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Article . 2022
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Article . 2022 . Peer-reviewed
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Asymptotic waiting time analysis of finite source $M/GI/1$ retrial queueing systems with conflicts and unreliable server

Asymptotic waiting time analysis of finite source \(M/GI/1\) retrial queueing systems with conflicts and unreliable server
Authors: Nazarov, Anatoly A.; Sztrik, János; Kvach, Anna;

Asymptotic waiting time analysis of finite source $M/GI/1$ retrial queueing systems with conflicts and unreliable server

Abstract

Summary: The goal of the present paper is to analyze the steady-state distribution of the waiting time in a finite source \(M=G=1\) retrial queueing system where conflicts may happen and the server is unreliable. An asymptotic method is used when the number of source \(N\) tends to infinity, the arrival intensity from the sources, the intensity of repeated calls tend to zero, while service intensity, breakdown intensity, recovery intensity are fixed. It is proved that the limiting steady-state probability distribution of the number of transitions/retrials of a customer into the orbit is geometric, and the waiting time of a customer is generalized exponentially distributed. The average total service time of a customer is also determined. Our new contribution to this topic is the inclusion of breakdown and recovery of the server. Prelimit distributions obtained by means of stochastic simulation are compared to the asymptotic ones and several numerical examples illustrate the power of the proposed asymptotic approach.

Country
Russian Federation
Related Organizations
Keywords

approximations, asymptotic methods, queues with repeated attempts, Queueing theory (aspects of probability theory), очереди повторных попыток, асимптотические методы, системы массового обслуживания с конечными источниками, аппроксимация, conflict and unreliable server, ненадежные серверы, Queues and service in operations research, finite source queueing system

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green