Chapter 8 - Games on Transportation Networks

Abstract

Transportation problems have always been attracting the attention of researchers and engineers owing to their importance for real life. Such problems arise in passenger and freight traffic analysis (railways, airlines), arrangement of transportation hubs, etc. Traffic control is a pressing problem of this class, mostly for large cities and megalopolises. A growing number of vehicles, both in the segments of private and public transport, has overloaded road infrastructure and caused hours-long traffic jamming, inconvenience for pedestrians, an increased number of traffic accidents, and so on. In transportation modeling, also one has to take into account the existing passenger traffic flows on different routes. An important role is played by the correspondence matrix, which characterizes the intensity of passenger traffic between different stops. In this chapter we show how to construct the correspondence matrix using the statistical data. The volumes of passenger traffic on different routes partially affect public transport scheduling (the intensity and direction of bus service). Optimal service intensity can be found as a solution of convex game as shown in this chapter. We use the Wardrop principle to find an equilibrium in a game with transport vehicles as players and routes as their strategies. This game is a congestion game with a potential. Equilibrium calculation comes to potential minimization. Below we will illustrate this using an example of a transportation network composed of parallel routes.