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Optimal control of queueing networks: an approach via fluid models

Part of: Stochastic systems and control Computer system organization Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Nicole Bäuerle
Nicole Bäuerle*
Affiliation:
University of Ulm
*
∗ Postal address: Department of Mathematics VII, University of Ulm, D-89069 Ulm, Germany. Email address: baeuerle@mathematik.uni-ulm.de
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Abstract

We consider a general control problem for networks with linear dynamics which includes the special cases of scheduling in multiclass queueing networks and routeing problems. The fluid approximation of the network is used to derive new results about the optimal control for the stochastic network. The main emphasis lies on the average-cost criterion; however, the β-discounted as well as the finite-cost problems are also investigated. One of our main results states that the fluid problem provides a lower bound to the stochastic network problem. For scheduling problems in multiclass queueing networks we show the existence of an average-cost optimal decision rule, if the usual traffic conditions are satisfied. Moreover, we give under the same conditions a simple stabilizing scheduling policy. Another important issue that we address is the construction of simple asymptotically optimal decision rules. Asymptotic optimality is here seen with respect to fluid scaling. We show that every minimizer of the optimality equation is asymptotically optimal and, what is more important for practical purposes, we outline a general way to identify fluid optimal feedback rules as asymptotically optimal. Last, but not least, for routeing problems an asymptotically optimal decision rule is given explicitly, namely a so-called least-loaded-routeing rule.

Keywords

Stochastic networkaverage-cost optimality equationasymptotic optimalitydeterministic control problemstability

MSC classification

Primary: 90B15: Network models, stochastic 93E20: Optimal stochastic control
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 2 , June 2002 , pp. 313 - 328
Copyright
Copyright © Applied Probability Trust 2002 

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Footnotes

Work supported in part by a grant from the University of Ulm.

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