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An algorithmic approach for analysis of finite-source retrial systems with unreliable servers

机译:服务器不可靠的有限源重试系统分析的算法方法

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This paper aims at presenting an approach for analyzing finite-source retrial systems with servers subject to breakdowns and repairs, using Generalized Stochastic Petri Nets (GSPNs). This high-level formalism allows a simple representation of such systems with different breakdown disciplines. From the GSPN model, a Continuous Time Markov Chain (CTMC) can be automatically derived. However, for multiserver retrial systems with unreliable servers, the models may have a huge state space. Using the GSPN model as a support, we propose an algorithm for directly computing the infinitesimal generator of the CTMC without generating the reachability graph. In addition, we develop the formulas of the main stationary performance and reliability indices, as a function of the number of servers, the size of the customer source and the stationary probabilities. Through numerical examples, we discuss the effect of the system parameters and the breakdown disciplines on performance.
机译:本文旨在提出一种使用广义随机Petri网(GSPN)分析服务器故障和维修的有限源重试系统的方法。这种高级形式主义可以简单地表示具有不同分类规则的此类系统。从GSPN模型中,可以自动导出连续时间马尔可夫链(CTMC)。但是,对于服务器不可靠的多服务器重试系统,模型可能具有巨大的状态空间。利用GSPN模型作为支持,我们提出了一种无需生成可达性图即可直接计算CTMC的无穷小生成器的算法。此外,我们根据服务器数量,客户来源的大小和固定概率来开发主要固定性能和可靠性指标的公式。通过数值示例,我们讨论了系统参数和故障准则对性能的影响。

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