Markov-modulated queueing systems
Markov-modulated queueing systems
复制标题
马尔可夫调制排队系统
DOI：
10.1007/bf01149193
复制
发表时间：
1989
期刊：
影响因子：
1.2
通讯作者：
Yixin Zhu
中科院分区：
文献类型：
--
作者：
N. Prabhu;Yixin Zhu
马尔可夫调制排队系统是指主要到达和服务机制受到次要马尔可夫过程中的阶段变化影响的系统。这种影响可能是外部的，也可能是内部的，并且可能代表环境变化或服务中断等因素。这种模型的一个重要例子出现在分组交换中，其中生成分组的呼叫被识别为在无限服务器系统中服务的客户。在本文中，我们首先调查了马尔可夫调制排队系统的许多不同模型。然后我们分析一个模型，其中工作负载过程和辅助过程共同构成马尔可夫复合泊松过程。我们使用基于无穷小生成器的技术导出等待时间、空闲时间和繁忙时间的属性。该模型首先由 G.J.K.雷特肖特和 J.H.A. de Smit 使用 Wiener-Hopf 技术，他们的主要兴趣是队列长度和等待时间。
Markov-modulated queueing systems are those in which the primary arrival and service mechanisms are influenced by changes of phase in a secondary Markov process. This influence may be external or internal, and may represent factors such as changes in environment or service interruptions. An important example of such a model arises in packet switching, where the calls generating packets are identified as customers being served at an infinite server system. In this paper we first survey a number of different models for Markov-modulated queueing systems. We then analyze a model in which the workload process and the secondary process together constitute a Markov compound Poisson process. We derive the properties of the waiting time, idle time and busy period, using techniques based on infinitesimal generators. This model was first investigated by G.J.K. Regterschot and J.H.A. de Smit using Wiener-Hopf techniques, their primary interest being the queue-length and waiting time.