Near optimal control of queueing networks over a finite time horizon

We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partition...

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Bibliographic Details
Published in:Annals of operations research Vol. 170; no. 1; pp. 233 - 249
Main Authors: Nazarathy, Yoni, Weiss, Gideon
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2009
Springer Nature B.V
Subjects:
Approximation
Business and Management
Combinatorics
Job shops
Linear programming
Mathematical models
Operations research
Operations Research/Decision Theory
Optimization
Queuing
Servers
Statistical analysis
Studies
Theory of Computation
Wireless networks
Continuous linear programming
Infinite virtual queues
Fluid approximations
Multi-class queueing networks
Queueing control
Maximum pressure policies
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:We propose a method for the control of multi-class queueing networks over a finite time horizon. We approximate the multi-class queueing network by a fluid network and formulate a fluid optimization problem which we solve as a separated continuous linear program. The optimal fluid solution partitions the time horizon to intervals in which constant fluid flow rates are maintained. We then use a policy by which the queueing network tracks the fluid solution. To that end we model the deviations between the queuing and the fluid network in each of the intervals by a multi-class queueing network with some infinite virtual queues. We then keep these deviations stable by an adaptation of a maximum pressure policy. We show that this method is asymptotically optimal when the number of items that is processed and the processing speed increase. We illustrate these results through a simple example of a three stage re-entrant line.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-008-0443-x