A Comparative Analysis of the Effect of Route Set Size in Logit and Weibit-Based Stochastic Traffic Assignment

This study presents a comprehensive comparative analysis of the effect of route set size on stochastic user equilibrium (SUE) traffic assignment, focusing on both logit-based (Multinomial Logit (MNL) and Path Size Logit (PSL)) and weibit-based models (Multinomial Weibit (MNW) and Path Size Weibit (PSW)). The primary objective is to investigate the influence of route set size on traffic patterns and determine the minimum requisite number of routes for flow stabilization within the SUE framework. The analysis, conducted on the Winnipeg network using a customized Self-Regulated Averaging (SRA) scheme, yields three key findings. First, all models successfully converged, but the weibit-based models (MNW and PSW) converged faster than the logit-based models. Second, an analysis of perceived total travel time demonstrated that the majority of efficiency gains from route inclusion diminish after a threshold of approximately maximum 30 routes to 40 routes per O-D pair, indicating this number is sufficient for achieving stable SUE results in both model families. Third, the weibit-based model was found to be more sensitive to route overlap effects, continuing to adjust flow patterns up to maximum 45 routes per O-D pair, and exhibiting a greater tendency to allocate flow to less overlapping outer roads. This highlights the superior capability of the weibit formulation, which accounts for heterogeneous perception variance, to achieve a more behaviorally realistic equilibrium compared to the logit models.