The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering IMPACT OF ADAPTIVE CRUISE CONTROL ON THE FORMATION OF SELF-ORGANIZED TRAFFIC JAMS ON HIGHWAYS

...................................................................................................................... iii LIST OF FIGURES .............................................................................................................. vi ACKNOWLEDGEMENTS .................................................................................................... ix CHAPTER 1 – INTRODUCTION ........................................................................................... 2 1.1 Motivation .................................................................................................................. 2 1.1.1 Self-organization and Emergence .................................................................. 3 1.1.2 Traffic jams and Adaptive cruise control .......................................................... 5 1.2 Problem Statement ..................................................................................................... 6 1.3 Outline of Remaining Chapters ................................................................................... 7 CHAPTER 2 – LITERATURE REVIEW .................................................................................... 8 2.1 Fundamental Diagram of Traffic Flow ........................................................................ 8 2.2 Existing Modeling Techniques .................................................................................... 11 2.2.1 Microscopic Modeling ...................................................................................... 11 2.2.2 Macroscopic Modeling ..................................................................................... 13 2.2.3 Mesoscopic Modeling....................................................................................... 15 2.2.4 Selection of a Traffic Flow Modeling Technique .............................................. 17 2.3 Adaptive cruise control ............................................................................................... 18 2.3.1 Adaptive cruise control algorithms .................................................................. 19 2.3.2 Studies on impact of ACC on traffic flow .......................................................... 23 2.4 Self-organization and traffic jams ............................................................................... 24 2.4.1 Analysis of self-organizing systems .................................................................. 24 2.4.2 Self-organizing traffic jams ............................................................................... 26 2.5 Summary ..................................................................................................................... 28 CHAPTER 3 – THE MASTER EQUATION APPROACH ............................................................ 29 3.1 System description and behavior ............................................................................... 29 3.2 The Master equation .................................................................................................. 32 3.2.1 The Markov process assumption ...................................................................... 32 3.2.2 The Chapman-Kolomogorov equations ............................................................ 33 3.2.3 Derivation of the master equation ................................................................... 34 3.3 Stationarity and detailed balance ............................................................................... 38 3.3.1 Stationarity condition ....................................................................................... 38 3.3.2 Detailed balance ............................................................................................... 39