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Optimal Control of a Stochastic Processing System Driven by a Fractional Brownian Motion Input

Part of: Special processes Operations research and management science Computer system organization

Published online by Cambridge University Press:  01 July 2016

Arka P. Ghosh ,
Alexander Roitershtein  and
Ananda Weerasinghe
Arka P. Ghosh*
Affiliation:
Iowa State University
Alexander Roitershtein*
Affiliation:
Iowa State University
Ananda Weerasinghe*
Affiliation:
Iowa State University
*
∗ Postal address: Department of Statistics, Iowa State University, 3216 Snedecor Hall, Ames, IA 50011, USA. Email address: apghosh@iastate.edu
∗∗ Postal address: Department of Mathematics, Iowa State University, 420 Carver Hall, Ames, IA 50011, USA. Email address: roiterst@iastate.edu
∗∗∗ Postal address: Department of Mathematics, Iowa State University, 414 Carver Hall, Ames, IA 50011, USA. Email address: ananda@iastate.edu
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Abstract

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We consider a stochastic control model driven by a fractional Brownian motion. This model is a formal approximation to a queueing network with an ON-OFF input process. We study stochastic control problems associated with the long-run average cost, the infinite-horizon discounted cost, and the finite-horizon cost. In addition, we find a solution to a constrained minimization problem as an application of our solution to the long-run average cost problem. We also establish Abelian limit relationships among the value functions of the above control problems.

Keywords

Stochastic controlcontrolled queueing networkheavy traffic analysisfractional Brownian motionself-similaritylong-range dependence

MSC classification

Primary: 60K25: Queueing theory 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Secondary: 90B18: Communication networks
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 183 - 209
Copyright
Copyright © Applied Probability Trust 2010 

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