中文摘要：

考虑多级适应性休假的M^X／G／1排队系统的离去过程．运用全概率分解，更新过程理论和拉普拉斯-斯蒂尔吉变换，讨论了从初始状态i（i=0，1，…）出发，在（0，t]中服务完顾客的平均数，揭示了离去过程的特殊结构，并由此得到了一些特殊排队模型的相应指标．

英文摘要：

This paper studies the departure process of M^X/G/1 queueing model with adaptive multistage vacation. By using direct probability decomposition, renewal theory and the Laplace-Stieltjes transform, we discuss the expected number of departures occurring in the time interval （0, t] from the beginning of the initial state i（i = 0, 1,…）. Furthermore, the special structure belonged to the departure process of queueing models is uncovered, Especially we obtain some corresponding results for special queueing systems.