Load-balancing for multi-skilled servers with Bernoulli routing

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Date
2022
Author
Miguélez García, Fernando
Doncel Vicente, Josu ORCID
Prabhu, Balakrishna J.
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Annals of Operations Research 312 : 949-971 (2022)
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http://hdl.handle.net/10810/57343
Abstract
[EN] 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.
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© The Author(s) 2022. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Except where otherwise noted, this item's license is described as © The Author(s) 2022. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.