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First in Line Waiting Times as a Tool for Analysing Queueing Systems

Author

Listed:
  • G. M. Koole

    (VU University Amsterdam, 1081 HV Amsterdam, The Netherlands)

  • B. F. Nielsen

    (Technical University of Denmark, 2800 Kgs. Lyngby, Denmark)

  • T. B. Nielsen

    (Technical University of Denmark, 2800 Kgs. Lyngby, Denmark)

Abstract

We introduce a new approach to modelling queueing systems where the priority or the routing of customers depends on the time the first customer has waited in the queue. This past waiting time of the first customer in line, W FIL , is used as the primary variable for our approach. A Markov chain is used for modelling the system where the states represent both the number of free servers and a discrete approximation to W FIL . This approach allows us to obtain waiting time distributions for complex systems, such as the N-design routing scheme widely used, e.g., in call centers and systems with dynamic priorities.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1258-1266
    DOI: 10.1287/opre.1120.1089
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    References listed on IDEAS

    as
    1. James R. Jackson, 1961. "Queues with Dynamic Priority Discipline," Management Science, INFORMS, vol. 8(1), pages 18-34, October.
    2. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    3. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    4. M. Posner, 1973. "Single-Server Queues with Service Time Dependent on Waiting Time," Operations Research, INFORMS, vol. 21(2), pages 610-616, April.
    5. Alan Cobham, 1954. "Priority Assignment in Waiting Line Problems," Operations Research, INFORMS, vol. 2(1), pages 70-76, February.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Legros, Benjamin, 2021. "Routing analyses for call centers with human and automated services," International Journal of Production Economics, Elsevier, vol. 240(C).
    2. Benjamin Legros, 2021. "Age-based Markovian approximation of the G/M/1 queue," Post-Print hal-03605431, HAL.
    3. 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.
    4. Benjamin Legros, 2021. "Routing analyses for call centers with human and automated services," Post-Print hal-03605426, HAL.
    5. Benjamin Legros & Sihan Ding & Rob Mei & Oualid Jouini, 2017. "Call centers with a postponed callback offer," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(4), pages 1097-1125, October.
    6. Michael Manitz & Marc-Philip Piehl, 2024. "A fast staffing algorithm for multistage call centers with impatient customers and time-dependent overflow," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 32(3), pages 763-791, September.

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