### Abstract

We consider a fluid flow model with infinite buffer. We compute the Laplace-Stieltjes transform of the sojourn time proceeding in two steps. We first compute the stationary distribution of the buffer at arrival instants, using a change of clock. Secondly, we compute the transform of the time spent to empty the buffer. Numerical examples of sojourn time in a fluid flow are finally examined.

Original language | English |
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Title of host publication | Queueing Theory and Network Applications |

Subtitle of host publication | 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings |

Editors | Tuan Phung-Duc, Shoji Kasahara, Sabine Wittevrongel |

Publisher | Springer |

Pages | 295-313 |

Number of pages | 19 |

Volume | 11688 |

ISBN (Print) | 978-3-030-27180-0 |

DOIs | |

Publication status | Published - 27 Aug 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11688 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Keywords

- Markov-modulated fluid flow
- Sojourn time
- Laplace-Stieljes transform

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## Cite this

Deiana, E., Remiche, M-A., & Latouche, G. (2019). Sojourn Time Distribution in Fluid Queues. In T. Phung-Duc, S. Kasahara, & S. Wittevrongel (Eds.),

*Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings*(Vol. 11688, pp. 295-313). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11688 LNCS). Springer. https://doi.org/10.1007/978-3-030-27181-7_18