A reservation based cyclic server queue with limited service
Pages 70 - 77
Abstract
In this paper, we examine a problem which is an extension of the limited service in a queueing system with a cyclic server. In this service mechanism, each queue, after receiving service in cycle j, makes a reservation for its service requirement in cycle j + 1. In this paper, we consider symmetric case only, i.e., the arrival rates to all the queues are the same. The main contribution to queueing theory is that we propose an approximation for the queue length and sojourn-time distributions for this discipline. Most approximate studies on cyclic queues, which have been considered before, examine the means only. Our method is an iterative one, which we prove to be convergent by using stochastic dominance arguments. We examine the performance of our algorithm by comparing it to simulations and show that the results are very good.
References
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F. Akashi, K. Kobayashi, J. Namiki, K. Watanabe (1988) Multipoint communication system having polling and reservation schemes, U.S.Patent No. ~,7~2,512, May 3, 1988.
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O.J. Boxma and B.W. Meister (1987) Waitingtime approximations for cyclic-service systems with switchover times, Performance Evaluation, Vol. 7, pp. 299-308.
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W. Bux and H.L. Truong (1983) Mean-delay approximation for cyclic service queuelng systems, Performance Evaluation, Vol. 3, pp. 187-196.
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M. Eisenberg (1972)Queues with periodic service and changeover times, Operations Research, Vol. 20, pp. 440-451.
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S.W. Fuhrmann (1985) Symmetric queues served in cyclic order, Operations Research Letters, Vol. 4, pp. 139-144.
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S.W. Fuhrmann and Y.T. Wang (1988)Analysis of cyclic service systems with limited service: Bounds and Approximations, Performance Evaluation, Vol. 9, pp. 35-54.
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M. Sidi and H. Levy (1990) Customers routing in polling systems, Performance-90 (P.J.B. King, I. Mitrani and R.J. Pooley ads.), pp. 319-329, North Holland, Amsterdam.
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K.S. Watson (1984) Performance evaluation of cyclic service strategies- a survey, Proc. Performance 84 (E. Gelenbe ed.) pp. 521-533, North Holland, Amsterdam.
Index Terms
- A reservation based cyclic server queue with limited service
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June 1992
260 pages
June 1992267 pages
Copyright © 1992 ACM.
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Association for Computing Machinery
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Publication History
Published: 01 June 1992
Published in SIGMETRICS Volume 20, Issue 1
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