Abstract
In this chapter, the results obtained in Chaps. 2–4 are illustrated by applications to perturbed M/M-type queuing systems with bounded and unbounded buffers. We are especially interested in the applications of the results of Chap. 4 related to the first-rare-event times, based on Markov renewal processes with transition periods and extending phase spaces for modulating semi-Markov processes. We present necessary and sufficient conditions for convergence in distribution of first-rare-event times for a number of models of perturbed M/M-type queuing systems with bounded and unbounded buffers. This chapter includes two sections.
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References
Gyllenberg, M., Silvestrov, D.S. (2008). Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems. De Gruyter Expositions in Mathematics, 44, Walter de Gruyter, Berlin, ix+579 pp.
Silvestrov, D.S. (1980a). Semi-Markov Processes with a Discrete State Space. Library for the Engineer in Reliability, Sovetskoe Radio, Moscow, 272 pp.
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Silvestrov, D. (2022). First-Rare-Event Times for Perturbed M/M-Type Queuing Systems. In: Perturbed Semi-Markov Type Processes I. Springer, Cham. https://doi.org/10.1007/978-3-030-92403-4_7
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DOI: https://doi.org/10.1007/978-3-030-92403-4_7
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