Approximating Time Delays in Solving Continuous-Time Dynamic User Equilibria

摘要

We develop an approximation scheme, called pseudo-derivative (PD)" to solving the dynamic userequilibrium (DUE) problem. The PD approximation can convert time-varying, state dependentdelays usually involved in DUE to a constant time delay. We study the properties of the proposedPD and the resulting approximate DUE (ADUE) problem after applying the approximation. Someissues of the ADUE, such as the possible violation of the °ow conservation at network nodes arealso discussed and resolved. It turns out that the original DUE problem can be solved iterativelywith an ADUE solved in each iteration. Numerical results are shown on a small testing networkand the Sioux Falls network. The results show that the iterative algorithm can converge to somereasonable soultion, although a formal convergence proof result is not established in the paper.