This article focuses on queuing systems with doubly stochastic Poisson regenerative input flow and an infinite number of servers. Service times have the heavy-tailed distribution. The analogs of the law of large numbers and the central limit theorem for the number of occupied servers are obtained. These theorems follow from results for systems with general doubly stochastic Poisson processes [1]. As examples, we consider systems in which the input flow is controlled by a semi-Markov modulated and Markov modulated processes.
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*This work was supported by the Russian Foundation for Basic Research, grant № 13-01-00653 A.
Proceedings of the XXXII International Seminar on Stability Problems for Stochastic Models, Trondheim, Norway, June 16–21, 2014.
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Chernavskaya, E.A. Limit Theorems for Queuing Systems with Regenerative Doubly Stochastic Input Flow*. J Math Sci 214, 34–43 (2016). https://doi.org/10.1007/s10958-016-2756-7
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DOI: https://doi.org/10.1007/s10958-016-2756-7