Multiscale queueing analysis

Vinay J. Ribeiro, Rudolf H. Riedi, Richard G. Baraniuk

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


This paper introduces a new multiscale framework for estimating the tail probability of a queue fed by an arbitrary traffic process. Using traffic statistics at a small number of time scales, our analysis extends the theoretical concept of the critical time scale and provides practical approximations for the tail queue probability. These approximations are non-asymptotic; that is, they apply to any finite queue threshold. While our approach applies to any traffic process, it is particularly apt for long-range-dependent (LRD) traffic. For LRD fractional Brownian motion, we prove that a sparse exponential spacing of time scales yields optimal performance. Simulations with LRD traffic models and real Internet traces demonstrate the accuracy of the approach. Finally, simulations reveal that the marginals of traffic at multiple time scales have a strong influence on queueing that is not captured well by its global second-order correlation in non-Gaussian scenarios.

Original languageEnglish (US)
Pages (from-to)1005-1018
Number of pages14
JournalIEEE/ACM Transactions on Networking
Issue number5
StatePublished - Oct 2006


  • Admission control
  • Critical time scale
  • Fractional Brownian motion
  • Long-range dependence
  • Marginals
  • Multifractals
  • Multiscale
  • Network provisioning
  • Queueing
  • Wavelets

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture
  • Information Systems


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