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运筹学学报 ›› 2012, Vol. 16 ›› Issue (2): 65-76.

• 运筹学 • 上一篇    下一篇

基于Geo/Geo/1(E,SV)排队系统的均衡止步策略

刘维奇1,2, 马琰2, 李继红1   

  1. 1.  山西大学管理学院，太原 030006
    2.  山西大学数学科学学院，太原 030006
  • 收稿日期:2011-09-23 修回日期:2012-02-16 出版日期:2012-06-15 发布日期:2012-06-15
  • 通讯作者: 马琰 E-mail:myhicharge@126.com
  • 基金资助:

    教育部人文社会科学研究项目(10YJC630114, 07JA630027), 博士后研究项目(92169)

Equilibrium balking strategy in the Geo/Geo/1(E,SV) queueing system

 Liu Weiqi1,2, Ma Yan1, Li Jihong1   

  1. 1. College of Management, Shanxi University, Taiyuan 030006, China
    2. College of Mathematical Sciences, Shanxi University, Taiyuan 030006, China
  • Received:2011-09-23 Revised:2012-02-16 Online:2012-06-15 Published:2012-06-15
  • Contact: Ma Yan E-mail:myhicharge@126.com

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被引次数

3

摘要： 基于单重休假Geo/Geo/1排队系统,研究顾客的均衡止步策略,首次将休假服务机制引入到离散时间排队经济学模型中. 顾客基于“收入--支出”结构,自主决定去留. 利用拟生灭过程理论,运用差分方程求解技巧,对系统进行了稳态分析,得到了顾客的平均逗留时间；进而构造适当的函数,给出了寻找均衡止步策略的具体方法并证明之；而后分析了在均衡策略下, 系统的稳态行为和社会收益；最后通过数值实验讨论了系统参数对均衡行为的影响.

关键词: 排队经济学, 纳什均衡, 预期净收益, 拟生灭链, 差分方程, 稳态分布, 均衡止步策略, 社会收益

Abstract: This paper considered the equilibrium balking strategy of customers in the Geo/Geo/1 queue with single vacation. To the authors' knowledge, this is the first time that the vacation policy is introduced into the economics of the discrete-time queue. The customers decide for themselves whether to enter the system or balk based on a natural  reward-cost structure. Using the theory of the quasi-birth-death process and the standard approach for solving difference equation, we obtain the stationary distribution of the system and the mean sojourn time of an arriving customer. Then by introducing appropriate functions, we provide an algorithm to identify the equilibrium balking strategy. Furthermore, the resulting stationary system behavior is explored and the equilibrium social benefit is derived. Finally, we illustrate the effects of the parameters on the equilibrium behavior via numerical experiments.

Key words:  economics of queues, Nash equilibrium, expected net benefit, quasi-birth-death chain, difference equations, stationary distribution,  equilibrium balking strategy, social benefit