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Stationarity and control of a tandem fluid network with fractional Brownian motion input

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

Published online by Cambridge University Press:  01 July 2016

Chihoon Lee  and
Ananda Weerasinghe
Chihoon Lee*
Affiliation:
Colorado State University
Ananda Weerasinghe*
Affiliation:
Iowa State University
*
∗ Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA. Email address: chihoon@stat.colostate.edu
∗∗ Postal address: Department of Mathematics, Iowa State University, Ames, IA 50011, USA.
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Abstract

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We consider a stochastic control model for a queueing system driven by a two-dimensional fractional Brownian motion with Hurst parameter 0 < H < 1. In particular, when H > ½, this model serves to approximate a controlled two-station tandem queueing model with heavy-tailed ON/OFF sources in heavy traffic. We establish the weak convergence results for the distribution of the state process and construct an explicit stationary state process associated with given controls. Based on suitable coupling arguments, we show that each state process couples with its stationary counterpart and we use it to represent the long-run average cost functional in terms of the stationary process. Finally, we establish the existence result of an optimal control, which turns out to be independent of the initial data.

Keywords

Stochastic controlcontrolled queueing systemheavy traffic theoryfractional Brownian motiontandem queuelong-range dependenceself-similarity

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 43 , Issue 3 , September 2011 , pp. 847 - 874
Copyright
Copyright © Applied Probability Trust 2011 

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