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Structural results on a batch acceptance problem for capacitated queues

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  • Eren Çil
  • E. Örmeci
  • Fikri Karaesmen

Abstract

The purpose of this paper is to investigate the structural properties of the optimal batch acceptance policy in a Markovian queueing system where different classes of customers arrive in batches and the buffer capacity is finite. We prove that the optimal policy can possess certain monotonicity properties under the assumptions of a single-server and constant batch sizes. Even though our proof cannot be extended to cases where either one of the assumptions is relaxed, we numerically observe that the optimal policy can still possess the same properties when only the single-server assumption is relaxed. Finally, we present counterexamples that show the non-monotone structure of the optimal policy when the batch sizes are not constant. Copyright Springer-Verlag 2007

Suggested Citation

  • Eren Çil & E. Örmeci & Fikri Karaesmen, 2007. "Structural results on a batch acceptance problem for capacitated queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 263-274, October.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:263-274
    DOI: 10.1007/s00186-006-0137-6
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    References listed on IDEAS

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    1. Ghoneim, Hussein A. & Stidham, Shaler, 1985. "Control of arrivals to two queues in series," European Journal of Operational Research, Elsevier, vol. 21(3), pages 399-409, September.
    2. Eungab Kim & Mark P. Van Oyen, 1998. "Beyond the cμ rule: Dynamic scheduling of a two-class loss queue," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 17-36, September.
    3. Sergei V. Savin & Morris A. Cohen & Noah Gans & Ziv Katalan, 2005. "Capacity Management in Rental Businesses with Two Customer Bases," Operations Research, INFORMS, vol. 53(4), pages 617-631, August.
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    1. Ziani, Sofiane & Rahmoune, Fazia & Radjef, Mohammed Said, 2015. "Customers’ strategic behavior in batch arrivals M2/M/1 queue," European Journal of Operational Research, Elsevier, vol. 247(3), pages 895-903.
    2. Özkan, Can & Karaesmen, Fikri & Özekici, Süleyman, 2013. "Structural properties of Markov modulated revenue management problems," European Journal of Operational Research, Elsevier, vol. 225(2), pages 324-331.
    3. Xufeng Yang & Wen Jiao & Juliang Zhang & Hong Yan, 2022. "Capacity management for a leasing system with different equipment and batch demands," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3004-3020, July.
    4. Olga Bountali & Apostolos Burnetas & Lerzan Örmeci, 2022. "Join, balk, or jettison? The effect of flexibility and ranking knowledge in systems with batch arrivals," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3505-3524, September.

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