Approximating time delays in solving continuous-time dynamic user equilibria
Authors: Rui Ma, Xuegang Jeff Ban, Jong-Shi Pang, Henry X. Liu
We develop an approximation scheme, called “pseudo-derivative (PD)” to solving the dynamic user equilibrium (DUE) problem. The PD approximation can convert time-varying, state dependent delays usually involved in DUE to a constant time delay. We study the properties of the proposed PD and the resulting approximate DUE (ADUE) problem after applying the approximation. Some issues of the ADUE, such as the possible violation of the flow conservation at network nodes are also discussed and resolved. It turns out that the original DUE problem can be solved iteratively with an ADUE solved in each iteration. Numerical results are shown on a small test network and the Sioux Falls network. The results show that the iterative algorithm can converge to some reasonable solution, although a formal convergence proof result is not established in the paper.