The application of Gravity-type Interactive Markov Chain to Solve Stochastic User equribrium problem in a network

• Main Authors: Tung, Chia-Wen, 董珈汶
• Other Authors: Shang-Hsin Hsieh
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/64820329209323694300

碩士 === 國立交通大學 === 交通運輸研究所 === 86 === The Gravity-type Interactive Markov models(GIM models) were introduced by Smith and Hsieh in 1994,in which migration flows in each time period are postulated to vary directly with some population-dependent measure of attractiveness and inversely with some symmetric measure of migration costs. From the viewpoint of theoretical analysis, the choice behavior of individuals inGIM models is similar to that of drivers in selecting routes in logit-based stochastic traffic assignment problems. This study is trying to formulate the GIM model of the stochastic traffic assignment in a road network. The followings will be the goal of this study: (1). Prove that the steady-state conditions of the GIM model is equivalent to the stochastic user equilibrium (SUE) conditions of the problems.(2).Develop a new algorithm for solving the SUE of the problems.(3).Compare the GIM algorithm with exiting algorithm, e.g. Frank-Wolfe method, MSA.(4).Analyze the convergence to the SUE of the GIM algorithm. This method has implemented by Mathmatica. The computation of different algorithms on different examples shows that the adjustment ratio have a great influence on the speed of convergence. And the level of overlapping in the network is slight, we can solve the stochastic user equilibrium problems that haveoverlapping links in the network by GIM algorithm.