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Bursts And Gaps Of Markov Renewal Arrival Processes

In: Recent Advances In Stochastic Operations Research

Author

Listed:
  • ANTÓNIO PACHECO

    (Department of Mathematics and CEMAT, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal)

  • HELENA RIBEIRO

    (Department of Mathematics and CEMAT, Escola Superior de Tecnologia e Gestão, Polytechnic Institute of Leiria, Morro do Lena, Alto Vieiro, 2411-901 Leiria, Portugal)

Abstract

We investigate bursts and gaps of Markov renewal arrival processes (MRPs), which are able to model bursty traffic. A burst is a maximal interval of time during which all interarrival times are smaller or equal to some value ν. A gap begins at the time at which a burst ends and is the maximal interval of time during which all interarrival times are greater than ν. We show that bursts and gaps of MRPs may be interpreted as sojourn times in sets of states of related semi-Markov processes (SMPs). Firstly, we partition the state space of an SMP in two subsets and compute moments of the sojourn times in those sets, as well as of the cycle durations, where a cycle is constituted by a visit to one of the sets followed by a visit to the other one. This procedure is used to analyze bursts and gaps of the customer departure process from M/G/1/K queues.

Suggested Citation

  • António Pacheco & Helena Ribeiro, 2007. "Bursts And Gaps Of Markov Renewal Arrival Processes," World Scientific Book Chapters, in: Tadashi Dohi & Shunji Osaki & Katsushige Sawaki (ed.), Recent Advances In Stochastic Operations Research, chapter 17, pages 245-262, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812706683_0017
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