Traffic Network Assignment Research Based On Game Theory

Since 21st century,the means of transportation have changed radically all over the world and due to the increasing economic level there are lots of means for people to travel more conveniently and comfortably,i.t.highway,airplane,high-speed rail and so on.With the rapid development of transportation,the situation of real traffic becomes more and more complex and heavy.Therefore it is an urgent subject for scholars to research that how to predict,plan and control the multifarious conditions of heavy traffic problem.In this dissertation,based on the characteristics of the traffic network,three kinds of game models are proposed to predict and plan the assignment of traffic flows.After creating those three models,relevant properties are proved and corresponding algorithms are invented to solve real problems.The main work and achievements of this paper are showed below:1.Multiple objective game on the traffic network.It is known that road users are selfish but selfless as well because one of their goals is to maximize their private profits and the other one is to gain the maximum profits of the whole network.Different from the weak Pareto equilibrium and strong Pareto equilibrium which have strong relations with the weighted game,ideal equilibrium which is independent relatively is proposed in terms of the given traffic network.Then several properties of the equilibrium are showed and an effective algorithm which combines mixed penalty function method with the quasi-Newton method is given to get the equilibrium and flow assignments.2.Users game.According to the characteristics of users who always pursue the maximum of private profits,a new concept of equilibrium called N-path User Equilibrium with Recourse(NPUER),i.t.the equilibrium under the condition of limited paths set and knowledge of network when traversing,is proposed from a more practical traffic network based on the previous researching papers.Then the existence and uniqueness as well as other relevant properties of NPUER are proved with the method of convex programming.Moreover,an algorithm combined with Frank-Wolfe method is invented and applied into an experiment which reveals an interesting phenomenon to provide meaningful construction to traffic administrations.3.Stackelberg game between administration and users.Due to the different,or even contradict,optimal goals of administration and road users,a Stackelberg game model with incomplete information which coordinates those goals of different players is given.And then the proof of transformation from game model into MPEC is showed via method of variable inequalities.After that we offer an augmented Larange method based on transforming the bi-level optimization problem into one level via gap function to solve the MPEC.