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Optimization of Open Queuing Networks with Batch Services

Author

Listed:
  • Elena Stankevich

    (Department of System Analysis and Automatic Control, Faculty of Computer Science and Information Technologies, Saratov State University, 83 Astrakhanskaya St., 410012 Saratov, Russia
    These authors contributed equally to this work.)

  • Igor Tananko

    (Department of System Analysis and Automatic Control, Faculty of Computer Science and Information Technologies, Saratov State University, 83 Astrakhanskaya St., 410012 Saratov, Russia
    These authors contributed equally to this work.)

  • Michele Pagano

    (Department of Information Engineering, University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, open queuing networks with Poisson arrivals and single-server infinite buffer queues are considered. Unlike traditional queuing models, customers are served (with exponential service time) in batches, so that the nodes are non-work-conserving. The main contribution of this work is the design of an efficient algorithm to find the batch sizes which minimize the average response time of the network. As preliminary steps at the basis of the proposed algorithm, an analytical expression of the average sojourn time in each node is derived, and it is shown that this function, depending on the batch size, has a single minimum. The goodness of the proposed algorithm and analytical formula were verified through a discrete-event simulation for an open network with a non-tree structure.

Suggested Citation

  • Elena Stankevich & Igor Tananko & Michele Pagano, 2022. "Optimization of Open Queuing Networks with Batch Services," Mathematics, MDPI, vol. 10(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:3027-:d:894749
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    References listed on IDEAS

    as
    1. Wiebke Klünder, 2018. "Decomposition of Open Queueing Networks with Batch Service," Operations Research Proceedings, in: Andreas Fink & Armin Fügenschuh & Martin Josef Geiger (ed.), Operations Research Proceedings 2016, pages 575-581, Springer.
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