Effective bandwidth for a single server queueing system with fractional Brownian input

Sunggon Kim, Seung Yeob Nam, Dan Keun Sung

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The traffic patterns of today's IP networks exhibit two important properties: self-similarity and long-range dependence. The fractional Brownian motion is widely used for representing the traffic model with the properties. We consider a single server fluid queueing system with input process of a fractional Brownian motion type. Packet-loss probability and mean delay are considered as QoS. We show that there is a scaling property among the stationary queue-length distributions of different input parameters and service rates. We also evaluate the scaling factor. From the scaling property, we drive formulas for the effective bandwidth to guarantee the QoS in a single source and multiple sources cases. The formulas indicate that it is essential to evaluate the distribution functions of a type of random variables. For multiple sources the shape of an admissible region and multiplexing gain are analyzed. Finally, numerical examples are shown to validate the proposed scheme.

Original languageEnglish
Pages (from-to)203-223
Number of pages21
JournalPerformance Evaluation
Issue number2-3
StatePublished - Jul 2005


  • Admissible region
  • Effective bandwidth
  • Fluid queueing system
  • Fractional Brownian motion
  • Multiplexing gain


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