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Methods for Computing a System with Instantaneous Feedback and Variable Input Stream Intensity
Automation and Remote Control ( IF 0.7 ) Pub Date : 2020-11-06 , DOI: 10.1134/s0005117920090052
A. Z. Melikov , S. H. Aliyeva , M. O. Shahmaliyev

We study the Markov model of a servicing system with one server and instantaneous feedback. After servicing is complete, a part of the calls, according to the Bernoulli scheme, either leave the system or immediately return to receive re-servicing, which requires a positive (random) server switching time. The intensity of the incoming stream depends on the state of the server, which can be in operating mode or in switching mode. We find the ergodicity condition for the corresponding two-dimensional Markov chain and propose three methods for studying it: the method of generating functions, the method of spectral expansion, and the method of space merging. We present the results of numerical experiments.



中文翻译:

具有瞬时反馈和可变输入流强度的系统的计算方法

我们研究具有一台服务器和即时反馈的服务系统的马尔可夫模型。维修完成后,根据Bernoulli方案,部分呼叫将离开系统或立即返回以接受重新维修,这需要积极的(随机)服务器切换时间。输入流的强度取决于服务器的状态,服务器可以处于操作模式或切换模式。我们找到了相应的二维马尔可夫链的遍历条件,并提出了三种研究方法:生成函数的方法,谱扩展的方法和空间合并的方法。我们提出数值实验的结果。

更新日期:2020-11-06
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