A path marginal cost approximation algorithm for system optimal quasi-dynamic traffic assignment

Abstract

This study introduces an efficient path-based System-Optimal Quasi-Dynamic Traffic Assignment (SOQDTA) framework that benefits from the computational efficiency of static traffic assignment models, yet captures the realism of traffic flow, with less complexity and a lower computational burden, compared to dynamic traffic assignment models. To solve the proposed SOQDTA problem, we have developed a novel Path Marginal Cost (PMC) approximation algorithm, based on a Quasi-Dynamic Network Loading (QDNL) procedure (Bliemer et al., 2014), that incorporates a first order node model, and thus produces realistic path travel times consistent with queuing theory, and similar to those of dynamic network loading models, but at a lower computational cost. The model considers capacity constrained static flows, residual vertical/point queues and no spillback. The proposed SOQDTA model is applied to the test network of Sioux Falls and is demonstrated to result in system optimal traffic flow patterns that improve total system travel times compared to the user equilibrium solution. In the case study experiment, the convergence of the algorithm is demonstrated using a relative gap function. A sensitivity analysis is performed to realize the impact of perturbation size on the solution quality, and a discussion is presented on the selection of perturbation size for general network applications.