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

Chihoon Lee, Ananda Weerasinghe

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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 > 1/2 , 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.

Original languageEnglish
Pages (from-to)847-874
Number of pages28
JournalAdvances in Applied Probability
Volume43
Issue number3
DOIs
StatePublished - Sep 2011

Keywords

  • Controlled queueing system
  • Fractional Brownian motion
  • Heavy traffic theory
  • Long-range dependence
  • Self-similarity
  • Stochastic control
  • Tandem queue

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