Weak convergence in queueing theory

Author:

Iglehart Donald L.

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.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference42 articles.

1. Whitt W. (1974) Exponential heavy traffic approximations for GI/G/s queues. Ann. Probability. To appear.

2. Complements to heavy traffic limit theorems for the GI/G/1 queue

3. Weak convergence theorems for priority queues: preemptive-resume discipline

4. Multiple channel queues in heavy traffic. III: random server selection

5. Whitt W. (1968) Weak convergence theorems for queues in heavy traffic. Ph. D. thesis, Cornell University. Technical Report No. 2, Department of Operations Research, Stanford University.

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