Fluid queue driven by an M/M/1 queue

Fluid queue driven by an M/M/1 queue

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Article ID: iaor1995775
Country: United States
Volume: 16
Issue: 3/4
Start Page Number: 373
End Page Number: 386
Publication Date: May 1994
Journal: Queueing Systems
Authors: ,
Keywords: fluid queue
Abstract:

A fluid queue receiving its input from the output of a preceding M/M/1 queue is considered. The input can be characterized as a Markov modulated rate process and the well known spectral decomposition technique can be applied. The novel features in this system relate to the nature of the spectrum, which is shown to be composed of a continuous part and one or two discrete points depending on whether the load of the fluid queue is less or greater than the output to input rate ratio. Explicit expressions of the generalized eigenvectors are given in terms of Chebyshev polynomials of the second kind, and the resolution of unity is determined. The solution for the buffer content distribution is obtained as a simple integral expression. Numerical examples are given.

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