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Queueing System with Potential for Recruiting Secondary Servers

Author

Listed:
  • Srinivas R. Chakravarthy

    (Department of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI 48504, USA)

  • Alexander N. Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Sergey A. Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Olga S. Dudina

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

Abstract

In this paper, we consider a single server queueing system in which the arrivals occur according to a Markovian arrival process ( MAP ). The served customers may be recruited (or opted from those customers’ point of view) to act as secondary servers to provide services to the waiting customers. Such customers who are recruited to be servers are referred to as secondary servers. The service times of the main as well as that of the secondary servers are assumed to be exponentially distributed possibly with different parameters. Assuming that at most there can only be one secondary server at any given time and that the secondary server will leave after serving its assigned group of customers, the model is studied as a QBD -type queue. However, one can also study this model as a GI / M /1-type queue. The model is analyzed in steady state, and a few illustrative numerical examples are presented.

Suggested Citation

  • Srinivas R. Chakravarthy & Alexander N. Dudin & Sergey A. Dudin & Olga S. Dudina, 2023. "Queueing System with Potential for Recruiting Secondary Servers," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:624-:d:1047397
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    References listed on IDEAS

    as
    1. Isi Mitrani, 2013. "Managing performance and power consumption in a server farm," Annals of Operations Research, Springer, vol. 202(1), pages 121-134, January.
    2. Chakravarthy, Srinivas R. & Agnihothri, Saligrama R., 2008. "A server backup model with Markovian arrivals and phase type services," European Journal of Operational Research, Elsevier, vol. 184(2), pages 584-609, January.
    3. Martin W.P Savelsbergh & Marlin W. Ulmer, 2022. "Challenges and opportunities in crowdsourced delivery planning and operations," 4OR, Springer, vol. 20(1), pages 1-21, March.
    4. Efrosinin, Dmitry & Sztrik, Janos, 2018. "An algorithmic approach to analysing the reliability of a controllable unreliable queue with two heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 271(3), pages 934-952.
    5. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    6. Li, Hui & Yang, Tao, 2000. "Queues with a variable number of servers," European Journal of Operational Research, Elsevier, vol. 124(3), pages 615-628, August.
    7. Srinivas R. Chakravarthy, 2007. "A Multi-Server Queueing Model With Markovian Arrivals And Multiple Thresholds," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 223-243.
    8. Srinivas R. Chakravarthy & Alexander N. Dudin, 2017. "A queueing model for crowdsourcing," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 221-236, March.
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