First-Rare-Event Times for Perturbed M/M-Type Queuing Systems

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 7 in Perturbed Semi-Markov Type Processes I, 2022, pp 165-199 from Springer

Abstract: 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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-92403-4_7

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DOI: 10.1007/978-3-030-92403-4_7

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