带有工作休假的可见M/M/2排队系统均衡策略研究

Research on Equilibrium Strategies of Observable M/M/2 Queue with Working Vacations

摘要: 本文研究了带有工作休假的可见M/M/2排队系统的均衡止步策略和社会最优策略。在带有工作休假的M/M/2排队中，两个服务台独立工作，并且在休假期间以较低的服务速率进行工作，而不是完全停止工作。顾客到达排队系统后，根据对队长和服务台状态的观察，并结合收支结构，决定是否进入排队或止步。基于带有工作休假的M/M/2排队系统，本文研究了完全可见情形下的顾客均衡止步策略，并且从社会收益的角度分析了顾客的纳什均衡策略，得到了所有顾客遵循相同均衡阈值策略下的社会最优策略。最后，通过数值例子说明了系统参数对社会收益的影响，得到社会收益关于排队系统在正常忙期与工作休假期间服务时间和休假时间呈负相关的结论。

Abstract: The equilibrium balking strategies and social optimal strategies are investigated in the paper for observable M/M/2 queue with working vacations. In such an M/M/2 queue with working vacations, two servers work independently and work with a lower service rate rather than stopping work altogether during the vacation period. Upon customers arrive at the queuing system, they decide whether to join or balk the queue based on observation of the queue length and the status of the servers, along with the reward-cost structure of the system. Based on the M/M/2 queue with working vacations, we study customers’ equilibrium joining strategies in the fully observable case. We analyse customers’ equilibrium strategies in terms of the social welfare, and obtain the social optimal strategies under which all customers follow the same equilibrium threshold strategies. Fi-nally, a numerical example is given to illustrate the influence of system parameters on social wel-fare. It is found that the social welfare is negatively related to the service time during normal busy period and working vacation period and vacation time.