具有风险敏感性顾客的离散时间排队系统策略研究  

Strategies Research on the Discrete-time Queueing System with Risk-sensitive Customers

作　　者：曹灿 刘再明[3] 高珊[4] 伍逸凡 CAO CAN;LIU ZAIMING;GAO SHAN;WU YIFAN(College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,China;College of Mathematics and Statistics,Jishou University,Jishou 416000,China;School of Mathematics and Statistics,Central South University,Changsha 410083,China;School of Mathematicsand Statistics,FFuyang Normal University,Fuyang 236037,China;School of Computer science and engineering,Central South University,Changsha 410083,China)

机构地区：[1]衡阳师范学院数学与统计学院,衡阳421002 [2]吉首大学数学与统计学院,吉首416000 [3]中南大学数学与统计学院,长沙410083 [4]阜阳师范大学数学与统计学院,阜阳236037 [5]中南大学计算机学院,长沙410083

出　　处：《应用数学学报》2024年第2期284-311,共28页Acta Mathematicae Applicatae Sinica

基　　金：国家自科基金项目(批准号:12071487);湖南省教育厅科学研究项目(批准号:20C1521);安徽省自然科学基金项目(批准号:2108085MA08);衡阳师范学院科研启动项目(批准号:2023QD25)资助项目。

摘　　要：结合博弈论研究排队系统中顾客的策略行为成为当前排队论研究的一个热点.本文研究了离散时间排队系统中风险敏感性顾客的策略行为.不同于经典排队经济学的是,本文的效用函数是期望-方差二次效用函数.根据纳什均衡和马氏过程理论,该文分别研究了在完全可视和完全不可视两种情况下Geo/Geo/1排队系统中风险敏感性顾客的博弈行为.得到了风险敏感性顾客的个体最优策略、社会最优策略和服务商利润最优策略.研究发现,风险敏感系数越小,顾客越喜欢冒险,加入系统的意愿越强.数值实验探索了风险敏感系数对顾客策略行为的影响.The research on customer strategy behavior in queueing system combined with game theory is a hot topic in the current queueing theory.This paper studies the strategic behavior of risk-sensitive customers in discrete-time queueing systems.Different from the classical economics of queues,the utility function in this paper is an expectation-variance quadratic utility function.Based on the Nash equilibrium and Markov process theory,we study the game behavior of Geo/Geo/1 queueing system with risk-sentitive customers under fully observable case and fully unobservable case,respectively.The individual optimal joining strategy,the joining strategy for the social net welfare and the server's profit optimization are obtained.It is found that the smaller the risk sensitivity coeficient is,the more customers like to take risks and the stronger the willingness to join the system.Some numerical experiments are provided to illustrate the effect of the risk sensitivity coefficient on the customer strategic behavior.

关 键 词：离散时间 风险敏感性顾客 策略研究 纳什均衡 社会最优 二次效用函数 

分 类 号：O226[理学—运筹学与控制论]