental Engineering Thesis Supervisor Certi(cid:12)ed by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dr. Haris N. Koutsopoulos Operations Research Analyst Thesis Supervisor Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrew J. Whittle Chairman, Departmental Committee on Graduate Studies Modeling Drivers’ Acceleration and Lane Changing Behavior by Kazi Iftekhar Ahmed Submitted to the Department of Civil and Environmental Engineering on January 8, 1999, in partial ful(cid:12)llment of the requirements for the degree of Doctor of Science in Transportation Systems and Decision Sciences Abstract This thesis contributes to the development of microscopic tra(cid:14)c performance models which includes the acceleration and lane changing models. It enhances the existing models and develops new ones. Another major contribution of this thesis is the empirical work, i.e., estimating the models using statistically rigorous methods and microscopic data collected from real tra(cid:14)c. Theaccelerationmodelde(cid:12)nestworegimesoftra(cid:14)c(cid:13)ow: thecar{followingregime and the free{(cid:13)ow regime. In the car{following regime, a driver is assumed to fol- low his/her leader, while in the free{(cid:13)ow regime, a driver is assumed to try to at- tain his/her desired speed. A probabilistic model, that is based on a time headway threshold, is used to determine the regime the driver belongs to. Heterogeneity across drivers is captured through the headway threshold and reaction time distributions. The parameters of the car{followingand free{(cid:13)ow acceleration models along with the headway threshold and reaction time distributions are jointly estimated using the maximum likelihood estimation method. The lane changing decision process is modeled as a sequence of three steps: de- cision to consider a lane change, choice of a target lane, and gap acceptance. Since acceptable gaps are hard to (cid:12)nd in a heavily congested tra(cid:14)c, a forced mergingmodel that captures forced lane changing behavior and courtesy yielding is developed. A discretechoicemodelframeworkisusedtomodeltheimpactofthesurroundingtra(cid:14)c environment and lane con(cid:12)guration on drivers’ lane changing decision process. The models are estimated using actual tra(cid:14)c data collected from Interstate 93 at the Central Artery, located in downtown Boston, MA, USA. In addition to assessing the model parameters from statistical and behavioral standpoints, the models are validated using a microscopic tra(cid:14)c simulator. Overall, the empirical results are encouraging, and demonstrate the e(cid:11)ectiveness of the modeling framework. Thesis Supervisor: Moshe E. Ben-Akiva Title: Professor of Civil and Environmental Engineering Massachusetts Institute of Technology Thesis Supervisor: Dr. Haris N. Koutsopoulos Title: Operations Research Analyst Volpe National Transportation Systems Center Cambridge, MA, USA. 4 To Abbu, Ammu, my son, Sabih, and my wife, Lubna 5 Thesis Committee Moshe E. Ben-Akiva (Chairman) Professor Department of Civil and Environmental Engineering Massachusetts Institute of Technology Haris N. Koutsopoulos Operations Research Analyst Volpe National Transportation Systems Center Ismail Chabini Assistant Professor Department of Civil and Environmental Engineering Massachusetts Institute of Technology Mithilesh Jha Research Associate Center for Transportation Studies Massachusetts Institute of Technology 6 Acknowledgments I acknowledge with deep sense of gratitude the guidance, invaluable advice, and con- stant inspiration provided by my supervisors Prof. Moshe Ben{Akiva and Dr. Haris Koutsopoulos during the course of my studies. I feel privilegedto get the opportunity to work with them for the last (cid:12)ve years. I have learned a lot from them during the course of this research. I am grateful to the other members of my dissertation committee|Prof. Ismail Chabini and Dr. Mithilesh Jha, for their advice, feed back, and inspiration during the course of this research. My special thanks goes to the following individuals without whose contribution this thesis could not be completed: Dr. Qi Yang, Dr. Kalidas Ashok, Prof. Rabi Mishalani, Prof. Michel Bierlaire, Alan Chachich, Dave Cuneo, Masroor Hasan, Dr. Owen Chen, Russel Spieler, Tania Amin, Khwaja Ehsan, Shahnaz Islam, and Prof. Sha(cid:12)qul Islam. I am also thankful to the CA/T project at the ITS Research Program for (cid:12)nan- cially supporting my (cid:12)ve years of studies at MIT. I would like to thank my friends, fellow students, and administrative sta(cid:11) at the CEE Department, CTS, and ITS O(cid:14)ce, that made my life at MIT an enjoyable experience, especially,Adriana,Amalia,Andras,Atul,Bruno,Cheryl,Chris,Cynthia, Denise, Didier, Dinesh, Dale, Deiki, Dong, Hari, Hong, Je(cid:11), Jessei, John, Jon, Joan, Juli, Krishna, Lisa, Mark, Masih, Nagi, Niranjan, Pat, Paula, Peter, Prodyut Da, Shenoi, Scott, Sreeram, Sridevi, Sudhir, Susan, Tomer, Winston, and Yan. Thanks are due to fellow Bangladeshis Adnan, Fahria and Zeeshan, Minu and Monjur, Oni and Arif, Rima, Rita and Mukul, Rumi and Saquib, Sabah and Mah- mood, and Shampa and Sabet, for their friendship and support. Finally, I wish I knew a better way to express my indebtedness to my wife, Lubna, my three year old son, Sabih, for their unconditional support, endless love, to my parents for their encouragement and inspiration throughout my life that helped me outgrow again and again. 