摘要:
在离散时间Geo/Geo/1多重工作休假排队模型的基础上,同时引入负顾客和N-策略,并在模型中规定正顾客在忙期和假期内的到达率不同.在这个新模型下,得到了一些新结论并改进了一些原有的相关结论.在工作休假期,服务员不完全停止服务,而是以较正常服务率低的速率服务顾客,这可以降低顾客因不耐烦排队离开所造成的损失,同时又可提高经济效益.到达的负顾客不接受服务,只是一对一抵消队首正接受服务的正顾客,若系统中无正顾客,负顾客自动消失.在某次休假结束时,系统中顾客数不少于N则终止休假,否则继续休假.考虑实际因素,根据忙期和休假期内的不同服务率规定不同的到达率.通过拟生灭链矩阵分析方法,求出了这个排队系统的队长平稳分布、随机分解、忙期分析.最后通过两个数值实例分析了参数对队长的影响.%This paper is on the basis of a Geo/Geo/1 queue with multiple working vacations ,in addition to negative customers and N-policy , and for this model , the positive customers have different arrival rates in the normal busy period and working vacation period . Some new conclusions and the improvement of the conclusions in previous literatures are obtained in this new model . The server serves at a lower rate rather than stops service during the vacations , w hich can not only reduce the loss that the impatient customers leave the queue because of waiting in a long time ,but also improve the economical efficiency . The arrived negative customers don't accept service , only remove positive customers at the head one by one , if there is no positive customer in the system , negative customers will disappear automatically . At the end of some vacation ,if the customer numbers in system are not less than N , the system will stop vacation , otherwise ,continues to have vacation . With the consideration of real factors , customers have different arrival rates because of different service rates in the busy period and vacation period . T he equilibrium distribution of the queue length , the stochastic decomposition and the busy period analysis of the queuing system are obtained by using the matrix-analytical method of quasi birth-death chains . Two numerical examples are given to illustrate the impact of parameters on the queue length .