基于M/M/1/SV排队的均衡门限策略

考虑单重休假M/M/1排队, 在部分可视的前提下, 研究顾客的均衡门限策略, 首次将单重休假机制引入到连续时间排队经济学模型中. 系统的决策主体是顾客, 突破了以往只注重服务机构单方面行为的局限. 基于“收入-支出”结构, 利用马尔可夫过程理论, 通过求解差分方程, 分析了系统的稳态行为, 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 均衡纯门限策略, 均衡混合门限策略的具体方法并证明之; 而后在不同的策略下, 得出了系统的稳态分布和均衡社会收益; 最后, 通过数值实验分析了均衡行为的各指标对系统参数的敏感性. 研究结果为顾客决策提供了优化建议, 同时为管理者研究系统中的定价问题提供了理论参考.

Equilibrium threshold strategy in the M/M/1/SV queue

This paper considered the equilibrium threshold strategies of customers in the M/M/1/SV queue, given that customers were informed of only the queue length. To the authors' knowledge, this is the first time that the single vacation policy is introduced into the economics of continuous-time queue. In the system, customers had the right to decide for themselves whether to join or to balk, which broke through the transition that researchers only paid attention to the servers. Based on the “reward-cost” structure and the theory of Markov process, the stationary behavior of the system was analyzed by solving the difference equation and the mean sojourn time was derived. Then by introducing appropriate functions, we provided an algorithm to identify the equilibrium pure and mixed threshold strategies. Moreover, the stationary distribution of the system under the corresponding strategy was analyzed and the social benefit was obtained. Finally, we illustrated the effects of the parameters on the equilibrium behavior via numerical experiments. The results not only provide the customers with optimal strategies but also provide the managers with a good reference to the pricing problem in the queueing system.