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Multi-objective performance improvements of general finite single-server queueing networks

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Abstract

Optimizing the performance of general finite single-server acyclic queueing networks is a challenging problem and has been the subject of many studies. The version of the optimization problem treated here considers the minimization of the buffer areas and the service rates simultaneously with the maximization of the throughput. These are conflicting objectives, and the most appropriate methodology appears to be a multi-objective methodology. In fact, algorithms have previously been proposed, and the aim here is to show that the use of a mixed methodology can occasionally improve solutions without a significant increase in the computational costs. This paper shows that improvements in throughput can be achieved through a solution of a type of stochastic knapsack problem, which consists of redistributing the buffer spaces between the lines while preserving the overall capacity using a simulated annealing algorithm; that is, one objective is improved (the throughput) without worsening the other (the overall allocated capacity). A set of computational experiments are presented to demonstrate the effectiveness of the proposed approach. Additionally, some of the insights presented here may help scientists and practitioners in finite single-server queueing network planning.

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(adapted from Cruz et al. 2008)

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(adapted from MacGregor Smith and Cruz MacGregor Smith and Cruz 2005)

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Acknowledgements

This research has been partially funded by the Brazilian agencies CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico of the Ministry for Science and Technology), under Grant #304671/2014-2, and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais) under Grant #CEX-PPM-00564-17.

Funding

The Brazilian government funding agencies mentioned above had no role in the study.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de Minas Gerais, Belo Horizonte, MG, 31270-901, Brazil

    F. R. B. Cruz

  2. Departamento de Estatística, Universidade Federal de Ouro Preto, Ouro Preto, MG, 35400-000, Brazil

    A. R. Duarte & G. L. Souza

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  1. F. R. B. Cruz
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  2. A. R. Duarte
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  3. G. L. Souza
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Correspondence to F. R. B. Cruz.

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Cruz, F.R.B., Duarte, A.R. & Souza, G.L. Multi-objective performance improvements of general finite single-server queueing networks. J Heuristics 24, 757–781 (2018). https://doi.org/10.1007/s10732-018-9379-8

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  • DOI: https://doi.org/10.1007/s10732-018-9379-8

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