This article is cited in 2 papers

Single server queueing system with dependent interarrival times

V. G. Ushakov^ab, N. G. Ushakov<sup>cd

a</sup> Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^b Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov, Moscow State University, 1-52 Leninskiye Gory, Moscow 119991, GSP-1, Russian Federation
^c Institute of Microelectronics Technology and High-Purity Materials of the Russian Academy of Sciences, 6 Academician Osipyan Str., Chernogolovka, Moscow Region 142432, Russian Federation
^d Norwegian University of Science and Technology, 15A S. P. Andersensvei, Trondheim 7491, Norway

Abstract: The paper studies a single server queueing system with an infinite number of positions in the queue and random distribution of the service time. The incoming flow of claims is a Poisson flow with a random intensity. The current intensity value is selected from a finite set with given probabilities at the start of the countdown to the next receipt of the claim. Sequential intensities form a Markov chain of a special kind. Particular cases of such flows are hyperexponential flows and flows arising in the study of Bayesian models of queueing systems with a discrete prior distribution. Considered flows describe well the work of queueing systems operating in a random environment with a finite set of different states and Markov relationship between them. Furthermore, such flows can accurately approximate real flows in data networks. The nonstationary behavior of the queue length is studied.

Keywords: Poisson flow; random intensity; hyperexponential flow; Markov chain; single server; queue length.

Received: 02.03.2017

DOI: 10.14357/19922264170212

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