A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic

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Abstract

We consider a family of non-deterministic fluid models that can be approximated under heavy traffic conditions by a multidimensional reflected fractional Brownian motion (rfBm). Specifically, we prove a heavy traffic limit theorem for multi-station fluid models with feedback and non-deterministic arrival process generated by a large enough number of heavy tailed ON/OFF sources, say N. Scaling in time by a factor r and in state space conveniently, and letting N and r approach infinity (in this order) we prove that the scaled immediate workload process converges in some sense to a rfBm. © 2006 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)188-201
JournalStochastic Processes and their Applications
Volume117
DOIs
Publication statusPublished - 1 Feb 2007

Keywords

  • Fluid model
  • Heavy traffic
  • On-off sources
  • Queueing network
  • Reflected fractional Brownian motion
  • Workload process

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