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A join the shorter queue model in heavy traffic

Part of: Special processes Operations research and management science Markov processes

Published online by Cambridge University Press:  14 July 2016

Stephen R. E. Turner
Stephen R. E. Turner*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, University of Cambridge, 1 Wilberforce Road, Cambridge, CB3 0WB, UK. Email address: sret1@cam.ac.uk
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Abstract

We prove a new heavy traffic limit result for a simple queueing network under a ‘join the shorter queue’ policy, with the amount of traffic which has a routeing choice tending to zero as heavy traffic is approached. In this limit, the system considered does not exhibit state space collapse as in previous work by Foschini and Salz, and Reiman, but there is nevertheless some resource pooling gain over a policy of random routeing.

Keywords

Queueing networkjoin the shorter queueresource poolingstate space collapse

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J60: Diffusion processes 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 212 - 223
Copyright
Copyright © 2000 by The Applied Probability Trust 

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