### Abstract

Markov fluid models with fluid level dependent behaviour are considered in this paper. One of the main difficulties of the analysis of these models is to handle the case when in a given state the fluid rate changes sign from positive to negative at a given fluid level. We refer to this case as zero transition. The case when this sign change is due to a discontinuity of the fluid rate function results in probability mass at the given fluid level. We show that the case when the sign change is due to a continuous finite polynomial function of the fluid rate results in a qualitatively different behaviour: no probability mass develops and different stationary equations apply. We consider this latter case of sign change, present its stationary description and propose a numerical procedure for its evaluation.

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

Pages (from-to) | 1149-1161 |

Number of pages | 13 |

Journal | Performance Evaluation |

Volume | 68 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2011 |

### Fingerprint

### Keywords

- Differential equation
- Fluid level dependence
- Markov fluid model
- Stationary behaviour

### ASJC Scopus subject areas

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

### Cite this

*Performance Evaluation*,

*68*(11), 1149-1161. https://doi.org/10.1016/j.peva.2011.07.006

**Fluid level dependent Markov fluid models with continuous zero transition.** / Balázs, Márton; Horváth, Gábor; Kolumbán, Sándor; Kovács, Péter; Telek, M.

Research output: Contribution to journal › Article

*Performance Evaluation*, vol. 68, no. 11, pp. 1149-1161. https://doi.org/10.1016/j.peva.2011.07.006

}

TY - JOUR

T1 - Fluid level dependent Markov fluid models with continuous zero transition

AU - Balázs, Márton

AU - Horváth, Gábor

AU - Kolumbán, Sándor

AU - Kovács, Péter

AU - Telek, M.

PY - 2011/11

Y1 - 2011/11

N2 - Markov fluid models with fluid level dependent behaviour are considered in this paper. One of the main difficulties of the analysis of these models is to handle the case when in a given state the fluid rate changes sign from positive to negative at a given fluid level. We refer to this case as zero transition. The case when this sign change is due to a discontinuity of the fluid rate function results in probability mass at the given fluid level. We show that the case when the sign change is due to a continuous finite polynomial function of the fluid rate results in a qualitatively different behaviour: no probability mass develops and different stationary equations apply. We consider this latter case of sign change, present its stationary description and propose a numerical procedure for its evaluation.

AB - Markov fluid models with fluid level dependent behaviour are considered in this paper. One of the main difficulties of the analysis of these models is to handle the case when in a given state the fluid rate changes sign from positive to negative at a given fluid level. We refer to this case as zero transition. The case when this sign change is due to a discontinuity of the fluid rate function results in probability mass at the given fluid level. We show that the case when the sign change is due to a continuous finite polynomial function of the fluid rate results in a qualitatively different behaviour: no probability mass develops and different stationary equations apply. We consider this latter case of sign change, present its stationary description and propose a numerical procedure for its evaluation.

KW - Differential equation

KW - Fluid level dependence

KW - Markov fluid model

KW - Stationary behaviour

UR - http://www.scopus.com/inward/record.url?scp=80053349685&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053349685&partnerID=8YFLogxK

U2 - 10.1016/j.peva.2011.07.006

DO - 10.1016/j.peva.2011.07.006

M3 - Article

VL - 68

SP - 1149

EP - 1161

JO - Performance Evaluation

JF - Performance Evaluation

SN - 0166-5316

IS - 11

ER -