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

Author

Listed:
  • F. R. B. Cruz

    (Universidade Federal de Minas Gerais)

  • A. R. Duarte

    (Universidade Federal de Ouro Preto)

  • G. L. Souza

    (Universidade Federal de Ouro Preto)

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.

Suggested Citation

  • F. R. B. Cruz & A. R. Duarte & G. L. Souza, 2018. "Multi-objective performance improvements of general finite single-server queueing networks," Journal of Heuristics, Springer, vol. 24(5), pages 757-781, October.
    • Handle: RePEc:spr:joheur:v:24:y:2018:i:5:d:10.1007_s10732-018-9379-8
    DOI: 10.1007/s10732-018-9379-8
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    References listed on IDEAS

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    1. Laoucine Kerbache & F. S. Q. Alves & H. C. Yehia & L.A.C Pedrosa & F.R.B. Cruz, 2011. "Upper Bounds on Performance Measures of Heterogeneous M/M/c Queues," Post-Print hal-00609498, HAL.
    2. Laoucine Kerbache & J.Macgregor Smith, 1987. "The generalized expansion method for open finite queueing networks," Post-Print hal-00484457, HAL.
    3. Toshikazu Kimura, 1996. "A Transform-Free Approximation for the Finite Capacity M / G / s Queue," Operations Research, INFORMS, vol. 44(6), pages 984-988, December.
    4. Lin, Feng-Tse, 2008. "Solving the knapsack problem with imprecise weight coefficients using genetic algorithms," European Journal of Operational Research, Elsevier, vol. 185(1), pages 133-145, February.
    5. Kerbachea, Laoucine & MacGregor Smith, J., 1987. "The generalized expansion method for open finite queueing networks," European Journal of Operational Research, Elsevier, vol. 32(3), pages 448-461, December.
    6. Smith, J. MacGregor & Cruz, F.R.B. & van Woensel, T., 2010. "Topological network design of general, finite, multi-server queueing networks," European Journal of Operational Research, Elsevier, vol. 201(2), pages 427-441, March.
    7. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    8. Tom van Woensel & Frederico R B Cruz, 2014. "Optimal Routing in General Finite Multi-Server Queueing Networks," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-15, July.
    9. Arnoud Bruin & A. Rossum & M. Visser & G. Koole, 2007. "Modeling the emergency cardiac in-patient flow: an application of queuing theory," Health Care Management Science, Springer, vol. 10(2), pages 125-137, June.
    10. Cruz, F.R.B. & van Woensel, T. & MacGregor Smith, J. & Lieckens, K., 2010. "On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks," European Journal of Operational Research, Elsevier, vol. 201(1), pages 183-193, February.
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    Cited by:

    1. H. S. R. Martins & F. R. B. Cruz & A. R. Duarte & F. L. P. Oliveira, 2019. "Modeling and optimization of buffers and servers in finite queueing networks," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 123-150, March.
    2. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.

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