带有负顾客和《p,N〉策略启动期的Geo/Geo/1多重休假排队

摘要

本文考虑了多重休假的Geo/Geo/1离散时间排队模型,并引入〈p,N〉策略启动时间和负顾客,其中〈p,N〉策略约束启动期的开始,到达的负顾客不接受服务,只一对一抵消正在接受服务的正顾客.运用拟生灭过程和矩阵几何解的方法,我们首先讨论了队长稳态分布的存在条件,并得到了队长稳态分布的表达式；进一步,我们得到了稳态下系统队长的条件随机分解表达式及由休假引起的附加队长的分布表达式.%This paper considers a Geo/Geo/1 discrete time queueing model with multiple vacations, in which the , N> policy of the set-up time and negative customers are introduced. The start-up period is constrained by the , N> policy. When negative customers arrive, they need no service, but remove positive customers who are receiving service one by one. Using the quasi-birth-and-death process and the matrix-geometric approach, we first discuss the equilibrium conditions for the steady-state distribution of the queue length. And the concise expressions for the steady-state distribution of the queue length are derived. Furthermore, the conditional stochastic decomposition structure of the queue length under steady state and the distribution of the additional queue length caused by vacations are also obtained.