中文摘要：

考虑顾客到达率可变的多重休假Geo/G/1排队系统的离去过程.运用全概率分解,更新过程理论和u-变换,讨论了从任意初始状态出发,在（0^＋,n^＋]中离去顾客的平均数,得到系统在（0^＋,n^＋]中离去顾客平均数的瞬态分解表达式,以及其稳态分解结果.揭示了系统离去更新过程的特殊结构：离去更新过程被分解为两部分,一部分是系统服务状态（忙,闲）过程,另一部分是忙期中的服务更新过程,从而简化了对离去过程的研究.在排队网络中,由于一个排队系统的输出即为下游排队系统的输入,因此,本文所得结果对研究排队网络有重要意义.

英文摘要：

We study the departure process of a multi-vacation Geo/G/1 queue with variable input rate.Using probability techniques,renewal process theory and utransform, we discuss the expected number of departures during the time interval （0^＋,n^＋]initiated with general state.The decomposed expression of the expected number of departures during the time interval（0^＋,n^＋]and the corresponding steady result are obtained.It displays the especial structure of the departure renewal process,i.e., the departure renewal process consists of two parts,server busy-state process（busy or idle） and the service renewal process in server busy period,which simplifies the discussion on the departure renewal process.Since the departure process also often corresponds to an arrival process in downstream queues,the results obtained here are significant to study queueing network.