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A Multiserver Queueing System with Impatient Customers

Author

Listed:
  • Nam Kyoo Boots

    (Department of Econometrics, Vrije University, 1081 HV Amsterdam, The Netherlands)

  • Henk Tijms

    (Department of Econometrics, Vrije University, 1081 HV Amsterdam, The Netherlands)

Abstract

Many real-world situations involve queueing systems in which customers wait for service for a limited time only and leave the system if service has not begun within that time. This paper considers a multiserver queueing system with impatient customers, where the customers arrive according to a Poisson process and the service requirements have a general distribution. A simple and insightful solution is presented for the loss probability. The solution is exact for exponential services and is an excellent heuristic for general service times.

Suggested Citation

  • Nam Kyoo Boots & Henk Tijms, 1999. "A Multiserver Queueing System with Impatient Customers," Management Science, INFORMS, vol. 45(3), pages 444-448, March.
    • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:3:p:444-448
    DOI: 10.1287/mnsc.45.3.444
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    References listed on IDEAS

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    1. Adan, I. J. B. F. & van de Waarsenburg, W. A. & Wessels, J., 1996. "Analyzing EkErc queues," European Journal of Operational Research, Elsevier, vol. 92(1), pages 112-124, July.
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    Citations

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    Cited by:

    1. Yoshiaki Inoue & Onno Boxma & David Perry & Shelley Zacks, 2018. "Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 303-350, August.
    2. Nam Boots & Henk Tijms, 1999. "AnM/M/c queue with impatient customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 213-220, December.
    3. Urtzi Ayesta & Peter Jacko & Vladimir Novak, 2017. "Scheduling of multi-class multi-server queueing systems with abandonments," Journal of Scheduling, Springer, vol. 20(2), pages 129-145, April.
    4. Tkachenko Andrey, 2013. "Multichannel queuing systems with balking and regenerative input fl ow," HSE Working papers WP BRP 14/STI/2013, National Research University Higher School of Economics.
    5. Kim, Bara & Kim, Jeongsim, 2018. "Extension of the loss probability formula to an overloaded queue with impatient customers," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 54-62.
    6. Slotnick, Susan A. & Sobel, Matthew J., 2005. "Manufacturing lead-time rules: Customer retention versus tardiness costs," European Journal of Operational Research, Elsevier, vol. 163(3), pages 825-856, June.
    7. Bert Zwart, 2015. "Loss rates in the single-server queue with complete rejection," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(3), pages 299-315, June.
    8. Wang, Qinan, 2004. "Modeling and analysis of high risk patient queues," European Journal of Operational Research, Elsevier, vol. 155(2), pages 502-515, June.

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