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Authors:
Miron Vinarskiy
Keywords: queuing network; multi-queue node; finite buffer; retrial; delay.
Abstract:
We study a model of an open exponential queuing network where each node comprises several M/M/1 queues that share a common waiting space (a buffer) of limited capacity. A customer arriving to a node with a fully occupied buffer is blocked and re-injected by the source after a delay into the network. The process is repeated until the customer completes his service in the network and exits it. Input flow to each node is a superposition of the external Poisson flow, the flows coming from other nodes, and the retrials. The assumption made is that input flow to a node is a Poisson process. Under this assumption, two results are presented: an analytical evaluation of the network throughput and a method of an approximate analysis of the network model. The approach for both is based on iteratively solving a system of non-linear equations for unknown nodal flow rates. Existence and uniqueness of the solutions, obtained by the iterative algorithms, are rigorously proven in both cases. Required network and node performance characteristics are presented. The method provides low bound estimates for a moderately loaded (non-congested) network.
Pages: 17 to 24
Copyright: Copyright (c) IARIA, 2018
Publication date: July 22, 2018
Published in: conference
ISSN: 2308-3484
ISBN: 978-1-61208-655-2
Location: Barcelona, Spain
Dates: from July 22, 2018 to July 26, 2018