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Point Processes Competing for Runs: A New Tool for their Investigation

Author

Listed:
  • Marcel F. Neuts

    (The University of Arizona)

  • Jian-Min Li

    (The University of Adelaide)

Abstract

As part of a broader search for statistical descriptors of the burstiness of stationary point processes including teletraffic streams, we consider a stationary point process with two types of labeled events. With two positive integers r 1 and r 2 specified beforehand, an event of type 2 is the end of a 1-run if it is preceded by at least r 1 events of type 1 for which there are no intervening events of type 2. Similarly, the end of a 2-run is an event of type 1 preceded by at least r 2 events of type 2 without intervening events of type 1. By working with the tractable and versatile Markovian arrival process (MAP) we are able to derive descriptors that can shed light on its behavior. Examples and illustrative figures are included.

Suggested Citation

  • Marcel F. Neuts & Jian-Min Li, 1999. "Point Processes Competing for Runs: A New Tool for their Investigation," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 29-53, July.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:1:d:10.1023_a:1010008123195
    DOI: 10.1023/A:1010008123195
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    References listed on IDEAS

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    1. He, Qi-Ming & Neuts, Marcel F., 1998. "Markov chains with marked transitions," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 37-52, May.
    2. Marcel F. Neuts, 1996. "Descriptors for point processes based on runs: the Markovian arrival process," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-20, January.
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