Modeling and solving continuous-time instantaneous dynamic user equilibria: A differential complementarity systems approach

Ban, Xuegang (Jeff), Jong-Shi Pang, Henry X. Liu and Rui Ma

Transportation Research Part B: Methodological, 2012, vol. 46, issue 3, 389-408

Abstract: This paper is the second of a two-part research wherein we undertake a mathematically rigorous investigation of the continuous-time dynamic user equilibrium (DUE) problem using the recently introduced mathematical paradigm of differential complementarity systems (DCSs). Based on the thorough study of continuous-time single-destination point-queue models in the previous part, we first extend this special case to multiple destinations respecting the First-In–First-Out property of travel flows. A DCS with constant time delay is then introduced to formulate the continuous-time model of instantaneous dynamic traffic equilibria (IDUE) with a fixed demand profile. We develop a time decomposition scheme based on link free flow travel times to convert the delay DCS to a series of DCSs without time delays that are solved by a numerical time-stepping method. We provide rigorous numerical treatment of the time-decomposed IDUE model, including solvability of the discrete-time complementarity problems and convergence of the numerical trajectories to a continuous-time solution. We present numerical results to validate the IDUE on a small network and also on the Sioux Falls network.

Keywords: Dynamic traffic assignment; Continuous-time instantaneous dynamic user equilibrium; Differential variational inequality; Differential complementarity system; Time delay ordinary differential equation; Convergence (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (14)

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DOI: 10.1016/j.trb.2011.11.002

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