A general stochastic process for day-to-day dynamic traffic assignment: Formulation, asymptotic behaviour, and stability analysis

- A stochastic process model for general networks including modelling of habit and learning behaviour through simple filters.
- An asymptotic approximation to the mean process.
- A stability analysis of the mean process through a deterministic process, comparing the effects of finite or infinite memory, modelled through a moving average or an exponential smoothing filter respectively.

This paper presents a general modelling approach to day-to-day dynamic assignment to a congested network through discrete-time stochastic and deterministic process models including an explicit modelling of users' habit as a part of route choice behaviour, through an exponential smoothing filter, and of their memory of network conditions on past days, through a moving average or an exponentially smoothing filter. An asymptotic analysis of the mean process is carried out to provide a better insight. Results of such analyses are also used for deriving conditions, about values of the system parameters, assuring that the mean process is dissipative and/or converges to some kind of attractor. Numerical small examples are also provided in order to illustrate the theoretical results obtained.