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Superposition of renewal processes and an application to multi-server queues

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  • Kella, Offer
  • Stadje, Wolfgang

Abstract

The aim of this paper is to compare the waiting times of customers in multiple-server queues, where the idle times are removed, with different numbers of servers. For this purpose we develop some results regarding the vector-valued marked point process whose points are arrival epochs of the superposition of renewal processes with different continuous inter-arrival distribution and the marks are the vectors of forward recurrence times of the various renewal processes at these arrival epochs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:17:p:1914-1924
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    References listed on IDEAS

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    1. Alsmeyer, Gerold, 1996. "Superposed continuous renewal processes A Markov renewal approach," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 311-322, February.
    2. Susan L. Albin, 1986. "Delays for Customers from Different Arrival Streams to a Queue," Management Science, INFORMS, vol. 32(3), pages 329-340, March.
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    Cited by:

    1. Stadje, Wolfgang, 2012. "Embedded Markov chain analysis of the superposition of renewal processes," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1497-1503.

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