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Mathematical Problems in Engineering
Volume 6 (2000), Issue 5, Pages 439-460

Fluid queues driven by an M/M/1/N queue

1Department of Mathematics and Computer Science, University of Antwerpen, Universiteitsplein 1, Antwerpen B-2610, Belgium
2Department of Mathematics, Indian Institute of Technology, Madras, Chennai 600 036, India

Received 17 January 2000

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we consider fluid queue models with infinite buffer capacity which receives and releases fluid at variable rates in such a way that the net input rate of fluid into the buffer (which is negative when fluid is flowing out of the buffer) is uniquely determined by the number of customers in an M/M/1/N queue model (that is, the fluid queue is driven by this Markovian queue) with constant arrival and service rates. We use some interesting identities of tridiagonal determinants to find analytically the eigenvalues of the underlying tridiagonal matrix and hence the distribution function of the buffer occupancy. For specific cases, we verify the results available in the literature.