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Beyond the cμ rule: Dynamic scheduling of a two-class loss queue

Author

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  • Eungab Kim
  • Mark P. Van Oyen

Abstract

We consider scheduling a single server in a two-class M/M/1 queueing system with finite buffers subject to holding costs and rejection costs for rejected jobs. We use dynamic programming to investigate the structural properties of optimal policies. Provided that the delay of serving a job is always less costly than rejecting an arrival, we show that the optimal policy has a monotonic threshold type of switching curve; otherwise, numerical analysis indicates that the threshold structure may not be optimal. Copyright Springer-Verlag Berlin Heidelberg 1998

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:48:y:1998:i:1:p:17-36
    DOI: 10.1007/PL00003992
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    Citations

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    Cited by:

    1. Niño Mora, José, 2005. "Marginal productivity index policies for scheduling a multiclass delay-/loss-sensitive queue," DES - Working Papers. Statistics and Econometrics. WS ws053906, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. 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.
    3. Kim, Eungab, 2004. "Stochastic vendor managed replenishment with demand dependent shipment," European Journal of Operational Research, Elsevier, vol. 152(3), pages 723-744, February.
    4. Kim, Eungab, 2005. "Optimal inventory replenishment policy for a queueing system with finite waiting room capacity," European Journal of Operational Research, Elsevier, vol. 161(1), pages 256-274, February.
    5. Eungab Kim & Kaphoon Lee & Suk-Ho Kang, 2006. "Optimal purchasing policy in a two-component assembly system with different purchasing contracts for each component," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 301-327, May.

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