### Abstract

Language | Undefined |
---|---|

Pages | 149-169 |

Number of pages | 21 |

Journal | Mathematical methods of operations research |

Volume | 70 |

Issue number | 1 |

DOIs | |

State | Published - 2009 |

### Keywords

- Feedback regulation
- Spectral expansion
- EWI-20933
- Congestion control
- METIS-292501
- Fluid queues
- IR-80266

### Cite this

*Mathematical methods of operations research*,

*70*(1), 149-169. DOI: 10.1007/s00186-008-0235-8

}

*Mathematical methods of operations research*, vol 70, no. 1, pp. 149-169. DOI: 10.1007/s00186-008-0235-8

**A feedback fluid queue with two congestion control thresholds.** / Malhotra, R.; Mandjes, M.R.H. ; Scheinhardt, Willem R.W.; van den Berg, Hans Leo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A feedback fluid queue with two congestion control thresholds

AU - Malhotra,R.

AU - Mandjes,M.R.H.

AU - Scheinhardt,Willem R.W.

AU - van den Berg,Hans Leo

PY - 2009

Y1 - 2009

N2 - Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.

AB - Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.

KW - Feedback regulation

KW - Spectral expansion

KW - EWI-20933

KW - Congestion control

KW - METIS-292501

KW - Fluid queues

KW - IR-80266

U2 - 10.1007/s00186-008-0235-8

DO - 10.1007/s00186-008-0235-8

M3 - Article

VL - 70

SP - 149

EP - 169

JO - Mathematical methods of operations research

T2 - Mathematical methods of operations research

JF - Mathematical methods of operations research

SN - 1432-2994

IS - 1

ER -