Analysis of Stochastic Time-dependent Transportation Network

Abstract

Modeling transportation network as a stochastic and time-dependent network has become a trend. Instead of exploring the dynamic of the stochastic and time-dependent properties of transportation networks, a majority of the literature treat the statistical distribution of the transportation network as a fixed function and try to find an optimal path or an optimal routing policy. In this paper, we analyze the transportation network from the perspective of game theory and try to find the driven force that sharpens the stochastic and time-dependent properties of transportation network. We model the travel time as a random process that is determined not only by the length of the corresponding link, but also by the number of drivers that are traveling on this link. Based on this modeling method, we model the path selection process of all the drivers in the network as a non-cooperative game, where all the drivers try to maximize their utility function by selecting a path that is emanating from their points of departure to their destinations. A day-to-day repeated game process is addressed and a formal definition of Nash equilibrium is also given. At last, the main contributions of this paper is summarized and the future work is discussed.