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A Uniformization Approach for the Dynamic Control of Queueing Systems with Abandonments

Author

Listed:
  • Benjamin Legros

    (EM Normandie, Laboratoire Métis, 75016 Paris, France)

  • Oualid Jouini

    (CentraleSupélec, Université Paris-Saclay, Laboratoire Genie Industriel, 92290 Chatenay-Malabry, France)

  • Ger Koole

    (Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, Netherlands)

Abstract

We consider queueing systems with general abandonment. Abandonment times are approximated by a particular Cox distribution with all phase exponential rates being the same. We prove that this distribution arbitrarily closely approximates any nonnegative distribution. By explicitly modeling the waiting time of the first customer in line, we obtain a natural bounded jump Markov process allowing for uniformization. This approach is useful to solve, via dynamic programming, various optimization problems where the objectives and/or constraints involve the distributions of the performance measures, not only their expected values. It is also useful for the performance analysis of queueing systems with general abandonment times.

Suggested Citation

  • Benjamin Legros & Oualid Jouini & Ger Koole, 2018. "A Uniformization Approach for the Dynamic Control of Queueing Systems with Abandonments," Operations Research, INFORMS, vol. 66(1), pages 200-209, January.
    • Handle: RePEc:inm:oropre:v:66:y:2018:i:1:p:200-209
    DOI: 10.1287/opre.2017.1652
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    References listed on IDEAS

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    1. G. M. Koole & B. F. Nielsen & T. B. Nielsen, 2012. "First in Line Waiting Times as a Tool for Analysing Queueing Systems," Operations Research, INFORMS, vol. 60(5), pages 1258-1266, October.
    2. Benjamin Legros, 2016. "Unintended consequences of optimizing a queue discipline for a service level defined by a percentile of the waiting time," Post-Print hal-02065945, HAL.
    3. Oualid Jouini & Ger Koole & Alex Roubos, 2013. "Performance indicators for call centers with impatient customers," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 341-354.
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    Citations

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    Cited by:

    1. Benjamin Legros, 2021. "Age-based Markovian approximation of the G/M/1 queue," Post-Print hal-03605431, HAL.
    2. Oualid Jouini & Saif Benjaafar & Bingnan Lu & Siqiao Li & Benjamin Legros, 2022. "Appointment-driven queueing systems with non-punctual customers," Queueing Systems: Theory and Applications, Springer, vol. 101(1), pages 1-56, June.
    3. Gregor Selinka & Raik Stolletz & Thomas I. Maindl, 2022. "Performance Approximation for Time-Dependent Queues with Generally Distributed Abandonments," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 20-38, January.

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