Day-to-Day Evolution of Traffic Flow with Dynamic Rerouting in Degradable Transport Network

Abstract

Random events like accidents and vehicle breakdown, degrade link capacities and lead to uncertain travel environment. And whether travelers adjust route or not depends on the utility difference (dynamic rerouting behavior) rather than a constant. Considering travelers’ risk-taking behavior in uncertain environment and dynamic rerouting behavior, a new day-to-day traffic assignment model is established. In the proposed model, an exponential-smoothing filter is adopted to describe travelers’ learning for uncertain travel time. The cumulative prospect theory is used to reflect route utility and its reference point is adaptive and set to be the minimal travel time under a certain on-time arrival probability. Rerouting probability is determined by the difference between expected utility and perceived utility of previously chosen route. Rerouting travelers choose new routes in a logit model while travelers who do not choose to reroute travel on their previous routes again. The proposed model’s several mathematical properties, including fixed point existence, uniqueness, and stability condition, are investigated through theoretical analyses. Numerical experiments are also conducted to validate the proposed heuristic stability condition, show the effects of four main parameters on dynamic natures of the system, and investigate the differences of the system based on expected utility theory and cumulative prospect theory and with static rerouting behavior and dynamic rerouting behavior.