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Upper bounds on work in system for multichannel queues

Published online by Cambridge University Press:  14 July 2016

Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.

Abstract

Previously derived sample path upper bounds for multi-channel work in system and work in queue are shown to be false. A new proof is given for the corresponding stochastic bounds on these quantities.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1987 

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References

Daley, D. (1985) Some optimality properties of the first-come first-served discipline for G/G/s queues. Manuscript.Google Scholar
Foss, S. G. (1980) Approximation of multichannel queueing systems. Siberian Math. J. 21, 851857.CrossRefGoogle Scholar
Loulou, R. (1983) Two sample-path inequalities for G/G/k queues. INFOR 21, 136144.Google Scholar
Smith, D. and Whitt, W. (1981) Resource sharing for efficiency in traffic systems. Bell Syst. Tech. J. 60, 3955.CrossRefGoogle Scholar
Stoyan, D. (1976) A critical remark on a system approximation in queueing theory. Math. Operationsforsch. Statist. 7, 953956.CrossRefGoogle Scholar
Stoyan, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.Google Scholar
Whitt, W. (1981) On stochastic bounds for the delay distribution in the GI/G/s queue. Operat. Res. 29, 604608.CrossRefGoogle Scholar
Wolff, R. (1977) An upper bound for multi-channel queues. J. Appl. Prob. 14, 884888.CrossRefGoogle Scholar
Wolff, R. (1984) Conditions for finite ladder height and delay moments. Operat. Res. 32, 909916.CrossRefGoogle Scholar
Wolfson, B. (1984) Some moment results for certain tandem and multiple-server queues. J. Appl. Prob. 21, 901910.CrossRefGoogle Scholar