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On the comparison of waiting times in tandem queues

Published online by Cambridge University Press:  14 July 2016

Shun-Chen Niu
Shun-Chen Niu*
Affiliation:
The Cleveland State University
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Abstract

Using a definition of partial ordering of distribution functions, it is proven that for a tandem queueing system with many stations in series, where each station can have either one server with an arbitrary service distribution or a number of constant servers in parallel, the expected total waiting time in system of every customer decreases as the interarrival and service distributions becomes smaller with respect to that ordering. Some stronger conclusions are also given under stronger order relations. Using these results, bounds for the expected total waiting time in system are then readily obtained for wide classes of tandem queues.

Keywords

TANDEM QUEUESTOTAL WAITING TIMESPARTIAL ORDERINGSBOUNDS

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 707 - 714
Copyright
Copyright © Applied Probability Trust 

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References

Bessler, S. A. and Veinott, A. F. Jr (1966) Optimal policy for a dynamic multi-echelon inventory model. Naval Res. Logist. Quart. 13, 355–389.Google Scholar
Niu, S. C. (1977) Bounds and comparisons for some queueing systems. ORC 77–32, Operations Research Center, University of California, Berkeley.Google Scholar
Niu, S. C. (1980) Bounds for the expected delays in some tandem queues. J. Appl. Prob. 17, 831–838.Google Scholar
Rolski, T. and Stoyan, D. (1976) On the comparison of waiting times in GI/G/1 queues. Operat. Res. 24, 197–200.Google Scholar
Ross, S. M. (1978) Average delay in queues with nonstationary Poisson arrivals. J. Appl. Prob. 15, 602–609.Google Scholar
Stoyan, D. (1977a) Bounds and approximations in queueing through monotonicity and continuity. Operat. Res. 24, 851–863.Google Scholar
Stoyan, D. (1977b) Qualitative Eigenschaften und Abschatzungen Stochastischer Modelle. Akademie-Verlag, Berlin.Google Scholar
Stoyan, D. and Stoyan, H. (1969) Monotonieeigenschaften der Kindenwartezeiten im Modell GI/G/1. Z. Angew. Math. 49, 729–734.Google Scholar
Stoyan, D. and Stoyan, H. (1976) Some qualitative properties of single server queues. Math. Nachr. 70, 29–34.Google Scholar
Tembe, S. V. and Wolff, R. W. (1974) Optimal order of service in tandem queues. Operat. Res. 22, 824–832.Google Scholar