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Nonlinear approximation of characteristics of a fork–join queueing system with Pareto service as a model of parallel structure of data processing

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  • Gorbunova, A.V.
  • Lebedev, A.V.

Abstract

A fork–join system with Pareto service time distribution is considered as a model of a parallel structure of data processing. For an approximation of the mean response time of the system and its standard deviation, we apply the approach based on a combination of simulation with linear regression and the method of nonlinear Nelder–Mead optimization. Previously, no analysis of fork–join queueing systems with M|G|1 subsystems was carried out due to the complexity of its implementation. Nevertheless, the approach proposed here is capable of delivering approximations of various types of the correlation coefficients of the sojourn times of subtasks in a given system. The analytic expressions derived below are shown to deliver good approximations to these characteristics, as evidenced by numerical experiments. Application of the proposed approach can be extended to systems with more involved architecture, and, in particular, to systems with non-Poisson input flow and various options of distributing of service times of tasks.

Suggested Citation

  • Gorbunova, A.V. & Lebedev, A.V., 2023. "Nonlinear approximation of characteristics of a fork–join queueing system with Pareto service as a model of parallel structure of data processing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 409-428.
    • Handle: RePEc:eee:matcom:v:214:y:2023:i:c:p:409-428
    DOI: 10.1016/j.matcom.2023.07.029
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    References listed on IDEAS

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    1. Carl M. Harris, 1968. "The Pareto Distribution as a Queue Service Discipline," Operations Research, INFORMS, vol. 16(2), pages 307-313, April.
    2. Rani, Shobha & Jain, Madhu & Meena, Rakesh Kumar, 2023. "Queueing modeling and optimization of a fault-tolerant system with reboot, recovery, and vacationing server operating under admission control policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 408-425.
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    4. Weina Wang & Mor Harchol-Balter & Haotian Jiang & Alan Scheller-Wolf & R. Srikant, 2019. "Delay asymptotics and bounds for multitask parallel jobs," Queueing Systems: Theory and Applications, Springer, vol. 91(3), pages 207-239, April.
    5. Kumar, Anshul & Jain, Madhu, 2023. "Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 259-281.
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    7. Dmitry Efrosinin & Natalia Stepanova, 2021. "Estimation of the Optimal Threshold Policy in a Queue with Heterogeneous Servers Using a Heuristic Solution and Artificial Neural Networks," Mathematics, MDPI, vol. 9(11), pages 1-14, May.
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