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A Queueing Reward System with Several Customer Classes

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  • Bruce L. Miller

    (The RAND Corporation, Santa Monica, California)

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    Abstract

    This paper considers an n-server queueing system with m customer classes distinguished by the reward associated with serving customers of that class. Our objective is to accept or reject customers so as to maximize the expected value of the rewards received over an infinite planning horizon. By making the assumptions of Poisson arrivals and a common exponential service time this problem can be formulated as an infinite horizon continuous time Markov decision problem. In §3 we customize the general algorithm for solving continuous time Markov decision problems to our queueing model. In §4 we obtain qualitative results about the form of the optimal policy. §6 reports the results of simulation tests which compare heuristic policies for our model when the service times associated with each customer class have arbitrary distributions. The "winning" policy is based on a rather intricate theorem whose proof comprises §5.

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    File URL: http://dx.doi.org/10.1287/mnsc.16.3.234
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 16 (1969)
    Issue (Month): 3 (November)
    Pages: 234-245

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    Handle: RePEc:inm:ormnsc:v:16:y:1969:i:3:p:234-245

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    Cited by:
    1. Eugene Feinberg, 2005. "On essential information in sequential decision processes," Computational Statistics, Springer, vol. 62(3), pages 399-410, December.
    2. Papier, Felix & Thonemann, Ulrich W., 2011. "Capacity rationing in rental systems with two customer classes and batch arrivals," Omega, Elsevier, vol. 39(1), pages 73-85, January.
    3. Son, Jae-Dong, 2007. "Customer selection problem with profit from a sideline," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1084-1102, January.
    4. Li, Xueping & Wang, Jiao & Sawhney, Rapinder, 2012. "Reinforcement learning for joint pricing, lead-time and scheduling decisions in make-to-order systems," European Journal of Operational Research, Elsevier, vol. 221(1), pages 99-109.
    5. van Wijk, A.C.C. & Adan, I.J.B.F. & van Houtum, G.J., 2012. "Approximate evaluation of multi-location inventory models with lateral transshipments and hold back levels," European Journal of Operational Research, Elsevier, vol. 218(3), pages 624-635.
    6. van Jaarsveld, W.L. & Dekker, R., 2009. "Finding optimal policies in the (S - 1, S ) lost sales inventory model with multiple demand classes," Econometric Institute Research Papers EI 2009-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

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