Day-to-day dynamics with advanced traveler information

This paper studies how the advanced traveler information affects the stability of the day-to-day flow evolution of a transportation system. Two scenarios are investigated regarding the types of information provided, where one type is the historical travel time and the other the forecasted travel time. Given the information, travelers are assumed to form their own perception/prediction on travel time and further choose the routes. The day-to-day dynamics under the two above-mentioned scenarios are formulated using both discrete-time and continuous-time models, and their respective local stability is analyzed. Findings from the discrete-time and continuous-time models are compared, which show that: (i) the discrete-time models behave in a more complex fashion than the continuous-time models, and (ii) the conclusions drawn from the discrete-time modeling and continuous-time modeling can be consistent, different or contradictory, which depends on the system parameters, network structure, the travel time functions and the route choice probability functions.