STABILITY ANALYSIS OF REGENERATIVE QUEUES
STABILITY ANALYSIS OF REGENERATIVE QUEUES
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再生队列的稳定性分析
DOI：
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发表时间：
2008
期刊：
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通讯作者：
R. Delgado
中科院分区：
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作者：
R. Delgado
非马尔可夫排队系统的稳定性是过去十年中深入研究的主题之一。众所周知，稳定性是一个困难和实际的问题，需要精细和费力的数学技术，特别是在马尔可夫队列的限制之外。稳定性分析建立了基本过程保持稳定的预定义参数区域。应用了各种稳定性概念。我们提到了弱稳定性和强稳定性，Chen [4]，全局弱稳定性，全局路径稳定性，Dai和Vande Vate [10]，等等。在许多论述这一主题的著作中，我们提到陈和曼德尔鲍姆[6]，陈[4]，陈和姚[5]，戴[7]，戴[8]，戴和韦斯[11]，戴和范德维特[10]。同时，流体方法不是直接的，因为我们最初研究相关联的流体极限模型的稳定性/不稳定性（并且处理确定性流体过程而不是原始随机过程）来建立相应的离散过程的相似性质。关于稳定性分析方法（重点是网络）的最新概述是论文[12]。与上述方法不同，我们的稳定性方法是基于基本再生过程的再生特性[1，32]。我们专注于再生队列，因为它们有许多应用程序（例如，[30，31]）。此外，Harris递归马尔可夫链的再生扩展了这种方法的一个领域，[1]。著名的专著[16]包含了马尔可夫链稳定性分析的详细描述。对于马尔可夫设置，这种方法与
One of the topics which were intensively studied in the last decade is the stability of non-Markovian queueing systems. It is well-known that stability is one of the hard and actual problems and requires refinement and laborious mathematical technique especially outside the limits of Markovian queues. Stability analysis establishes the region of predefined parameters where the stability of the basic process holds. Various notions of stability are applied. We mention weak and strong stability, Chen [4], global weak stability, global pathwise stability, Dai and Vande Vate [10], and so on. An effective and developed approach to stability analysis of a wide class queueing systems and networks is the fluid approximation. Among many works which treat this topic we mention Chen and Mandelbaum [6], Chen [4], Chen and Yao [5], Dai [7], Dai [8], Dai and Weiss [11], Dai and Vande Vate [10]. At the same time, the fluid approach is not direct in the sense that we study originally the stability/instability of the associated fluid limit model (and deal with deterministic fluid processes instead of original stochastic ones) to establish the similar property of the corresponding queueing process. The most recent overview on stability analysis methods (with focus on networks) is the paper [12]. Unlike the mentioned above approaches, our approach to the stability is based on the regeneration property of the basic queueing process [1, 32]. We focus on the regenerative queues since they have numerous applications (for instance, [30, 31]). Also the regeneration of Harris recurrent Markov chains extends an area of this approach, [1]. The notable monograph [16] contains detailed description of stability analysis of Markov chains. For Markovian setting, this approach has paralellism with the one described in