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A Multi-server Queueing Model with Markovian Arrivals and Phase Type Cooperative Services - Simulation Approach Read chapter Read first chapter

2015 | OriginalPaper | Chapter

The \(M/GI/\infty \) System Subject to Semi-Markovian Random Environment

Authors : Anatoly Nazarov, Galina Baymeeva

Published in: Information Technologies and Mathematical Modelling - Queueing Theory and Applications

Publisher: Springer International Publishing

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Abstract

In this paper we consider an \(M/GI/\infty \) queueing system operating in a semi-Markovian random environment. That is, the arrival rate and service-time distribution change according to the external semi-Markov process state transitions. The service policy subject to environment transitions is as follows: the service-time distribution of the present customers does not change until their service is finished. The purpose of our study is to obtain the probability distribution of the number of customers in the system under asymptotic condition of high arrival rate and frequent environment transitions. To do this, we first apply the method of supplementary variable and the original method of dynamic screening to our system. We then conduct the asymptotic analysis of the system to obtain the discrete probability distribution.

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previous chapter On a Flow of Repeated Customers in Stable Tandem Cyclic Queueing Systems
next chapter Probability Density Function for Modulated MAP Event Flows with Unextendable Dead Time
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Metadata
Title
The System Subject to Semi-Markovian Random Environment
Authors
Anatoly Nazarov
Galina Baymeeva
Copyright Year
2015
Book
Information Technologies and Mathematical Modelling - Queueing Theory and Applications

Print ISBN: 978-3-319-25860-7

Electronic ISBN: 978-3-319-25861-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-25861-4_11

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