Slope-based Path Shift Propensity Algorithm for the Static Traffic Assignment Problem

This paper presents a path-based traffic assignment algorithm for solving the static deterministic user equilibrium traffic assignment problem. It uses the concepts of the path shift-propensity factor and the sensitivity of path costs with respect to path flows in the flow update process, and is labeled as the slope-based path shift-propensity algorithm (SPSA). It seeks to enable faster convergence, incorporates behavioral realism in the flow update process, and maintains simplicity of execution for easy deployment in practice. The behavioral rationale behind the proposed algorithm is explained. The mathematical exposition of the algorithm and its proof of convergence are articulated. Numerical experiments are conducted using test networks to benchmark the performance of SPSA. The computational performance of the SPSA is compared with those of two versions of the recently developed path-based algorithm labeled slope-based multipath algorithm (SMPA), the widely-used Frank-Wolfe (F-W) algorithm, and a variant of the F-W algorithm labeled the social pressure algorithm (SPA). They illustrate that the rate of convergence of the SPSA is very close to that of the SMPA and significantly better than those of the F-W algorithm and the SPA. One version of the SMPA performs better than the SPSA in terms of convergence, though the latter is easier to implement and hence a potential substitute for SMPA in practice. Further, the results vindicate the notion that the SPSA is a feasible deployment option under the computational capabilities available today.