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K competing queues with customer abandonment: optimality of a generalised $$c \mu $$ c μ -rule by the Smoothed Rate Truncation method

Author

Listed:
  • S. Bhulai

    (Vrije Universiteit Amsterdam)

  • H. Blok

    (Eindhoven University of Technology)

  • F. M. Spieksma

    (Universiteit Leiden)

Abstract

We consider a K-competing queues system with the additional feature of customer abandonment. Without abandonment, it is optimal to allocate the server to a queue according to the $$c \mu $$ c μ -rule. To derive a similar rule for the system with abandonment, we model the system as a continuous-time Markov decision process. Due to impatience, the Markov decision process has unbounded jump rates as a function of the state. Hence it is not uniformisable, and so far there has been no systematic direct way to analyse this. The Smoothed Rate Truncation principle is a technique designed to make an unbounded rate process uniformisable, while preserving the properties of interest. Together with theory securing continuity in the limit, this provides a framework to analyse unbounded rate Markov decision processes. With this approach, we have been able to find close-fitting conditions guaranteeing optimality of a strict priority rule.

Suggested Citation

  • S. Bhulai & H. Blok & F. M. Spieksma, 2022. "K competing queues with customer abandonment: optimality of a generalised $$c \mu $$ c μ -rule by the Smoothed Rate Truncation method," Annals of Operations Research, Springer, vol. 317(2), pages 387-416, October.
    • Handle: RePEc:spr:annopr:v:317:y:2022:i:2:d:10.1007_s10479-019-03131-3
    DOI: 10.1007/s10479-019-03131-3
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    References listed on IDEAS

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    1. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    2. H. Blok & F. M. Spieksma, 2017. "Structures of Optimal Policies in MDPs with Unbounded Jumps: The State of Our Art," International Series in Operations Research & Management Science, in: Richard J. Boucherie & Nico M. van Dijk (ed.), Markov Decision Processes in Practice, chapter 0, pages 131-186, Springer.
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