成批排队系统GI/M/I的忙时(busy cycle)

BUSY CYCLE OF THE QUEUEING SYSTEM GI/M/1 WITH BULK ARRIVAL AND BULK SERIVCE

§1.引言 尽管成批排队系统M/G/1的忙期(busy period)与忙时(busy cycle)已有若干作者作了成功的研究,但多年来成批到来成批服务的排队系统GI/M/1的相应研究却几乎没有进展。正如文献[1]中指出,此问题是困难的。 本文由研究嵌入马氏链与半马氏序列入手,考虑了成批排队系统GI/M/1。运用文中定理可以得到上述系统的忙时分布,忙时内服务的到来顾客的批数的分布。

In this paper we deal with the queueing system GI/M/1 with bulk arrival and bulk service as a semi-Markov sequence.We obtain its distributions of busy cycles and the number of customers served in a busy cycle (period).The limiting behavior of the embedded.Markov Chain of this system in also considered.