Optimization of Open Queuing Networks with Batch Services

Elena Stankevich (), Igor Tananko () and Michele Pagano ()
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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
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
Michele Pagano: Department of Information Engineering, University of Pisa, Via G. Caruso 16, 56122 Pisa, Italy

Mathematics, 2022, vol. 10, issue 16, 1-13

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.

Keywords: open queuing networks; batch service; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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