Highlights • The generalized Bayesian traffic model can consider different ways travelers tend to consider travel time reliability in route choice through different formations of perceived knowledge. • The Bayesian model with an infinitely long memory and mean-variance-based perceived knowledge will converge to the mean-variance UE condition. • The convergence of route choice dynamics to a UE condition is not affected by adding a bounded weight to the daily perceived knowledge. • Non-UE-based formulations of perceived knowledge also lead to fixed points for the mean route choice proportion.

Abstract Travel time reliability plays an important role in travelers’ route choice behaviors. Based on a previously developed generalized Bayesian traffic model, we propose different types of perceived knowledge (i.e., mean-variance-based type, relative gap-based type, and penalty-based type) to model travelers’ daily route choice behavior concerning travel time reliability. We theoretically demonstrate the flexibility of the generalized Bayesian model in capturing various existing UE-based travel behaviors and other non-UE-based travel behaviors (e.g., penalty-based) in stochastic transportation systems. Three major conclusions are obtained. First, the route choice dynamics induced by the Bayesian model with an infinitely long memory and mean-variance-based perceived knowledge will converge to the mean-variance UE condition. Second, the convergence of route choice dynamics to a UE condition is not affected by adding a bounded weight on the daily perceived knowledge. Thirdly, non-UE-based formulations of perceived knowledge also lead to fixed points for the mean route choice proportion. The convergences of the models with different types of perceived knowledge are verified based on numerical studies and the underlying day-to-day route choice dynamics with both recurrent and non-recurrent unreliability are examined.