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August 2000 Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality
Constantinos Maglaras
Ann. Appl. Probab. 10(3): 897-929 (August 2000). DOI: 10.1214/aoap/1019487513

Abstract

This paper describes a general approach for dynamic control of stochastic networks based on fluid model analysis, where in broad terms, the stochastic network is approximated by its fluid analog, an associated fluid control problem is solved and, finally, a scheduling rule for the original system is defined by interpreting the fluid control policy. The main contribution of this paper is to propose a general mechanism for translating the solution of the fluid optimal control problem into an implementable discrete-review policy that achieves asymptotically optimal performance under fluid scaling, and guarantees stability if the traffic intensity is less than one at each station. The proposed policy reviews system status at discrete points in time, and at each such point the controller formulates a processing plan for the next review period,based on the queue length vector observed, using the optimal control policy of the associated fluid optimization problem. Implementation of such a policy involves enforcement of certain safety stock requirements in order to facilitate the execution of the processing plans and to avoid unplanned server idleness. Finally, putting aside all considerations of system optimality, the following generalization is considered: every initial condition is associated with a feasible fluid trajectory that describes the desired system evolution starting at that point. A discrete-review policy is described that asymptotically tracks this target specification; that is, it achieves the appropriate target trajectory as its fluid limit.

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Constantinos Maglaras. "Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality." Ann. Appl. Probab. 10 (3) 897 - 929, August 2000. https://doi.org/10.1214/aoap/1019487513

Information

Published: August 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1083.60520
MathSciNet: MR1789983
Digital Object Identifier: 10.1214/aoap/1019487513

Subjects:
Primary: 60K25
Secondary: 60F17 , 90B35

Keywords: asymptotic optimality , discrete-review policies , fluid models , Queueing networks , trajectory tracking

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.10 • No. 3 • August 2000
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