Researchs On Network Equilibrium Based On Information Analysis

Network flow equilibrium assignment problem concerns with the distribution of the demand on the network. The information method, especially the maximum entropy method based on the concept of Kullback information for the equilibrium has received more and more attention recently. The analysis for network Nash equilibrium model based on the maximum entropy method according to the concept of Kullback information is introduced and they are applied to solving max-min problem, VIP and equilibrium programming.We developed the concept of Shannon entropy function by employing prior distribution information and Kullback entropy concepts to obtain the maximum entropy function of the max-min problem by introducing the expectation of the distribution to express the solution.The introduction of this dissertation is given in chapter 1, which briefly gives the present state and background of network flow equilibrium assignment problem and the information method, and the main results in the dissertation.The relation between system optimal and user equilibrium patterns is further discussed, user equilibrium is the system optimal state taking the real network costs as the marginal costs, and the realization of SO pattern are presented in chapter 2.The maximum entropy function approach to max-min problems is introduced and it is further developed to solve traditional inequalities, VIP as well as equilibrium programming. An entropy function for inequalities and a Kullback entropy expression for the gap function of the variational inequality problem (VIP) are presented. The solution of inequalities can be approached by obtaining the local minimum solution of a differentiable convex function optimization problem. We developed the concept of Shannon entropy function by employing prior distribution information and Kullback entropy concepts to obtain the maximum entropy function of the max-min problem and the gap function for VIP, equilibrium programming problem and the NLP are the special parametric optimizationproblems in chapter 3.In chapter 4, the mixed network equilibrium model is derived directly from the equilibrium programming and EP models for combined Wardrop principles under different information conditions are analyzed. The Kullback entropy expression for the gap function of the variational inequality problem (VIP) is presented and it is used to solve the traffic assignment problem (TAP).In chapter 5, an application of updating O/D information is presented by combing the concepts of network user equilibrium and Kullback relative information.Finally, the author sums up the research results in thesis and gives prospects of the further research in the fields.