Highlights • This paper developed a Bayesian traffic Model to analyze stochastic traffic dynamics. • The Dirichlet-based updating process provided a sound behavior modeling alternative. • The model will converge to statistical User Equilibrium with an infinity long memory. • The model quantifies contribution of different sources to overall traffic variations.

Abstract The rapid growth of transportation data offers new opportunities to analyze the interaction between travel behavior and transportation system performance, and particularly when issues such as uncertainty and reliability are considered. Many previous studies in this area described the stationary behavior of stochastic transportation systems using user equilibrium (UE) conditions. In contrast, this paper develops a generalized Bayesian model to analyze the dynamic behavior of stochastic transportation systems. In the proposed model, the variability of link volume and travel time stems from the stochasticity in travel demand, transportation supply (e.g. link capacity, free flow travel time, etc.) and route choice. To the best of our knowledge, this is among the first work that considers the three sources of stochasticity simultaneously. In addition, we propose a Bayesian updating approach based on the Dirichlet model to describe the route choice behavior. This approach allows researchers to consider a wide range of route choice behavior of bounded rationality in day-to-day traffic dynamics, including a knowledge updating mechanism based on different memory lengths and weighting factors. This framework is particularly suitable for data-driven studies supported by emerging transportation data due to the computing efficiency of the Dirichlet-based Bayesian updating mechanism and the sound behavioral foundation. This paper shows that the proposed Bayesian model with infinite memory leads to UE conditions under stochastic demand and supply. Subsequently, a numerical case study is conducted to illustrate different day-to-day route choice dynamics with different memory lengths of system performance. This paper also discusses the influence of the three sources of stochasticity towards the aggregated variance of link volumes and travel time. With enough longitudinal travel choice and transportation system performance data, the proposed Bayesian framework could be empirically calibrated and tested, which offers an attractive descriptive alternative to the conventional UE-based transportation system models.