期刊
AUTOMATIC CONTROL AND COMPUTER SCIENCES
卷 45, 期 3, 页码 123-132出版社
ALLERTON PRESS INC
DOI: 10.3103/S0146411611030035
关键词
continuous-time Markov chain; embedded Markov chain; stationary state probabilities; random environment; one-channel queueing system
We consider the birth-death process, the parameters of which are determined according to the external environment. The latter is described by a continuous-time Markov chain. In the literature, such processes are designated as Markov-modulated. They allow making such processes time-dependent. Therefore, stochastic models that are based on them prove to correspond closer to the real processes of the Internet, insurance systems, etc. The article expounds the methodology for computing stationary state probabilities for the considered processes. As an example, we analyze a one-line queueing system functioning in a random environment. The numerical data demonstrate the presence of a dependence that significantly alters the efficiency factors of the system.
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