带有负顾客和N-策略的Geo/Geo/1工作休假排队  

Geo/Geo/1 Working Vacation Queue with N-policy and Negative Customers

作　　者：郭宏侠[1] 徐秀丽[1] 耿杰[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《重庆师范大学学报（自然科学版）》2013年第1期59-62,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.71071134)

摘　　要：在离散时间Geo/Geo/1多重工作休假排队模型的基础上,加入了负顾客和N策略。这是一个新的模型,改进了已有的相关结论。工作休假是指在休假期间,服务员不是完全停止服务,而是低速率继续为顾客服务。这既可减少顾客因为不耐烦排队离开后所造成的损失,也可提高经济效益。在文中的负顾客不接受服务,并只起一对一抵消队首正接受服务的顾客的作用,即服从RCH(Remove customer from head)策略。通过嵌入马尔可夫链方法,得到转移概率矩阵。并使用拟生灭过程及矩阵几何解方法得到队长的稳态分布:πkj=p(L=k,J=j),(k,j)∈Ω,进一步得出了系统队长的随机分解的结果:LN(z)=L0(z)Ld(z)。Abstract： This paper is on the basis of a Geom/Geom/1 queue with multiple working vacations, in addition to negative customers, N-policy and set-up time. This is a new model. The results obtained the improvement of the conclusions in previous literatures. The working vacation policy means that the servers continue to serve at a lower rate rather than stop service during the vacation, which can not only reduce the loss that the impatient customers leaves the queue because of waiting in a long time, but also improve the economical efficiency. Negative customers need not accept service; remove positive customers only one by one at the head when they are served, which obeys RCH policy. An embedded Markov chain is used to obtain the state transferring probability matrix. Using quasi-birth and death process and matrix-geometric solution method, the paper gains concise expressions of the steady state distributions for queue length rrkj p（L=k,J=j） , （k,j） ∈π, and obtains the result of stochastic decomposition of the queue length LN （z） =Lo （z）Lj （z）.

关 键 词：工作休假 N策略 矩阵几何解 条件随机分解 

分 类 号：O226[理学—运筹学与控制论]