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The Method of Markov Processes with Macro States for Analysis of Unreliable Telecommunication Systems

机译:具有不可靠电信系统分析的宏状态马尔可夫过程方法

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摘要

The goal of this paper is to propose the analysis method of processes in an unreliable telecommunication system by the means of Markov changes. Moreover, our proposed analysis method based on macro states of Markov chains is much simpler than the detailed Markov processes applied previously by authors for analysis of such unreliable telecommunication systems [1-8]. A lot of effort has gone into the study of unreliable telecommunication systems. A rich literature exists in the area of data packets transmission process analysis in the telecommunication system by the means of Markov chains [9]. The majority of them analyze the processes in the system using detailed Markov chains [6, 7]. These papers present some examples of elementary Markov model for unreliable systems. Complex systems give rise to large and complicated Markov models. Several techniques are used for the automatic generation for large Markov chains models and balance equations [8, 10]. The literature on the research topic has hundreds of papers with exact analysis of such systems. One possible way to solve this problem is to use macro state Markov models. An implementation of macro state Markov model can simplify the evaluation of performance measures of complex systems, such as telecommunication networks. The present paper, on the other hand, obtains exact analytical results for the evaluation of telecommunication system performance measures using the investigation method based on macro state Markov process. We extend the application of Markov model for unreliable system investigation. The paper is organized as follows. The section I introduces to the necessity of the macro state Markov model for telecommunication system investigation. The unreliable data packet loss system with two data packet transmission channels is presented in the section II. The analysis, employing macro states Markov chains, of system with two unreliable channels loss system is described in the section III. The comparison of system performance measures is presented and discussed in the section IV. In the section V we give our conclusions.
机译:本文的目的是提出一种利用马尔可夫变化的方法,对不可靠的电信系统中的过程进行分析。此外,我们提出的基于马尔可夫链宏观状态的分析方法比作者先前用于分析此类不可靠电信系统的详细马尔可夫过程要简单得多[1-8]。对不可靠的电信系统的研究已经付出了很多努力。借助于马尔可夫链[9],在电信系统中数据包传输过程分析领域中存在着丰富的文献。他们中的大多数使用详细的马尔可夫链[6,7]分析系统中的过程。这些论文提供了一些不可靠系统的基本马尔可夫模型的例子。复杂的系统产生了庞大而复杂的马尔可夫模型。大型马尔可夫链模型和平衡方程[8,10]的自动生成使用了几种技术。关于该研究主题的文献有数百篇论文对这种系统进行了精确的分析。解决此问题的一种可能方法是使用宏状态马尔可夫模型。宏状态马尔可夫模型的实现可以简化对复杂系统(例如电信网络)的性能指标的评估。另一方面,本文采用基于宏观状态马尔可夫过程的研究方法,获得了准确的分析结果,用于电信系统性能指标的评估。我们将马尔可夫模型的应用扩展到不可靠的系统研究中。本文的结构如下。第一节介绍了宏观状态马尔可夫模型在电信系统研究中的必要性。第二节介绍了具有两个数据包传输通道的不可靠的数据包丢失系统。第三节介绍了采用宏观状态马尔可夫链对具有两个不可靠通道损耗系统的系统进行的分析。第四节介绍和讨论了系统性能指标的比较。在第五节,我们得出结论。

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