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Multichannel queuing systems with balking and regenerative input fl ow

Author

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  • Tkachenko Andrey

    (National Research University Higher School of Economics (Moscow, Russia) Industrial and Market Studies. The Researcher)

Abstract

Motivated by the application to telephone call centers this paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input ow and balking. Servers times are random variables but not necessary exponential. If a new customer encountering j other customers in the system then it stays for service with probability fj and gets rejection with probability 1 ?? fj . For such a system an ergodicity condition is established and functional heavy trac limit theorems are proved under critically loaded ( " 1) and overloaded conditions ( 1)

Suggested Citation

  • 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.
    • Handle: RePEc:hig:wpaper:wpbrp14sti2013
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    File URL: http://www.hse.ru/data/2013/07/23/1288606025/14STI2013.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Ward Whitt, 2005. "Engineering Solution of a Basic Call-Center Model," Management Science, INFORMS, vol. 51(2), pages 221-235, February.
    3. Nam Kyoo Boots & Henk Tijms, 1999. "A Multiserver Queueing System with Impatient Customers," Management Science, INFORMS, vol. 45(3), pages 444-448, March.
    4. C. J. Ancker & A. V. Cafarian, 1963. "Queuing with reneging and multiple heterogeneous servers," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 125-149, March.
    5. Ger Koole & Avishai Mandelbaum, 2002. "Queueing Models of Call Centers: An Introduction," Annals of Operations Research, Springer, vol. 113(1), pages 41-59, July.
    6. J. G. Dai & Shuangchi He, 2010. "Customer Abandonment in Many-Server Queues," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 347-362, May.
    7. Ward Whitt, 2006. "Fluid Models for Multiserver Queues with Abandonments," Operations Research, INFORMS, vol. 54(1), pages 37-54, February.
    8. Rouba Ibrahim & Ward Whitt, 2009. "Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments," Management Science, INFORMS, vol. 55(10), pages 1729-1742, October.
    9. C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging---II," Operations Research, INFORMS, vol. 11(6), pages 928-937, December.
    10. 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.
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    Cited by:

    1. L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.
    2. L. G. Afanaseva & S. A. Grishunina, 2020. "Stability conditions for a multiserver queueing system with a regenerative input flow and simultaneous service of a customer by a random number of servers," Queueing Systems: Theory and Applications, Springer, vol. 94(3), pages 213-241, April.
    3. Larisa Afanaseva & Elena Bashtova & Svetlana Grishunina, 2020. "Stability Analysis of a Multi-server Model with Simultaneous Service and a Regenerative Input Flow," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1439-1455, December.

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    More about this item

    Keywords

    multichannel queueing system; regenerative input ow; ergodicity; heavy trac limits; balking; reneging.;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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