Markov chains with block-structured state-dependent events: formulation and correlation analysis
Markov chains with block-structured state-dependent events: formulation and correlation analysis
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DOI：
10.1145/1837856.1837860
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
J. Artalejo;A. Gómez‐Corral
中科院分区：
文献类型：
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作者：
J. Artalejo;A. Gómez‐Corral
关于状态依赖参数排队系统的文献包括各种各样的特征，如有限种群、服务器休假、可变服务率、队列长度依赖、重试和到达时的准入控制。通过结合这些非齐次特征和阶段方法获得的随机模型的复杂性导致实际困难。从数值实现的角度来看，底层矩阵表示的大维度是一个需要注意的严重问题。具体来说，这是一个关键方面，如果一个任意的，甚至无限数量的马尔可夫到达过程和相位型分布。这些考虑与随机建模的块结构的状态依赖（BSTO）马尔可夫链的固有困难，为我们的研究提供了动力。在本文中，我们简要地介绍了在连续时间内构造一个特定的部分或整个随机系统，建模状态依赖的现象中存在的阶段。该方法的一个变体也适用于离散时间。我们专注于相关性结构，并提出了两个措施的事件之间的相关性。
The literature on queueing systems with state-dependent parameters includes a variety of features, such as finite populations, server vacations, variable service rates, queue length dependence, retrials, and control of the admission upon arrival. The complexity of the stochastic models obtained by combining these non-homogeneous features and the method of stages causes practical difficulties. From the point of view of the numerical implementation, the large dimensionality of the underlying matrix representations is a serious problem that requires attention. Specifically, this is a key aspect if an arbitrary, even infinite number of Markovian arrival processes and phase-type distributions are involved. These considerations on the inherent difficulties associated with the stochastic modeling of block-structured state-dependent (BSDE) Markov chains provide the motivation for our study. In this paper, we briefly present the BSDE approach to construct either a specific part or the whole stochastic system in continuous time, modeling a state-dependent phenomenon operating in the presence of phases. A variant of the approach also holds in discrete time. We focus on the correlation structure and present two measures of correlation between events.