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An approximate method for treating a class of multiqueue problems

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M. A. LeibowitzAuthors Info & Claims

IBM Journal of Research and Development, Volume 5, Issue 3

Pages 204 - 209

https://doi.org/10.1147/rd.53.0204

Published: 01 July 1961 Publication History

Abstract

The following problem is considered: N queues of unrestricted length are served in cyclic order by a single server. Input to each queue is Poisson, the service time distribution may be arbitrary, and a finite time is required by the server to go from one queue to the next. Supposing that at any queue the server serves all units which he finds when he arrives, what is the probability P_n that in a stationary state he finds exactly n units? The method for solving this problem is based on the notion of a "self-consistent" probability distribution and is actually applicable to a general class of multiqueue situations of which the one considered here is typical.

References

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P. M. Morse, Queues, Inventories and Maintenance, John Wiley, 1958.

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[2]

A. T. Barucha-Reid, Elements of the Theory of Markov Processes and Their Applications, McGraw-Hill, 1960. Page 419.

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F. G. Foster, Ann. Math. Stat. 24, 355 (1953).

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L. Landau and E. Lifschitz, Quantum Mechanics, Addison-Wesley, 1957.

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Sarkar DZangwill W(1989)Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems-Exact Results and ApplicationsManagement Science10.5555/2938399.293840435:12(1463-1474)Online publication date: 1-Dec-1989
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Bhuyan LGhosal DYang Q(1989)Approximate Analysis of Single and Multiple Ring NetworksIEEE Transactions on Computers10.1109/12.3085338:7(1027-1040)Online publication date: 1-Jul-1989
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Cheng WLiu J(1988)Performance of ARQ Schemes on Token Ring NetworksIEEE Transactions on Computers10.1109/12.222837:7(826-834)Online publication date: 1-Jul-1988
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cover image IBM Journal of Research and Development

IBM Journal of Research and Development Volume 5, Issue 3

July 1961

75 pages

ISSN:0018-8646

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IBM Corp.

United States

Publication History

Published: 01 July 1961

Received: 12 January 1961

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Sarkar DZangwill W(1989)Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems-Exact Results and ApplicationsManagement Science10.5555/2938399.293840435:12(1463-1474)Online publication date: 1-Dec-1989
https://dl.acm.org/doi/10.5555/2938399.2938404
Bhuyan LGhosal DYang Q(1989)Approximate Analysis of Single and Multiple Ring NetworksIEEE Transactions on Computers10.1109/12.3085338:7(1027-1040)Online publication date: 1-Jul-1989
https://dl.acm.org/doi/10.1109/12.30853
Cheng WLiu J(1988)Performance of ARQ Schemes on Token Ring NetworksIEEE Transactions on Computers10.1109/12.222837:7(826-834)Online publication date: 1-Jul-1988
https://dl.acm.org/doi/10.1109/12.2228
Keilson JServi L(1987)Dynamics of the M/G/1 Vacation ModelOperations Research10.5555/2772671.277268035:4(575-582)Online publication date: 1-Aug-1987
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Servi L(1986)D/G/1 Queues with VacationsOperations Research10.5555/2775890.277590334:4(619-629)Online publication date: 1-Aug-1986
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Wu RChen Y(1975)Analysis of a loop transmission system with round-robin scheduling of servicesIBM Journal of Research and Development10.1147/rd.195.048619:5(486-493)Online publication date: 1-Sep-1975
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Eisenberg M(1972)Queues with Periodic Service and Changeover TimeOperations Research10.1287/opre.20.2.44020:2(440-451)Online publication date: 1-Apr-1972
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Eisenberg M(1971)Two Queues with Changeover TimesOperations Research10.1287/opre.19.2.38619:2(386-401)Online publication date: 1-Apr-1971
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Leibowitz M(1962)A note on some fundamental parameters of multiqueue systemsIBM Journal of Research and Development10.1147/rd.64.04706:4(470-471)Online publication date: 1-Oct-1962
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A Direct Numerical Method for a Class of Queueing Problems

A class of multi-queue problems arising in communication systems

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