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Weak convergence in queueing theory

Published online by Cambridge University Press:  01 July 2016

Donald L. Iglehart
Donald L. Iglehart*
Affiliation:
Stanford University
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Abstract

In the last ten years the theory of weak convergence of probability measures has been used extensively in studying the models of applied probability. By far the greatest consumer of weak convergence has been the area of queueing theory. This survey paper represents an attempt to summarize the experience in queueing theory with the hope that it will prove helpful in other areas of applied probability. The paper is organized into the following sections: queues in light traffic, queues in heavy traffic, queues with a large number of servers, continuity of queues, rates of convergence, and special queueing models.

Keywords

CONTINUITY OF QUEUESDIFFUSION APPROMIXATIONSFUNCTIONAL CENTRAL LIMIT THEOREMSINVARIANCE PRINCIPLEQUEUEING THEORYQUEUES IN HEAVY TRAFFICQUEUES IN LIGHT TRAFFICQUEUES WITH MANY SERVERSWEAK CONVERGENCE
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 570 - 594
Copyright
Copyright © Applied Probability Trust 1973 

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