Transient Analysis of an M/M/1 Queue with Reneging, Catastrophes, Server Failures and Repairs

Transient Analysis of an M/M/1 Queue with Reneging, Catastrophes, Server Failures and Repairs Bull. Iran. Math. Soc. https://doi.org/10.1007/s41980-018-0037-6 ORIGINAL PAPER Transient Analysis of an M/M/1 Queue with Reneging, Catastrophes, Server Failures and Repairs 1 1 M. I. G. Suranga Sampath · Jicheng Liu Received: 1 November 2017 / Revised: 11 May 2018 / Accepted: 23 May 2018 © Iranian Mathematical Society 2018 Abstract An M/M/1 queue with reneging, catastrophes, server failures and repairs is considered. The arrivals follow a Poisson process and the servers serve according to an exponential distribution. On arrival a customer decides to join the queue and after joining the queue if a customer has to wait for the service longer than his expectation, he may renege. Explicit expression for the time-dependent probabilities of the system size is obtained in terms of the modified Bessel function of first kind by making use of Laplace transform and probability generating function techniques. The system queue length and failure distribution for steady state are derived. Additionally, time- dependent mean and variance are obtained. A numerical example is presented to study the behavior of the system. Keywords Single-server queue · Catastrophes · Server failure · Reneging Mathematics Subject Classification Primary 60K25; Secondary 68M20 · 90B22 1 Introduction The notion of catastrophes was introduced http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Iranian Mathematical Society Springer Journals

Transient Analysis of an M/M/1 Queue with Reneging, Catastrophes, Server Failures and Repairs

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Publisher
Springer Singapore
Copyright
Copyright © 2018 by Iranian Mathematical Society
Subject
Mathematics; Mathematics, general
ISSN
1017-060X
eISSN
1735-8515
D.O.I.
10.1007/s41980-018-0037-6
Publisher site
See Article on Publisher Site

Abstract

Bull. Iran. Math. Soc. https://doi.org/10.1007/s41980-018-0037-6 ORIGINAL PAPER Transient Analysis of an M/M/1 Queue with Reneging, Catastrophes, Server Failures and Repairs 1 1 M. I. G. Suranga Sampath · Jicheng Liu Received: 1 November 2017 / Revised: 11 May 2018 / Accepted: 23 May 2018 © Iranian Mathematical Society 2018 Abstract An M/M/1 queue with reneging, catastrophes, server failures and repairs is considered. The arrivals follow a Poisson process and the servers serve according to an exponential distribution. On arrival a customer decides to join the queue and after joining the queue if a customer has to wait for the service longer than his expectation, he may renege. Explicit expression for the time-dependent probabilities of the system size is obtained in terms of the modified Bessel function of first kind by making use of Laplace transform and probability generating function techniques. The system queue length and failure distribution for steady state are derived. Additionally, time- dependent mean and variance are obtained. A numerical example is presented to study the behavior of the system. Keywords Single-server queue · Catastrophes · Server failure · Reneging Mathematics Subject Classification Primary 60K25; Secondary 68M20 · 90B22 1 Introduction The notion of catastrophes was introduced

Journal

Bulletin of the Iranian Mathematical SocietySpringer Journals

Published: Jun 4, 2018

References

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