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Admission control strategies for tandem Markovian loss systems

Author

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  • Daniel F. Silva

    (Auburn University)

  • Bo Zhang

    (IBM Research AI)

  • Hayriye Ayhan

    (Georgia Institute of Technology)

Abstract

Motivated by communication networks, we study an admission control problem for a Markovian loss system comprised of two finite capacity service stations in tandem. Customers arrive to station 1 according to a Poisson process, and a gatekeeper, who has complete knowledge of the number of customers at both stations, decides whether to accept or reject each arriving customer. If a customer is rejected, a rejection cost is incurred. If an admitted customer finds that station 2 is full at the time of his service completion at station 1, he leaves the system and a loss cost is incurred. The goal is to find easy-to-implement policies that minimize long-run average cost per unit time. We formulate two intuitive, extremal policies and provide analytical results on their performances. We also present necessary and/or sufficient conditions under which each of these policies is optimal. Next, we show that for some states of the system it is always optimal to admit new arrivals. We also fully characterize the optimal policy when the capacity of each station is two and discuss some characteristics of optimal policies in general. Finally, we design heuristic admission control policies using these insights. Numerical experiments indicate that these heuristic policies yield near-optimal long-run average cost performance.

Suggested Citation

  • Daniel F. Silva & Bo Zhang & Hayriye Ayhan, 2018. "Admission control strategies for tandem Markovian loss systems," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 35-63, October.
    • Handle: RePEc:spr:queues:v:90:y:2018:i:1:d:10.1007_s11134-017-9569-3
    DOI: 10.1007/s11134-017-9569-3
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    References listed on IDEAS

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    1. Ku, Cheng-Yuan & Jordan, Scott, 2003. "Near optimal admission control for multiserver loss queues in series," European Journal of Operational Research, Elsevier, vol. 144(1), pages 166-178, January.
    2. A. Hordijk & L. C. M. Kallenberg, 1979. "Linear Programming and Markov Decision Chains," Management Science, INFORMS, vol. 25(4), pages 352-362, April.
    3. 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.
    4. Litvak, Nelly & van Rijsbergen, Marleen & Boucherie, Richard J. & van Houdenhoven, Mark, 2008. "Managing the overflow of intensive care patients," European Journal of Operational Research, Elsevier, vol. 185(3), pages 998-1010, March.
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    Cited by:

    1. Xinchang Wang & Sigrún Andradóttir & Hayriye Ayhan & Tonghoon Suk, 2020. "Revenue maximization in two‐station tandem queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(2), pages 77-107, March.

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