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Optimal control of queueing networks: an approach via fluid models

Bäuerle, Nicole

Abstract: We consider a general control problem for networks which includes the special cases of scheduling in multiclass queueing networks and routing 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 ß-discounted as well as the finite cost problem 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 condition 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 w.r.t. 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 ones. Last but not least for routing problems an asymptotically optimal decision rule is given explicitly, namely a so-called least-loaded-routing rule.

Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Jahr 2002
Sprache Englisch
Identifikator DOI: 10.1239/aap/1025131220
ISSN: 0001-8678
URN: urn:nbn:de:swb:90-437066
KITopen ID: 1000043706
Erschienen in Advances in Applied Probability
Band 34
Heft 2
Seiten 313-328
Schlagworte Stochastic network, average cost optimality equation, asymptotic optimality, deterministic control problem, stability
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