7 Contents 1 Introduction 18 1.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 Literature Review 25 2.1 Acceleration Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.1 Car{Following Models . . . . . . . . . . . . . . . . . . . . . . 26 2.1.2 General Acceleration Models . . . . . . . . . . . . . . . . . . . 34 2.1.3 Estimation of the Brake Reaction Time . . . . . . . . . . . . . 37 2.2 Lane Changing Models . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.1 Gap Acceptance Models . . . . . . . . . . . . . . . . . . . . . 42 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3 The Acceleration Model 46 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2 The Acceleration Model . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.2.1 The Car{Following Model . . . . . . . . . . . . . . . . . . . . 49 3.2.2 The Free{Flow Acceleration Model . . . . . . . . . . . . . . . 54 3.2.3 The Headway Threshold Distribution . . . . . . . . . . . . . . 56 3.2.4 The Reaction Time Distribution . . . . . . . . . . . . . . . . . 57 8 3.3 Likelihood Function Formulation . . . . . . . . . . . . . . . . . . . . 59 3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4 The Lane Changing Model 63 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.2 The Lane Changing Model . . . . . . . . . . . . . . . . . . . . . . . . 65 4.2.1 Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . 65 4.2.2 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . 67 4.2.3 Likelihood Function Formulation . . . . . . . . . . . . . . . . 71 4.2.4 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3 The Forced Merging Model . . . . . . . . . . . . . . . . . . . . . . . . 75 4.3.1 Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . 76 4.3.2 Model Formulation . . . . . . . . . . . . . . . . . . . . . . . . 77 4.3.3 Likelihood Function Formulation . . . . . . . . . . . . . . . . 78 4.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5 Data Requirements for Estimating Driver Behavior Models 85 5.1 Methodology for Estimating Instantaneous Speed and Acceleration from Discrete Trajectory Data . . . . . . . . . . . . . . . . . . . . . . 86 5.1.1 The Local Regression Procedure . . . . . . . . . . . . . . . . . 87 5.2 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.2.1 Description of the Data Collection Site . . . . . . . . . . . . . 91 5.2.2 Video Processing Software . . . . . . . . . . . . . . . . . . . . 93 5.2.3 Processing the Tra(cid:14)c Data . . . . . . . . . . . . . . . . . . . 94 5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6 Estimation Results 107 6.1 Estimation Results of the Acceleration Model . . . . . . . . . . . . . 107 6.1.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.2 Estimation Results of the Lane Changing Model . . . . . . . . . . . . 121 9 6.2.1 Estimation Results of the Discretionary Lane Changing Model 121 6.2.2 Estimation Results of the Mandatory Lane Changing Model . 133 6.2.3 Estimation Results of the Forced Merging Model . . . . . . . 140 6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7 Model Validation Using a Microscopic Tra(cid:14)c Simulator 146 7.1 MITSIM: a Microscopic Tra(cid:14)c Simulator . . . . . . . . . . . . . . . . 147 7.1.1 The Acceleration Model . . . . . . . . . . . . . . . . . . . . . 148 7.1.2 The Lane Changing Model . . . . . . . . . . . . . . . . . . . . 149 7.2 Validation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.2.1 Number of Replications . . . . . . . . . . . . . . . . . . . . . 153 7.2.2 Measures of Goodness{of{(cid:12)t . . . . . . . . . . . . . . . . . . . 154 7.3 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.3.1 The Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.3.2 Tra(cid:14)c Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 7.3.3 O{D Estimation from Tra(cid:14)c Counts . . . . . . . . . . . . . . 160 7.3.4 MITSIM Modi(cid:12)cations . . . . . . . . . . . . . . . . . . . . . . 163 7.3.5 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . 164 7.3.6 Validation Results . . . . . . . . . . . . . . . . . . . . . . . . 164 7.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 8 Conclusions and Future Research Directions 173 8.1 Summary of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 8.1.1 The Acceleration Model . . . . . . . . . . . . . . . . . . . . . 173 8.1.2 The Lane Changing Model . . . . . . . . . . . . . . . . . . . . 175 8.1.3 Validation by Microsimulation . . . . . . . . . . . . . . . . . . 176 8.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 8.3 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . 178 8.3.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 8.3.2 Estimation and Validation . . . . . . . . . . . . . . . . . . . . 179 8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 10