Departure processes and busy periods of a tandem network
Departure processes and busy periods of a tandem network
复制标题
汇接网络的出发流程和繁忙时段
作者：
Z. Lian;Ning Zhao
考虑一个单服务台串联排队网络，其到达第一站的过程为马尔可夫过程（MAP），服务时间为指数。利用降维扩展块（DREB）方法，将联合队长过程表示为一维扩展块的水平相关拟生灭（LDQBD）过程。这使得我们能够证明从每个站出发的过程是具有无限相位的MAP或IMAP，这意味着任何IMAP/M/1的出发过程都是IMAP。它还使我们能够很容易地研究每个车站的发车间隔时间和忙碌时间。
Consider a single-server tandem queueing network with a Markovian arrival process (MAP) to the first station and exponential service times. Using the dimension-reduction and expanding blocks (DREB) scheme, we formulate the joint queue length process into a single-dimensional level-dependent quasi-birth-death (LDQBD) process with expanding blocks. This allows us to show that the departure process from each station is a MAP with infinite phases or an IMAP, which implies that the departure process of any IMAP/M/1 is an IMAP. It also allows us to study the inter-departure time and the busy period in each station easily.