Modeling the Non-Identical Perception Variance in Day-to-Day Dynamics via Weibit-Based Network Loading Function

The Weibit choice model has gained increasing attention in transportation studies. Compared with the commonly used Logit model, the Weibit model inherently captures the heterogeneous travel perceptions by allowing non-identical variances for different alternatives. Nevertheless, how travelers’ heterogeneous perception errors may influence day-to-day (DTD) network dynamics, in which route choice decisions are made on each day, remains underexplored. In this study, we present several deterministic discrete DTD dynamic traffic models with Weibit-based network loading function, termed Weibit-based DTD dynamic models. We provide the asymptotic stability conditions of the Weibit stochastic equilibrium states based on the Jacobian matrices of the dynamical systems. We demonstrate how the features of non-identical perception variances and asymmetric response curve of the Weibit model can influence the evolution of network states and eventually the equilibrium points of the dynamical systems compared to the Logit case. Under fair comparison, the equilibrium states of Weibit DTD models are shown to have larger stable regions of adjustment rates than those of Logit DTD models. This research contributes to understanding the significance of considering travelers’ non-identical perception errors in DTD dynamics.