Fluid approximation to controlled jump Markov processes with local transitions

Authors:
Alexey Piunovskiy
Affiliations:
The University of Liverpool, Department of Mathematical Sciences, Liverpool, UK
Venue:
ECC'09 Proceedings of the 3rd international conference on European computing conference
Year:
2009

Citing 2
Cited 0

Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cµ-Rule

Operations Research
Introduction to Probability Models, Ninth Edition

Introduction to Probability Models, Ninth Edition

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Abstract

Under the heavy traffic condition, i.e. under large values of the scaling paramter n, it is sensible to replace the stochastic queueing model with the corresponding fluid model. After solving an optimal control problem for the latter one, the natural question arises: if we apply the obtained quasi-optimal control strategy to the underlying stochastic system, how far from the optimality will the objective be? We suggest a general method which makes it possible to estimate that accuracy only in the terms of initial data and show that the error approaches zero when the scaling parameter goes to infinity.