Elastic demand dynamic network user equilibrium: Formulation, existence and computation

Abstract

This paper is concerned with dynamic user equilibrium with elastic travel demand (E-DUE) when the trip demand matrix is determined endogenously. We present an infinite-dimensional variational inequality (VI) formulation that is equivalent to the conditions defining a continuous-time E-DUE problem. An existence result for this VI is established by applying a fixed-point existence theorem (Browder, 1968) in an extended Hilbert space. We present three algorithms based on the aforementioned VI and its re-expression as a differential variational inequality (DVI): a projection method, a self-adaptive projection method, and a proximal point method. Rigorous convergence results are provided for these methods, which rely on increasingly relaxed notions of generalized monotonicity, namely mixed strongly-weakly monotonicity for the projection method; pseudomonotonicity for the self-adaptive projection method, and quasimonotonicity for the proximal point method. These three algorithms are tested and their solution quality, convergence, and computational efficiency compared. Our convergence results, which transcend the transportation applications studied here, apply to a broad family of infinite-dimensional VIs and DVIs, and are the weakest reported to date.

32 pages, 6 figures, 2 tables

References in corpus (4)

• Existence of simultaneous route and departure choice dynamic user equilibrium
• Elastic demand dynamic network user equilibrium: Formulation, existence and computation
• Existence of optima and equilibria for traffic flow on networks
• Continuity of the Effective Path Delay Operator for Networks Based on the Link Delay Model

Cited by in corpus (6)

• Elastic demand dynamic network user equilibrium: Formulation, existence and computation
• Continuity of the path delay operator for dynamic network loading with spillback
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• System optimality versus self-organization in metro networks: An optimal transport analysis
• Computing Dynamic User Equilibria on Large-Scale Networks: From Theory to Software Implementation