Optimization and equilibrium in dynamic networks and applications in traffic systems

Abstract

This thesis discusses optimization problems and equilibrium in networks. There are three major parts of the thesis. In the first part, we discuss optimization in dynamic networks. We focus on two fundamental optimization problems in dynamic networks: the quickest flow problem and the quickest transshipment problem. The quickest flow problem is to find a minimum time needed to send a given amount of flow from one origin to one destination in a dynamic network. The quickest transshipment problem is similar to the quickest flow problem except with multiple origins and multiple destinations. We derive optimality conditions for the quickest flow problems and introduce simplified and more efficient algorithms for the quickest flow problems. For the quickest transshipment problem, we develop faster algorithms for several special cases and apply the approach to approximate an optimal solution more efficiently. In the second part, we discuss equilibrium in dynamic networks. We extend equilibrium results in static networks into dynamic networks and show that equilibria exist in a network where players either have the same origin or the same destination. We also introduce algorithms to compute such an equilibrium. Moreover, we analyze the average convergence speed of the best-response dynamics and connect equilibria in discrete network models to equilibria in continuous network models. In the third part, we introduce a new traffic information exchange system. The new system resolves the dilemma that broadcasting traffic predictions might affect drivers' behaviors and make the predictions inaccurate. We build game theoretic models to prove that drivers have incentives to use this system. In order to further test the effectiveness of such system, we run a series of behavioral experiments through an online traffic game. Experimental results show that drivers who use the system have a lower average travel time than the general public, and the system can help improve the average travel time of all drivers as the number of drivers who use this system increases.