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Netw Spat Econ (2010) 10:4971
DOI 10.1007/s11067-007-9022-y
Yu (Marco) Nie & H. M. Zhang
Published online: 1 June 2007# Springer Science + Business Media, LLC 2007
Abstract This paper studies the dynamic user optimal (DUO) traffic assignment problem considering simultaneous route and departure time choice. The DUO problem is formulated as a discrete variational inequality (DVI), with an embeded LWR-consistent mesoscopic dynamic network loading (DNL) model to encapsulate traffic dynamics. The presented DNL model is capable of capturing realistic traffic phenomena such as queue spillback. Various VI solution algorithms, particularly those based on feasible directions and a line search, are applied to solve the formulated DUO problem. Two examples are constructed to check equilibrium solutions obtained from numerical algorithms, to compare the performance of the algorithms, and to study the impacts of traffic interacts across multiple links on equilibrium solutions.
Keywords Dynamic user optimal traffic assignment . Dynamic network loading . Variational inequality . Feasible direction algorithms
1 Introduction
Predicting the temporal and spatial traffic evolution over road networks has attracted numerous research efforts since the 1970s, when transportation researchers began to recognize the limitations of static network equilibrium models (Wardrop 1952, Beckmann et al. 1956) in describing a system that essentially varies over time. These limitations include, among others, the inability of modeling departure time decisions and the formation and dissipation of queues when travel demands temporarily exceed road capacities at different locations, two important elements to consider in traffic congestion management.
(M.) Nie (*)
Y. (. Nie (*)
Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL, USA e-mail: mailto:[email protected]
Web End [email protected]
H. M. Zhang
Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USAe-mail: [email protected]
Solving the Dynamic User Optimal Assignment Problem Considering Queue Spillback
50 Y. Nie, H.M. Zhang
The earliest work to bring the time dimension into equilibrium analysis is perhaps Vickreys seminal paper on the morning commute problem (Vickrey 1969), in which traffic congestion takes the form of queuing behind a bottleneck caused by temporal demand surge. Vickreys bottleneck model stimulated numerous studies on the morning commute problem. Most of these studies focused on finding analytical equilibrium solutions and/or exploring economic and policy insights (e.g., Mahmassani and Herman 1984, Newell 1987, Arnott et al....