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An approximation for multi-server queues with deterministic reneging times

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  • Wei Xiong
  • Tayfur Altiok

Abstract

This work was motivated by the timeout mechanism used in managing application servers in transaction processing environments. In such systems, a customer who stays in the queue longer than the timeout period is lost. We modeled a server node with a timeout threshold as a multi-server queue with Poisson arrivals, general service time distribution and deterministic reneging times. We proposed a scaling approach, and a fast and accurate approximation for the expected waiting time in the queue. Copyright Springer Science+Business Media, LLC 2009

Suggested Citation

  • Wei Xiong & Tayfur Altiok, 2009. "An approximation for multi-server queues with deterministic reneging times," Annals of Operations Research, Springer, vol. 172(1), pages 143-151, November.
  • Handle: RePEc:spr:annopr:v:172:y:2009:i:1:p:143-151:10.1007/s10479-009-0534-3
    DOI: 10.1007/s10479-009-0534-3
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    References listed on IDEAS

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    1. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    2. Bong Dae Choi & Bara Kim & Dongbi Zhu, 2004. "MAP/M/c Queue with Constant Impatient Time," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 309-325, May.
    3. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    4. 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.
    5. O. J. Boxma & J. W. Cohen & N. Huffels, 1979. "Approximations of the Mean Waiting Time in an M / G / s Queueing System," Operations Research, INFORMS, vol. 27(6), pages 1115-1127, December.
    6. David L. Jagerman & Benjamin Melamed, 2003. "Models and Approximations for Call Center Design," Methodology and Computing in Applied Probability, Springer, vol. 5(2), pages 159-181, June.
    7. David Y. Sze, 1984. "OR Practice—A Queueing Model for Telephone Operator Staffing," Operations Research, INFORMS, vol. 32(2), pages 229-249, April.
    8. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
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    Cited by:

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