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|a Feedback control theory for dynamic traffic assignment /
|c Pushkin Kachroo, Kaan M.A. Özbay
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|a Second edition
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|a Cham, Switzerland :
|b Springer Science and Business Media :
|b Springer,
|c [2018]
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|c ©2018
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|a 1 online resource (xxxi, 272 pages : illustrations)
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|a Advances in industrial control
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|a Includes bibliographical references and index
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|a Intro; Series Editors' Foreword; Preface to the Second Edition; Preface to the First Edition; Acknowledgements; Contents; Abbreviations; List of Figures; List of Tables; Part I Introduction to Feedback Control and Dynamic Traffic Assignment; 1 Introduction; 1.1 Dynamic Traffic Routing; 1.1.1 Objectives; 1.2 Control Algorithm Design; 1.2.1 Sensing; 1.2.2 Actuation; 1.2.3 Automatic Control Versus Human-in-the-loop Control; 1.2.4 Overall System; 1.2.5 Traffic Analysis Notation; 1.3 Real-Time DTR; 1.4 Literature Review; 1.5 Feedback Control; 1.5.1 Control Design Steps
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|a 1.5.2 Feedback Control Example1.5.3 Other Issues; 1.6 Summary; 1.7 Exercises; 1.7.1 Questions; 1.7.2 Problems; References; 2 Traffic Assignment: A Survey of Mathematical Models and Techniques; 2.1 Introduction; 2.2 Mathematical Programming-Based Static Traffic Assignment Model; 2.2.1 User-Equilibrium; 2.2.2 System Optimal Solution; 2.2.3 Numerical Schemes; 2.3 Variational Inequality-Based Static Traffic Assignment Model; 2.4 Projected Dynamical Systems: Dynamic Variational Equation Model; 2.4.1 Dynamic Route Choice; 2.5 Dynamic Traffic Assignment
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|a 2.5.1 Dynamic Traffic Assignment: Discrete Time2.5.2 Dynamic Traffic Assignment: Continuous Time; 2.6 Travel Time and FIFO Issue; 2.7 Macroscopic Model for DTA; 2.7.1 Greenshields' Model; 2.7.2 Generalized/Weak Solution for the LWR Model; 2.7.3 Scalar Initial-Boundary Problem; 2.7.4 Macroscopic (PDE) Traffic Network; 2.7.5 Travel Time Dynamics; 2.8 Simulation-Based DTA; 2.8.1 Iterations for User-Equilibrium; 2.8.2 Calibration from Field Data; 2.9 Traffic Operation Design and Feedback Control; 2.10 Summary; 2.11 Exercises; 2.11.1 Questions; 2.11.2 Problems; References
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|a 3.7.1 Traffic Problem3.8 Method of Characteristics to Solve First Order PDEs; 3.9 Traffic Shock Wave Propagation; 3.9.1 Alternate Derivation for Shock Wave Speed; 3.9.2 Generalized/Weak Solution for the LWR Model; 3.9.3 Scalar Initial Boundary Problem; 3.10 Traffic Measurements; 3.11 Summary; 3.12 Exercises; 3.12.1 Questions; 3.12.2 Problems; References; 4 Modeling and Problem Formulation; 4.1 Introduction; 4.2 System Dynamics; 4.3 Feedback Control for Traffic as a Distributed Parameter System; 4.3.1 Diffusive Burgers' Equation; 4.3.2 DTR Formulation; 4.4 Discretized System Dynamics
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|a Part II Traffic Flow Theory and Traffic Assignment Modeling3 Traffic Flow Theory; 3.1 Introduction; 3.2 Lighthill-Whitham-Richards Model; 3.3 Traffic Density-Flow Relationships; 3.3.1 Greenshields' Model; 3.3.2 Greenberg Model; 3.3.3 Underwood Model; 3.3.4 Northwestern University Model; 3.3.5 Drew Model; 3.3.6 Pipes-Munjal Model; 3.3.7 Multiregime Models; 3.3.8 Diffusion Model; 3.4 Microscopic Traffic Characteristics; 3.5 Traffic Model; 3.6 Classification of PDEs; 3.6.1 Variables; 3.6.2 Order of the PDE; 3.6.3 Linearity; 3.6.4 Boundary Conditions; 3.7 Existence of Solutions
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|a This book develops a methodology for designing feedback control laws for dynamic traffic assignment (DTA) exploiting the introduction of new sensing and information-dissemination technologies to facilitate the introduction of real-time traffic management in intelligent transportation systems. Three methods of modeling the traffic system are discussed: partial differential equations representing a distributed-parameter setting; continuous-time ordinary differential equations (ODEs) representing a continuous-time lumped-parameter setting; and discreet-time ODEs representing a discrete-time lumped-parameter setting. Feedback control formulations for reaching road-user-equilibrium are presented for each setting and advantages and disadvantage of using each are addressed. The closed-loop methods described are proposed expressly to avoid the counter-productive shifting of bottlenecks from one route to another because of driver over-reaction to routing information. The second edition of Feedback Control Theory for Dynamic Traffic Assignment has been thoroughly updated with completely new chapters: a review of the DTA problem and emphasizing real-time-feedback-based problems; an up-to-date presentation of pertinent traffic-flow theory; and a treatment of the mathematical solution to the traffic dynamics. Techinques accounting for the importance of entropy are further new inclusions at various points in the text. Researchers working in traffic control will find the theoretical material presented a sound basis for further research; the continual reference to applications will help professionals working in highway administration and engineering with the increasingly important task of maintaining and smoothing traffic flow; the extensive use of end-of-chapter exercises will help the graduate student and those new to the field to extend their knowledge. Advances in Industrial Control reports and encourages the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control
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