Queue Replacement Approach to Dynamic User Equilibrium Assignment with Route and Departure Time Choice

TL;DR

This paper introduces a hybrid analytical-numerical method for solving dynamic user equilibrium problems with route and departure time choices, using a queue replacement principle linked to linear programming.

Contribution

It proposes the generalized queue replacement principle (GQRP) and a systematic LP-based procedure for exact DUE solutions with simultaneous route and departure time choices.

Findings

The method accurately computes DUE solutions on various network scales.

The GQRP provides a new equivalence between queueing delays and LP solutions.

Computational results confirm the approach's effectiveness.

Abstract

This study develops a hybrid analytical and numerical approach for dynamic user equilibrium (DUE) assignment with simultaneous route and departure time choice (RDTC) for homogeneous users. The core concept of the proposed approach is the generalized queue replacement principle (GQRP), which establishes an equivalence between the equilibrium queueing-delay pattern and the solution to a linear programming (LP) problem obtained by relaxing some conditions in the original DUE-RDTC problem. We first present a method for determining whether the GQRP holds. Based on the GQRP, we then develop a systematic procedure to obtain an exact DUE solution by sequentially solving two LPs: one for the equilibrium cost pattern, including queueing delays, and the other for the corresponding equilibrium flow pattern. Computational results on networks of varying scales confirm the effectiveness of the proposed method.