Optimization and equilibrium in dynamic networks and applications in traffic systems

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