A nonlinear equation system approach to the dynamic stochastic user equilibrium simultaneous route and departure time choice problem

In dynamic stochastic user equilibrium simultaneous route and departure time choice (DSUE-SRDTC) problems, route travel costs can be non-monotone even if route travel times are monotone with respect to route flows. As a result, the mapping function of the variational inequality (VI) problems for the...

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Bibliographic Details
Published in:Transportmetrica (Abingdon, Oxfordshire, UK) Vol. 11; no. 5; pp. 388 - 419
Main Authors: Long, Jiancheng, Szeto, W.Y., Shi, Qin, Gao, Ziyou, Huang, Hai-Jun
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 28.05.2015
Taylor & Francis Ltd
Subjects:
Algorithms
BFGS method
Convergence
dynamic stochastic user equilibrium
dynamic traffic assignment
Dynamical systems
Equilibrium
iterative method
Mapping
Mathematical analysis
Mathematical models
Nonlinear dynamics
Nonlinear equations
Optimization
simultaneous route and departure time choice
ISSN:2324-9935, 2324-9943
Online Access:Get full text
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Summary:In dynamic stochastic user equilibrium simultaneous route and departure time choice (DSUE-SRDTC) problems, route travel costs can be non-monotone even if route travel times are monotone with respect to route flows. As a result, the mapping function of the variational inequality (VI) problems for the DSUE-SRDTC problems can be non-monotone, and many existing solution algorithms developed for the DSUE-SRDTC problems do not guarantee convergence under this non-monotone condition. This paper formulates the DSUE-SRDTC problem with fixed demand as a system of nonlinear equations. The mapping function of the proposed system of nonlinear equations is defined by a dynamic route choice problem, which can also be formulated as a VI problem with a strictly monotone mapping function under some assumptions. This property enables that the solution algorithm for the DSUE-SRDTC problem can avoid the requirement of the monotonicity of the route travel cost functions for the convergence of the solution procedure. A backtracking inexact Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is adopted to solve the system of nonlinear equations, and iterative methods are developed to generate an initial solution for the BFGS method and solve the dynamic route choice problem. Finally, numerical examples are set up to show that the proposed method outperforms many existing algorithms for solving the DSUE-SRDTC problem in terms of guaranteeing solution convergence.
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ISSN:2324-9935
2324-9943
DOI:10.1080/23249935.2014.1003112