article

Analysis of a single server queue with semi-Markovian service interruption

Author:

Duan-Shin LeeAuthors Info & Claims

Queueing Systems: Theory and Applications, Volume 27, Issue 1/2

Pages 153 - 178

https://doi.org/10.1023/A:1019162014745

Published: 14 December 1997 Publication History

Abstract

In this paper we analyze a discrete-time single server queue where the service time equals one slot. The numbers of arrivals in each slot are assumed to be independent and identically distributed random variables. The service process is interrupted by a semi-Markov process, namely in certain states the server is available for service while the server is not available in other states. We analyze both the transient and steady-state models. We study the generating function of the joint probability of queue length, the state and the residual sojourn time of the semi-Markov process. We derive a system of Hilbert boundary value problems for the generating functions. The system of Hilbert boundary value problems is converted to a system of Fredholm integral equations. We show that the system of Fredholm integral equations has a unique solution.

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Cited By

Bruneel HWittevrongel S(2017)Analysis of a discrete-time single-server queue with an occasional extra serverPerformance Evaluation10.1016/j.peva.2017.08.009116:C(119-142)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.peva.2017.08.009
Zhu PLing TWei GYing B(2013)Minimizing Nested Interrupts of Secondary Users in Multi-Priority Cognitive Radio NetworksProceedings of the 6th International Conference on Internet and Distributed Computing Systems - Volume 822310.1007/978-3-642-41428-2_2(16-29)Online publication date: 28-Oct-2013
https://dl.acm.org/doi/10.1007/978-3-642-41428-2_2
Walraevens JFiems DBruneel H(2011)Performance analysis of priority queueing systems in discrete timeNetwork performance engineering10.5555/1996629.1996642(203-232)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.5555/1996629.1996642
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Published In

cover image Queueing Systems: Theory and Applications

Queueing Systems: Theory and Applications Volume 27, Issue 1/2

1997

199 pages

ISSN:0257-0130

Issue’s Table of Contents

Copyright © Copyright © 1997 Kluwer Academic Publishers.

Publisher

J. C. Baltzer AG, Science Publishers

United States

Publication History

Published: 14 December 1997

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Cited By

Bruneel HWittevrongel S(2017)Analysis of a discrete-time single-server queue with an occasional extra serverPerformance Evaluation10.1016/j.peva.2017.08.009116:C(119-142)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.peva.2017.08.009
Zhu PLing TWei GYing B(2013)Minimizing Nested Interrupts of Secondary Users in Multi-Priority Cognitive Radio NetworksProceedings of the 6th International Conference on Internet and Distributed Computing Systems - Volume 822310.1007/978-3-642-41428-2_2(16-29)Online publication date: 28-Oct-2013
https://dl.acm.org/doi/10.1007/978-3-642-41428-2_2
Walraevens JFiems DBruneel H(2011)Performance analysis of priority queueing systems in discrete timeNetwork performance engineering10.5555/1996629.1996642(203-232)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.5555/1996629.1996642
Demoor TFiems DWalraevens JBruneel H(2010)The preemptive repeat hybrid server interruption modelProceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications10.5555/1883941.1883948(59-71)Online publication date: 14-Jun-2010
https://dl.acm.org/doi/10.5555/1883941.1883948
Katayama TKobayashi KSeah W(2009)Performance analysis of an M/G/1 satellite node with urgent jobs of a central processing nodeProceedings of the 4th International Conference on Queueing Theory and Network Applications10.1145/1626553.1626565(1-5)Online publication date: 29-Jul-2009
https://dl.acm.org/doi/10.1145/1626553.1626565
Núñez-Queija R(1999)Sojourn times in a processor sharing queue with service interruptionsQueueing Systems: Theory and Applications10.1023/A:101917352328934:1/4(351-386)Online publication date: 14-Jun-1999
https://dl.acm.org/doi/10.1023/A%3A1019173523289

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