Dynamic pricing in discrete time stochastic day-to-day route choice models

The traffic assignment problem is primarily concerned with the study of user equilibrium and system optimum and it is often assumed that travelers are perfectly rational and have a complete knowledge of network conditions. However, from an empirical standpoint, when a large number of selfish users travel in a network, the chances of reaching an equilibrium are slim. User behavior in such settings can be modeled using probabilistic route choice models which define when and how travelers switch paths. This approach results in stochastic processes with steady state distributions containing multiple states in their support. In this paper, we propose an average cost Markov decision process model to reduce the expected total system travel time of the logit route choice model using dynamic pricing. Existing dynamic pricing methods in day-to-day network models are formulated in continuous time. However, the solutions from these methods cannot be used to set tolls on different days in the network. We hence study dynamic tolling in a discrete time setting in which the system manager collects tolls based on the state of the system on previous day(s). In order to make this framework practical, approximation schemes for handling a large number of users are developed. A simple example to illustrate the application of the exact and approximate methods is also presented.