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Multi-channel queues in heavy traffic

Published online by Cambridge University Press:  14 July 2016

Richard Loulou
Richard Loulou*
Affiliation:
McGill University, Montreal
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Abstract

In this paper, convergence theorems for heavy traffic queues are extended to multi-channel systems under general assumptions. Whitt (1968), and Iglehart and Whitt (1970) have proved weak convergence of the queue length process and the wait process for one-channel queues. Extensions to multi-server queues were established for the queue length process but only partly for the wait process (ρ = 1 only). We give here convergence theorems for the wait process when ρ > 1. Our approach uses weak convergence theory, but is different from previous ones in that we use the virtual delay as an intermediate result. The class of queues considered is more general than GI/G/m.

Keywords

CONGESTED QUEUESHEAVY TRAFFICWEAK CONVERGENCEMULTIPLE SERVER SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 769 - 777
Copyright
Copyright © Applied Probability Trust 1973 

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References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Iglehart, D. and Whitt, W. (1970) Multiple channel queues in heavy traffic. Adv. Appl. Prob. 2, 150–177, 355–369.Google Scholar
Loulou, R. (1971a) Weak convergence for multi-channel queues in heavy traffic. ORC Report No. 71–31. Operations Research Center, University of California, Berkeley.Google Scholar
Loulou, R. (1971b) General classes of multi-channel queues in heavy traffic. Faculty of Management, McGill University, November 1971.Google Scholar
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Whitt, W. (1968) Weak convergence theorems for queues in heavy traffic. Technical Report No. 2. Department of Operations Research, Stanford University.Google Scholar