中文摘要：

提出并研究了带负顾客的Geo/Geo/1多重工作休假排队模型,其中正顾客在工作休假期和正常忙期的到达率不同。通过拟生灭链矩阵分析的的方法,求出了这个排队系统的转移概率矩阵、队长平稳分布、队长均值、随机分解、忙期分析。最后建立了费用函数,为系统的优化设计提供参考,并给出两个数值实例分析了参数对队长的影响。

英文摘要：

A multiple working vacations Geo/Geo/1 queuing system with negative customers was proposed and studied in this paper. For this model, the positive customers have different arrival rates in the normal busy period and working vacation period. The quantities including the transition probability matrix of the queuing system, the equilibrium distri- bution of the queue length, the mean number of customers, the stochastic decomposition and the busy period analysis were obtained by using the matrix-analytical method of quasi birth-death chains. The cost function and two numerical examples were given to provide a basis for optimal design and illustrate the impact of parameters on the queue length.