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Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling

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Abstract

We present an introductory review of recent work on the control of open queueing networks. We assume that customers of different types arrive at a network and pass through the system via one of several possible routes; the set of routes available to a customer depends on its type. A route through the network is an ordered set of service stations: a customer queues for service at each station on its route and then leaves the system. The two methods of control we consider are the routing of customers through the network, and the sequencing of service at the stations, and our aim is to minimize the number of customers in the system. We concentrate especially on the insights which can be obtained from heavy traffic analysis, and in particular from Harrison's Brownian network models. Our main conclusion is that in many respects dynamic routingsimplifies the behaviour of networks, and that under good control policies it may well be possible to model the aggregate behaviour of a network quite straightforwardly.

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Author notes

  1. C. N. Laws

    Present address: Department of Statistics, University of Oxford, 1 South Parks Road, OX1 3TG, Oxford, England

Authors and Affiliations

  1. Statistical Laboratory, University of Cambridge, 16 Mill Lane, CB2 1SB, Cambridge, England

    F. P. Kelly & C. N. Laws

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  1. F. P. Kelly
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Supported by SERC grant GR/F 94194.

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Kelly, F.P., Laws, C.N. Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling. Queueing Syst 13, 47–86 (1993). https://doi.org/10.1007/BF01158929

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