Solving the Dynamic User Equilibrium Problem Via Sequential Convex Optimization for Parallel Horizontal Queuing Networks

This article considers the dynamic user equilibrium (DUE) problem for parallel networks. The network dynamics are modeled using a Godunov discretization of the Lighthill-Williams-Richards partial differential equation with a trapezoidal flux function. The model is augmented with an additional constraint that prevents vehicle holding which is a flaw in the discretization. The departure rates are assumed to be fixed. Under these assumptions, the authors show that the future allocation of the demand among the different paths at the origin has no effect on the travel time of the vehicles already in the network. This enables them to show that the DUE for a fixed time steps horizon can be decomposed into a series of static UE problems and solved sequentially. Thus, the DUE problem can be solved as a sequence of convex optimization problems.