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Approximate analysis of single-server tandem queues with finite buffers

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  • Remco Bierbooms
  • Ivo Adan
  • Marcel Vuuren

Abstract

In this paper, we study single-server tandem queues with general service times and finite buffers. Jobs are served according to the Blocking-After-Service protocol. To approximately determine the throughput and mean sojourn time, we decompose the tandem queue into single-buffer subsystems, the service times of which include starvation and blocking, and then we iteratively estimate the unknown parameters of the service times of each subsystem. The crucial feature of this approach is that in each subsystem successive service times are no longer assumed to be independent, but a successful attempt is made to include dependencies due to blocking by employing the concept of Markovian Arrival Processes. An extensive numerical study shows that this approach produces very accurate estimates for the throughput and mean sojourn time, outperforming existing methods, especially for longer tandem queues and for tandem queues with service times with a high variability. Copyright The Author(s) 2013

Suggested Citation

  • Remco Bierbooms & Ivo Adan & Marcel Vuuren, 2013. "Approximate analysis of single-server tandem queues with finite buffers," Annals of Operations Research, Springer, vol. 209(1), pages 67-84, October.
    • Handle: RePEc:spr:annopr:v:209:y:2013:i:1:p:67-84:10.1007/s10479-011-1021-1
    DOI: 10.1007/s10479-011-1021-1
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    References listed on IDEAS

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    1. Laoucine Kerbache & J.Macgregor Smith, 1987. "The generalized expansion method for open finite queueing networks," Post-Print hal-00484457, HAL.
    2. Tayfur Altiok, 1989. "Approximate Analysis of Queues in Series with Phase-Type Service Times and Blocking," Operations Research, INFORMS, vol. 37(4), pages 601-610, August.
    3. Kerbachea, Laoucine & MacGregor Smith, J., 1987. "The generalized expansion method for open finite queueing networks," European Journal of Operational Research, Elsevier, vol. 32(3), pages 448-461, December.
    4. Marcello Colledani & Tullio Tolio, 2011. "Performance evaluation of transfer lines with general repair times and multiple failure modes," Annals of Operations Research, Springer, vol. 182(1), pages 31-65, January.
    5. Marcel van Vuuren & Ivo Adan, 2009. "Performance analysis of tandem queues with small buffers," IISE Transactions, Taylor & Francis Journals, vol. 41(10), pages 882-892.
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    Cited by:

    1. Kozlowski, Dawid & Worthington, Dave, 2015. "Use of queue modelling in the analysis of elective patient treatment governed by a maximum waiting time policy," European Journal of Operational Research, Elsevier, vol. 244(1), pages 331-338.

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