GI\M\n系統中大量服务的排队过程

<正> §1.引言 我們知道,描述一个排队过程,需要三个因素:輸入过程,排队紀律,及服务机构.所謂GI|M|n,就是指这样的一个排队过程,它的 i)輸入过程,各顾客到来的时間区間的长度t相互独立、相同分布.其分布記

ON THE QUEUEING PROCESSES IN THE SYSTEM GI/M/n WITH BULK SERVICE

This paper concerns with the queueing process. GI/M/n with bulk service. By the Use of the embedded Markov chain method introduced by Kendall, we prove that the Markov chain associated with this queueing process is irreducible and aperiodic.Let the mean inter-arrival time. and mean service, time be a and b respectively, and let the maximum number of a batch of customers being served in a single counter be S. We prove that if b/a < nS, then the system is ergodic. The stationary distributions of the queue length and waiting time are also found.Finally, we obtain the distribution of the length of a busy period in terms of the number of participating customers.Particularly, if S = 1, our results are conform with that obtained by Kendall.