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Load-balancing for multi-skilled servers with Bernoulli routing

Author

Listed:
  • Fernando Miguelez

    (Universidad Publica de Navarra)

  • Josu Doncel

    (University of the Basque Country, UPV/EHU)

  • Balakrishna J. Prabhu

    (Université de Toulouse, CNRS)

Abstract

We study the optimal Bernoulli routing in a multiclass queueing system with a dedicated server for each class as well as a common (or multi-skilled) server that can serve jobs of all classes. Jobs of each class arrive according to a Poisson process. Each server has a holding cost per customer and use the processor sharing discipline for service. The objective is to minimize the weighted mean holding cost. First, we provide conditions under which classes send their traffic only to their dedicated server, only to the common server, or to both. A fixed point algorithm is given for the computation of the optimal solution. We then specialize to two classes and give explicit expressions for the optimal loads. Finally, we compare the cost of multi-skilled server with that of only dedicated or all common servers. The theoretical results are complemented by numerical examples that illustrate the various structural results as well as the convergence of the fixed point algorithm.

Suggested Citation

  • Fernando Miguelez & Josu Doncel & Balakrishna J. Prabhu, 2022. "Load-balancing for multi-skilled servers with Bernoulli routing," Annals of Operations Research, Springer, vol. 312(2), pages 949-971, May.
    • Handle: RePEc:spr:annopr:v:312:y:2022:i:2:d:10.1007_s10479-022-04532-7
    DOI: 10.1007/s10479-022-04532-7
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    References listed on IDEAS

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    1. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.
    2. Jinsheng Chen & Jing Dong & Pengyi Shi, 2020. "A survey on skill-based routing with applications to service operations management," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 53-82, October.
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