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.
Funder
This work was supported by the Ministry of science and education of the Russian Federation in the framework of the basic part of the scientific research state task
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
2 articles.
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1. Organization of Queuing Analysist of Complex Systems;Deterministic and Stochastic Approaches in Computer Modeling and Simulation;2023-10-06
2. On the Optimal Input Rate in Queues with Batch Service;Axioms;2023-07-01