Dynamic Network User Equilibrium

This book presents advanced research in a relatively new field of scholarly inquiry that is usually referred to as dynamic network user equilibrium, now almost universally abbreviated as DUE. It provides the first synthesis of results obtained over the last decade from applying the differential variational inequality (DVI) formalism to study the DUE problem. In particular, it explores the intimately related problem of dynamic network loading, which determines the arc flows and effective travel delays (or generalized travel costs) arising from the expression of departure rates at the origins of commuter trips between the workplace and home.

In particular, the authors show that dynamic network loading with spillback of queues into upstream arcs may be formulated as a differential algebraic equation system. They demonstrate how the dynamic network loading problem and the dynamic traffic user equilibrium problem may be solved simultaneously rather than sequentially, as well as how the first-in-first-out queue discipline may be maintained for each when Lighthill-Whitham-Richardson traffic flow theory is used. A number of recent and new extensions of the DVI-based theory of DUE and corresponding examples are presented and discussed. Relevant mathematical background material is provided to make the book as accessible as possible.

Introduction.- Mathematical Preliminaries.- The Variational Inequality Formulation of Dynamic User Equilibria.- The Differential Variational Inequality Formulation of Dynamic User Equilibria.- Existence of Dynamic User Equilibria.- Algorithms for Computing Dynamic User Equilibria.- Dynamic Network Loading: Non-Physical Queue Models.- Dynamic Network Loading: Physical Queue Models.- Numerical Results.

Terry L. Friesz is the Harold & Inge Marcus Chaired Professor of Industrial and Manufacturing Engineering at the Pennsylvania State University, USA. He earned his Ph.D. at Johns Hopkins University. His research interests include differential congestion games, freight systems, supply chains, spatial economics, pricing, and revenue management. He is Editor-in-Chief of Networks and Spatial Economics (Springer), Founding Series Editor of Complex Networks and Dynamic Systems (Springer), and the author of several Springer books.

Ke Han is Professor at School of Transportation and Logistics and Director of Institute of System Science and Engineering at Southwest Jiaotong University, China. He received his BSc degree from the University of Science and Technology of China, and his PhD at the Pennsylvania State University. He was appointed as Lecturer in 2013 and Senior Lecturer in 2018 at the Center for Transport Studies, Department of Civil and Environmental Engineering, Imperial College London, UK. His research interests include transportation, sustainability, and smart cities.