Heavy-traffic limit for a feed-forward fluid model with heterogeneous heavy-tailed On/Off sources

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Abstract

We consider a multi-station fluid model with arrivals generated by a large number of non-homogeneous heavy-tailed On/Off sources. If the model is feed-forward in the sense that fluid cannot flow from one station to other with lighter tail distributions, we prove that under heavy-traffic, the scaled workload converges in distribution to a reflected fractional Brownian motion process with a multi-dimensional Hurst parameter. As an application, we analyze the impact of having independent streams with variable parameters in high-speed telecommunication networks, on the asymptotic behavior of the maximum queue length. © 2012 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)41-63
JournalQueueing Systems
Volume74
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • Fluid model
  • Heavy tails
  • Heavy traffic
  • Heterogeneous On/Off sources
  • Maximum queue length
  • Reflected fractional Brownian motion
  • Skorokhod problem
  • Workload process

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