Fluid queue driven by an M/M/1 queue

Jorma Virtamo, Ilkka Norros

Research output: Contribution to journalArticleScientificpeer-review

46 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)373-386
Number of pages14
JournalQueueing Systems
Volume16
Issue number3-4
DOIs
Publication statusPublished - 1994
MoE publication typeA1 Journal article-refereed

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Fluids
Eigenvalues and eigenfunctions
Polynomials
Decomposition
Queue
Buffer
Integral
Spectral decomposition

Cite this

Virtamo, Jorma ; Norros, Ilkka. / Fluid queue driven by an M/M/1 queue. In: Queueing Systems. 1994 ; Vol. 16, No. 3-4. pp. 373-386.
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Virtamo, J & Norros, I 1994, 'Fluid queue driven by an M/M/1 queue', Queueing Systems, vol. 16, no. 3-4, pp. 373-386. https://doi.org/10.1007/BF01158963

Fluid queue driven by an M/M/1 queue. / Virtamo, Jorma; Norros, Ilkka.

In: Queueing Systems, Vol. 16, No. 3-4, 1994, p. 373-386.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Norros, Ilkka

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N2 - 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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