article

Stochastic Variations in Queuing Processes

Authors:

M. Eisen,

M. TainiterAuthors Info & Claims

Operations Research, Volume 11, Issue 6

Pages 922 - 927

https://doi.org/10.1287/opre.11.6.922

Published: 01 December 1963 Publication History

Abstract

In this paper we consider a queuing process in which there are two mean arrival and service rates. Not only does the system randomly change from one mode of service and arrival to the other, but units arrive at random and require varying amounts of service. Analytic expressions are obtained for the generating functions, the mean queue length, and the mean waiting time. Several practical illustrations are given.

References

[1]

T L SAATY, Elements of Queuing Theory, McGraw-Hill, New York, 1961.

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[2]

L TAKACS, Introduction to the Theory of Queues, Oxford U Press, New York, 1962.

Google Scholar

[3]

M EISEN, "Effects of Slowdowns and Failures on Stochastic Service Systems," To appear, Technometrics, August 1963.

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[4]

W FELLER, An Introduction to Probability Theory and Its Applications, Wiley, New York. 1957.

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Liu NKulkarni V(2009)Decomposition property for markov-modulated queues with applications to warranty managementProbability in the Engineering and Informational Sciences10.1017/S026996480900026623:3(433-447)Online publication date: 1-Jul-2009
https://dl.acm.org/doi/10.1017/S0269964809000266
Baykal-Gursoy MDuan ZLenzini LCruz R(2006)M/M/C queues with Markov modulated service processesProceedings of the 1st international conference on Performance evaluation methodolgies and tools10.1145/1190095.1190143(38-es)Online publication date: 11-Oct-2006
https://dl.acm.org/doi/10.1145/1190095.1190143
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Operations Research Volume 11, Issue 6

December 1963

176 pages

ISSN:0030-364X

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INFORMS

Linthicum, MD, United States

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Published: 01 December 1963

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Huang LQian L(2017)Age of Information for Transmissions over Markov ChannelsGLOBECOM 2017 - 2017 IEEE Global Communications Conference10.1109/GLOCOM.2017.8254444(1-6)Online publication date: 4-Dec-2017
https://dl.acm.org/doi/10.1109/GLOCOM.2017.8254444
Liu NKulkarni V(2009)Decomposition property for markov-modulated queues with applications to warranty managementProbability in the Engineering and Informational Sciences10.1017/S026996480900026623:3(433-447)Online publication date: 1-Jul-2009
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Baykal-Gursoy MDuan ZLenzini LCruz R(2006)M/M/C queues with Markov modulated service processesProceedings of the 1st international conference on Performance evaluation methodolgies and tools10.1145/1190095.1190143(38-es)Online publication date: 11-Oct-2006
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Takine T(2005)Single-Server Queues with Markov-Modulated Arrivals and Service SpeedQueueing Systems: Theory and Applications10.1007/s11134-004-5553-949:1(7-22)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.1007/s11134-004-5553-9
Federgruen AGreen L(1986)Queueing Systems with Service InterruptionsOperations Research10.5555/2768931.276894034:5(752-768)Online publication date: 1-Oct-1986
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Neuts MLucantoni D(1979)A Markovian Queue with N Servers Subject to Breakdowns and RepairsManagement Science10.1287/mnsc.25.9.84925:9(849-861)Online publication date: 1-Sep-1979
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Purdue P(1974)The M/M/1 Queue in a Markovian EnvironmentOperations Research10.1287/opre.22.3.56222:3(562-569)Online publication date: 1-Jun-1974
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