Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2000 / Article

Open Access

Volume 6 |Article ID 852632 | https://doi.org/10.1155/S1024123X00001423

R. B. Lenin, P. R. Parthasarathy, "Fluid queues driven by an M/M/1/N queue", Mathematical Problems in Engineering, vol. 6, Article ID 852632, 22 pages, 2000. https://doi.org/10.1155/S1024123X00001423

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

Received17 Jan 2000

Abstract

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.

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.


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