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Markov chain-based method for generating long-range dependence.

Richard G Clegg1, Maurice Dodson

  • 1Department of Mathematics, University of York, York YO10 5DD, United Kingdom. richard@richardclegg.org

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2005
PubMed
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This study introduces a simple model for generating time series with long-range dependence (LRD), ideal for modeling internet traffic data. The Markov modulated process offers a computationally tractable method for analyzing LRD phenomena.

Area of Science:

  • Statistics
  • Telecommunications Engineering
  • Computer Networks

Background:

  • Long-range dependence (LRD) is a statistical property observed in various natural and man-made time series.
  • Internet traffic data frequently exhibits LRD, posing challenges for traditional time series modeling.
  • Existing models for LRD may be computationally complex or analytically intractable.

Purpose of the Study:

  • To present a novel, computationally simple model for generating time series with long-range dependence (LRD).
  • To provide a tractable method for modeling Internet traffic, characterized by binary data (packets and gaps).
  • To offer an alternative to existing, potentially more complex, LRD modeling techniques.

Main Methods:

  • Development of a Markov modulated process based on an infinite Markov chain.

Related Experiment Videos

  • The model generates binary time series (ones and zeros) representing data packets and interpacket gaps.
  • Parameterization of the process to control the exhibited LRD properties.

    • Main Results:

    • The proposed model successfully generates time series exhibiting controllable long-range dependence.
    • The binary output is suitable for direct interpretation as Internet traffic characteristics.
    • The method demonstrates significant computational and analytical simplicity.

    Conclusions:

    • The Markov modulated infinite Markov chain model provides an effective and simple approach for generating LRD time series.
    • This model is particularly well-suited for modeling Internet traffic due to its binary nature and tractability.
    • The proposed method offers a promising, more manageable alternative for LRD analysis in telecommunications.