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A successive censoring algorithm for a system of connected LDQBD-processes

Author

Listed:
  • Niek Baer

    (University of Twente)

  • Ahmad Al Hanbali

    (King Fahd University of Petroleum and Minerals)

  • Richard J. Boucherie

    (University of Twente)

  • Jan-Kees van Ommeren

    (University of Twente)

Abstract

We consider a Markov Chain in which the state space is partitioned into sets where both transitions within sets and between sets have a special structure. Transitions within each set constitute a finite level dependent quasi-birth-and-death-process (LDQBD), and transitions between sets are restricted to six types of transitions. These latter types are needed to preserve the sets structure in the reduction step of our algorithm. Specifically, we present a successive censoring algorithm, based on matrix analytic methods, to obtain the stationary distribution of this system of connected LDQBD-processes.

Suggested Citation

  • Niek Baer & Ahmad Al Hanbali & Richard J. Boucherie & Jan-Kees van Ommeren, 2022. "A successive censoring algorithm for a system of connected LDQBD-processes," Annals of Operations Research, Springer, vol. 310(2), pages 389-410, March.
    • Handle: RePEc:spr:annopr:v:310:y:2022:i:2:d:10.1007_s10479-020-03903-2
    DOI: 10.1007/s10479-020-03903-2
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    References listed on IDEAS

    as
    1. Niek Baer & Richard J. Boucherie & Jan-Kees C. W. van Ommeren, 2019. "Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic," Transportation Science, INFORMS, vol. 53(2), pages 585-596, March.
    2. Brion N. Feinberg & Samuel S. Chiu, 1987. "A Method to Calculate Steady-State Distributions of Large Markov Chains by Aggregating States," Operations Research, INFORMS, vol. 35(2), pages 282-290, April.
    3. Dwi Ertiningsih & Michael N. Katehakis & Laurens C. Smit & Flora M. Spieksma, 2019. "Level product form QSF processes and an analysis of queues with Coxian interarrival distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 57-72, February.
    4. F. V. Lu & R. F. Serfozo, 1984. "M / M /1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies," Operations Research, INFORMS, vol. 32(5), pages 1116-1132, October.
    5. Yang Woo Shin, 2009. "Fundamental Matrix Of Transient Qbd Generator With Finite States And Level Dependent Transitions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(05), pages 697-714.
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