### Abstract

Original language | English |
---|---|

Pages (from-to) | 373-386 |

Number of pages | 14 |

Journal | Queueing Systems |

Volume | 16 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 1994 |

MoE publication type | A1 Journal article-refereed |

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### Cite this

*Queueing Systems*,

*16*(3-4), 373-386. https://doi.org/10.1007/BF01158963

}

*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.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Fluid queue driven by an M/M/1 queue

AU - Virtamo, Jorma

AU - Norros, Ilkka

N1 - Project code: TTE1207

PY - 1994

Y1 - 1994

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.

AB - 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.

U2 - 10.1007/BF01158963

DO - 10.1007/BF01158963

M3 - Article

VL - 16

SP - 373

EP - 386

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

IS - 3-4

ER -