### Abstract

In stochastic fluid models the drift at which the fluid level changes in the fluid buffer and the generator of the underlying process might depend on the discrete state of the system and on the fluid level itself. In this paper we analyse the stationary behaviour of finite buffer Markov fluid models in which the drift and the generator of the underlying continuous time Markov chain (CTMC) depends on both of these parameters. Especially, the case when the drift changes sign at a given fluid level is considered. This case requires a particular treatment, because at this fluid level probability mass might develop. When dealing with sign changes, new problems that were not addressed in previous works arises. The set of stationary equations is provided and a transformation of the unknowns is applied to obtain a solvable system description. Numerical examples introduce the behaviour of fluid systems with various discontinuities and sign changes of the drift.

Original language | English |
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Pages (from-to) | 241-261 |

Number of pages | 21 |

Journal | Performance Evaluation |

Volume | 65 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Mar 1 2008 |

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### Keywords

- Stationary distribution
- Stochastic fluid model

### ASJC Scopus subject areas

- Software
- Modelling and Simulation
- Hardware and Architecture
- Computer Networks and Communications

### Cite this

*Performance Evaluation*,

*65*(3-4), 241-261. https://doi.org/10.1016/j.peva.2007.06.027