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A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain

Published: 01 April 1973 Publication History

Abstract

This paper considers an n-phase generalization of the typical M/M/1 queuing model, where the queuing-type birth-and-death process is defined on a continuous-time n-state Marker chain. It shows that many models analyzed in the literature can be considered special cases of this framework. The paper focuses on the steady-state regime, and observes that, in general, closed-form results for the limiting probabilities are difficult to obtain, if at all possible. Hence, numerical methods should be employed. For an interesting special case, explicit results are obtained that are analogous to the classical solutions for the simple M/M/1 queue.

References

[1]
S. KARLIN, A First Course in Stochastic Processes, Academic Press, New York, 1966.
[2]
I. L. MITRANI AND B. AVI-ITZHAK, "A Many-Server Queue with Service Interruptions," Opns. Res. 16, 628-638(1968).
[3]
M. F. NEUTS, "A Queue Subject to Extraneous Phase Changes," Adv. in Appl. Prob. 3, 78-119 (1971).
[4]
U. YECHIALI AND P. NAOR, "Queuing Problems with Heterogeneous Arrivals and Service," Opns. Res. 19, 722-734 (1971).

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Published In

cover image Operations Research
Operations Research  Volume 21, Issue 2
April 1973
286 pages

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 April 1973

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  • (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
  • (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
  • (1994)Markovian queueing networks in a random environmentOperations Research Letters10.1016/0167-6377(94)90009-415:1(11-17)Online publication date: 1-Feb-1994
  • (1991)Asymptotic Analysis of a Heterogeneous Multiprocessor System in a Randomly Changing EnvironmentIEEE Transactions on Software Engineering10.1109/32.9919417:10(1069-1075)Online publication date: 1-Oct-1991

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