收费机制下一类随机需求混合交通均衡分配的非合作代价  

Price of Anarchy of a Mixed Traffic Equilibrium Assignment with Stochastic Demand Under Road Pricing

作　　者：余孝军 毛君竹 顾重秀 YU Xiaojun;MAO Junzhu;GU Chongxiu(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数统学院,贵州贵阳550025

出　　处：《应用数学》2023年第1期57-66,共10页Mathematica Applicata

基　　金：国家自然科学基金(71761005);贵州省研究生教育创新计划项目(黔教合YJSCXJH2020126)。

摘　　要：运用算法博弈论探讨一类随机需求混合交通均衡分配在收费机制下的非合作代价.首先,构建了收费机制下随机需求UE-CN混合交通均衡分配的变分不等式模型.其次,运用解析推导法分别得到单项式出行成本函数下是否将收费作为系统总成本一部分时,该类混合交通均衡分配的非合作代价上界表达式.在此基础上,探讨了出行需求服从对数正态分布时的非合作代价上界表达式.并以数值算例验证所得结论.The price of anarchy(PoA) of a mixed traffic equilibrium assignment with stochastic demand under road pricing is investigated by algorithmic game theory.Firstly,the variational inequality model for UE-CN mixed traffic equilibrium assignment with stochastic demand under road pricing is presented.Secondly,the upper bound formula of the PoA of this mixed traffic equilibrium is obtained by analytic derivation method when road pricing is considered as a part of the total travel cost or not under the monomial link travel cost function,respectively.Then,the upper bound formula of the PoA is discussed when demand follows lognormal distribution.Finally,a numerical example is given to verify the conclusions.

关 键 词：非合作代价 变分不等式 UE-CN混合交通均衡分配 随机需求 路段收费 

分 类 号：O225[理学—运筹学与控制论]