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Embedded Markov chain analysis of the superposition of renewal processes

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  • Stadje, Wolfgang

Abstract

For a superposition of i.i.d. renewal processes we derive in closed form the limiting distribution of an embedded counting process that describes the simultaneous presence of points from the individual renewal streams in consecutive inspection intervals of fixed given length.

Suggested Citation

  • Stadje, Wolfgang, 2012. "Embedded Markov chain analysis of the superposition of renewal processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1497-1503.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1497-1503
    DOI: 10.1016/j.spl.2012.04.010
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    References listed on IDEAS

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    1. Kella, Offer & Stadje, Wolfgang, 2006. "Superposition of renewal processes and an application to multi-server queues," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1914-1924, November.
    2. Alsmeyer, Gerold, 1996. "Superposed continuous renewal processes A Markov renewal approach," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 311-322, February.
    3. Susan L. Albin, 1986. "Delays for Customers from Different Arrival Streams to a Queue," Management Science, INFORMS, vol. 32(3), pages 329-340, March.
    4. Mitov, Kosto V. & Yanev, Nikolay M., 2006. "Superposition of renewal processes with heavy-tailed interarrival times," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 555-561, March.
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