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Analysis of Markov-modulated fluid polling systems with gated discipline
Journal of Industrial and Management Optimization ( IF 1.3 ) Pub Date : 2019-10-28 , DOI: 10.3934/jimo.2019124
Zsolt Saffer , , Miklós Telek , Gábor Horváth , ,

In this paper we present two different analytical descriptions of the fluid polling model with Markov modulated load and gated discipline. The fluid arrival to the stations is modulated by a common continuous-time Markov chain (the special case when the modulating Markov chains are independent is also included). The fluid is removed at the stations during the service period by a station dependent constant rate.The first analytical description is based on the relationships of steady-state fluid levels at embedded server arrival and departure epochs. We derive the steady-state vector Laplace transform of the fluid levels at the stations at arbitrary epoch and its moments. The second analytical description applies the method of supplementary variables and results in differential equations, from which the joint density function of the fluid levels can be obtained.We also propose computational methods for both analytical descriptions and provide numerical examples to illustrate the numeric computations.

中文翻译:

门控学科的马尔可夫调制流体投票系统分析

在本文中,我们对具有马尔可夫调制载荷和门控约束的流体轮询模型进行了两种不同的分析描述。到达工位的流体是通过一条公共的连续时间马尔可夫链进行调制的(也包括调制马尔可夫链相互独立的特殊情况)。在服务期间,将根据工作站的恒定速率在工作站上清除流体。第一个分析描述是基于嵌入式服务器到达和离开时期的稳态流体水平之间的关系。我们推导了在任意纪元及其时刻的站点上的液位的稳态矢量拉普拉斯变换。第二个分析说明应用了补充变量的方法并得出了微分方程,
更新日期:2019-10-28
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