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Embedded Markov chain analysis of the superposition of renewal processes


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  • Stadje, Wolfgang
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 8 ()
    Pages: 1497-1503

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1497-1503

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    Keywords: Superposition; Renewal process; Inspection interval; Embedded Markov chain; Asymptotic distribution;


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    1. 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.
    2. 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.
    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. Alsmeyer, Gerold, 1996. "Superposed continuous renewal processes A Markov renewal approach," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 311-322, February.
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