论文标题
具有两个站点的级联系统的稳定性及其扩展到多个电台
Stability of a cascade system with two stations and its extension for multiple stations
论文作者
论文摘要
我们考虑了一个两个站级联系统，如果车站大小的队列大小$ 1 $，包括服务的客户大小$ 1 $在车站上等待或外部到达客户，包括服务的客户大于给定的阈值级别$ c_ {1} \ ge 1 $，并且车站$ 2 $是空的。假设外部到达受到满足某些规律性条件和服务时间的独立更新过程的约束，每个站点是$ i.i.d. $，我们为马尔可夫流程提供了必要和充分的条件，以形容该系统在哈里斯的意义上是积极的经常性。该结果扩展到级联系统的级联系统，并将其串联为$ k $。此扩展名需要车站的实际交通强度$ 2,3，\ ldots，k-1 $ for $ k \ ge 3 $。我们最终注意到，如果稳定性的概念被某个样本路径条件取代，则续签到达的建模假设和$ i.i.d. $ i.d. $服务时间不是必不可少的。如果Markov进程描述了整个系统，则该稳定性概念与标准稳定性相同，该过程是Harris不可还原$ T $ - 过程。
We consider a two station cascade system in which waiting or externally arriving customers at station $1$ move to the station $2$ if the queue size of station $1$ including a customer being served is greater than a given threshold level $C_{1} \ge 1$ and if station $2$ is empty. Assuming that external arrivals are subject to independent renewal processes satisfying certain regularity conditions and service times are $i.i.d.$ at each station, we derive necessary and sufficient conditions for a Markov process describing this system to be positive recurrent in the sense of Harris. This result is extended to the cascade system with a general number $k$ of stations in series. This extension requires the actual traffic intensities of stations $2,3,\ldots, k-1$ for $k \ge 3$. We finally note that the modeling assumptions on the renewal arrivals and $i.i.d.$ service times are not essential if the notion of the stability is replaced by a certain sample path condition. This stability notion is identical with the standard stability if the whole system is described by the Markov process which is a Harris irreducible $T$-process.
