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Convergence of fixed-point algorithms for elastic demand dynamic user equilibrium

Terry L. Friesz, Ke Han and Amir Bagherzadeh

Transportation Research Part B: Methodological, 2021, vol. 150, issue C, 336-352

Abstract: In this paper we present sufficient conditions for convergence of projection and fixed-point algorithms used to compute dynamic user equilibrium with elastic travel demand (E-DUE). The assumption of strongly monotone increasing path delay operators is not needed. In its place, we assume path delay operators are merely weakly monotone increasing, a property assured by Lipschitz continuity, while inverse demand functions are strongly monotone decreasing. Lipschitz continuity of path delay is a very mild regularity condition. As such, nonmonotone delay operators may be weakly monotone increasing and satisfy our convergence criteria, provided inverse demand functions are strongly monotone decreasing. We illustrate convergence for nonmonotone path delays via a numerical example.

Keywords: Dynamic traffic assignment; Dynamic user equilibrium; Convergence; Differential variational inequalities (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.trb.2021.01.007

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