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

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.