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Strong Approximations of Irreducible Closed Queueing Networks

Part of: Stochastic processes Operations research and management science Markov processes Limit theorems Special processes

Published online by Cambridge University Press:  01 July 2016

Hanqin Zhang
Hanqin Zhang*
Affiliation:
Academia Sinica
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Abstract

A sequence of irreducible closed queueing networks is considered in this paper. We obtain that the queue length processes can be approximated by reflected Brownian motions. Using these approximations, we get rates of convergence of the distributions of queue lengths.

Keywords

CLOSED QUEUEING NETWORKREFLECTED BROWNIAN MOTIONSTRONG APPROXIMATIONRATE OF CONVERGENCELEVY-PROHOROV DISTANCE

MSC classification

Primary: 60F17: Functional limit theorems; invariance principles 60K25: Queueing theory 60G17: Sample path properties
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 90B10: Network models, deterministic 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 29 , Issue 2 , June 1997 , pp. 498 - 522
Copyright
Copyright © Applied Probability Trust 1997 

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