带有负顾客和N-策略的Geo/Geo/1排队模型均衡策略分析

Analysis of Geo/Geo/1 Queueing Model Equilibrium Strategy with Negative Customer and N-Policy

本文提出带有负顾客、N-策略休假和待机时间的Geo/Geo/1迟到达排队模型,并研究了此模型下的稳态条件、不同信息水平下顾客的策略和系统吞吐量的优化问题.负顾客到达发生在服务台在线阶段,其到达会抵消一个正在被服务的正顾客,即清除队列头部的顾客(RCH).为此,系统设置了N-策略休假机制,即系统处于休假时,服务台不提供服务,此时负顾客也不会到达系统;直到顾客数目累积至N时,休假自动结束,服务台开始运行并按FCFS原则提供服务.系统一旦变空,会有一段待机时间,待机结束后,服务台关闭并进入休假.模型借助N-策略设置避免了频繁启动和关闭服务台造成的损耗,同时削弱了负顾客对系统产生的不良影响.分析得到了顾客在不同信息水平下的策略行为,同时给予系统管理者对于N-策略和信息展示水平的选择参考.最后通过数值模拟,验证了N-策略的保护作用和系统性能指标的敏感性.

In this paper,Geo/Geo/1 late arrival queuing model with negative customer,N-policy vacation and standby time is proposed,and the steady-state condition,customer policy and throughput optimization problem under this model are studied.The arrival of a negative customer occurs during the service desk online phase,and its arrival offsets a positive customer being served,that is,the customer at the head of the queue(RCH).Therefore,the system sets the N-policy vacation mechanism,that is,when the system is on vacation,the service desk does not provide services,and the negative customers will not arrive at the system.When the number of customers accumulates to N,the vacation will automatically end,and the service desk will start to operate and provide services according to FCFS principle.Once the system is empty,there will be a standby period,and after the standby ends,the service desk closes and goes into vacation.With the help of N-policy,the model avoids the loss caused by frequent startup and shutdown of the service desk and weakens the adverse impact of negative customers on the system.The analysis obtains the customer’s strategic behavior under different information levels,and gives the system manager a reference for the choice of N-policy and information display level.Finally,the protective effect of N-policy and the sensitivity of system performance index are verified by numerical simulation.