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## A Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED (2000)

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Venue: | Proc. SIGCOMM 2000 |

Citations: | 411 - 21 self |

### Citations

2679 | Random Early Detection Gateways for Congestion Avoidance
- Floyd, Jacobson
- 1993
(Show Context)
Citation Context ...solution methodology has a great potential in analyzing and understanding various network congestion control algorithms. 1. INTRODUCTION Active queue management techniques have recently been proposed =-=[8]-=-, [3] to to both alleviate some congestion control problems for IP networks as well as provide some notion of quality of service. Modeling and analysis of such networks is important to understand thei... |

1332 | Modeling TCP Throughput: A Simple Model and its Empirical Validation
- Padhye, Firoiu, et al.
- 1998
(Show Context)
Citation Context ... [11], we modeled the behavior of TCP using jump process driven Stochastic Differential Equations [2]. The results showed a good match between predictions from this model and measurements reported in =-=[13]-=-. A deficiency of the model however was that the packet loss process was independent of the data flow. Our model remedies this deficiency by modeling a complete system, in which losses and TCP sending... |

464 | Explicit Allocation of Best Effort Packet Delivery Service
- Clark, Fang
- 1998
(Show Context)
Citation Context ...ion methodology has a great potential in analyzing and understanding various network congestion control algorithms. 1. INTRODUCTION Active queue management techniques have recently been proposed [8], =-=[3]-=- to to both alleviate some congestion control problems for IP networks as well as provide some notion of quality of service. Modeling and analysis of such networks is important to understand their dyn... |

217 | A study of active queue management for congestion control
- Firoiu, Borden
- 2000
(Show Context)
Citation Context ...n Section 2.2. In Section 2.3 we extend the techniques to include TCP timeouts. Last, we describe some optimizations in the case of identical TCP flows in Section 2.4. Such a system was alluded to in =-=[6]-=-. We first consider a system in which there is a single congested router with a transmission capacity of . Associated with this router is an active queue management (AQM) policy that is characterized ... |

212 |
Computer controlled systems, theory and design
- Åström, Wittenmark
- 1990
(Show Context)
Citation Context ...value of any variable by seconds Using a weight , , (5) It is useful to convert this equation into a differential equation. Given the form (5), the natural candidate is Then, in a sampled data system =-=[1]-=-, is given by (6) Note that the differential equation matches the discrete time system exactly at the sample points, and there is no accumulation of error as increases. Comparing the coefficients in (... |

171 | A self-configuring RED gateway
- Feng, Kandlur, et al.
- 1999
(Show Context)
Citation Context ...various RED parameters that work well in all scenarios. Consequently, there is considerable nervousness in the community regarding deployment of RED, and numerous variations of RED have been proposed =-=[5]-=-, [12], [4]. Some of the schemes have self-tuning parameters, while others maintain per-flow state. It is clear that there is a great need for thoroughly understanding the behavior of RED. We believe ... |

162 | Blue: A new class of active queue management algorithms
- Feng, Kandlur, et al.
- 1999
(Show Context)
Citation Context ... parameters that work well in all scenarios. Consequently, there is considerable nervousness in the community regarding deployment of RED, and numerous variations of RED have been proposed [5], [12], =-=[4]-=-. Some of the schemes have self-tuning parameters, while others maintain per-flow state. It is clear that there is a great need for thoroughly understanding the behavior of RED. We believe our techniq... |

137 | SRED: Stabilized RED
- Ott, Lakshman, et al.
- 1999
(Show Context)
Citation Context ...us RED parameters that work well in all scenarios. Consequently, there is considerable nervousness in the community regarding deployment of RED, and numerous variations of RED have been proposed [5], =-=[12]-=-, [4]. Some of the schemes have self-tuning parameters, while others maintain per-flow state. It is clear that there is a great need for thoroughly understanding the behavior of RED. We believe our te... |

111 | Analytic evaluation of RED performance
- May, Bonald, et al.
- 2000
(Show Context)
Citation Context ...ol traffic, potentially solving problems like flow synchronization, correlation of drop events while providing consistently high link utilizations. However, numerous problems have been cited with RED =-=[10]-=-. RED works well in certain scenarios, whereas it does very poorly, even worse than Drop-Tail, in other cases [6]. There is no clear understanding on how to tune various RED parameters that work well ... |

93 | Stochastic differential equation modeling and analysis of tcp windowsize behavior
- Misra, Gong, et al.
- 1999
(Show Context)
Citation Context ... We compare our results with those obtained using the well known ns simulator and make some observations about RED behavior. Finally, we present our conclusions in Section 4. 2. MODEL AND ANALYSIS In =-=[11]-=-, we modeled the behavior of TCP using jump process driven Stochastic Differential Equations [2]. The results showed a good match between predictions from this model and measurements reported in [13].... |

45 | Global fairness of additive-increase and multiplicative-decrease with heterogeneous roundtrip times
- Vojnovic, Boudec, et al.
(Show Context)
Citation Context ...e able to capture TCP dynamics. Now is the loss indication received by the source. It reaches the source approximately one round trip delay ( ) after a packet has been marked/dropped at the queue. In =-=[14]-=- an exact stochastic differential equation for TCP with feedback delay has been studied, in the context of fairness. Here we model the delay as the solution to the following equations In the proportio... |

32 |
Recommendation on Using the ‘Gentle_’ Variant of RED,” http://www.icir.org/floyd/red/gentle.html
- Floyd
- 2000
(Show Context)
Citation Context ...lso suggested that the discontinuity in the RED drop function (the jump from to 1 at ) is a cause of oscillations in RED. It has been suggested that making the drop function continuous via the gentle =-=[7]-=- should improve things in that regard. Our experiments show that the discontinuity is not the only cause of oscillations and that a simple fix by making the drop function continuous won’t remove them.... |

9 |
Stochastic control. Lecture Notes
- Brockett
- 2009
(Show Context)
Citation Context ...vations about RED behavior. Finally, we present our conclusions in Section 4. 2. MODEL AND ANALYSIS In [11], we modeled the behavior of TCP using jump process driven Stochastic Differential Equations =-=[2]-=-. The results showed a good match between predictions from this model and measurements reported in [13]. A deficiency of the model however was that the packet loss process was independent of the data ... |

8 | Recommendation on using the "gentle " variant of RED. http://www.aciri.org/floyd/red/gentle.html - Floyd - 2000 |

3 | Computed Controlled Systems: Theory - Åstrom, Witternmark - 1984 |

2 | Z-iteration: Efficient estimation of instantaneous measures in time-dependent multi-class systems
- Matta, Shankar
- 1995
(Show Context)
Citation Context ...m, one which we believe has not been addressed elsewhere. Our scheme has similar aims, to obtain transient behavior by numerical solution of a system of equations, to a heuristic approach proposed in =-=[9]-=-. It is however not clear how and why the heuristics work in cases reported. The rest of this paper is organized as follows. In Section 2, we develop our analytical model and describe the solution tec... |

1 | o F: We list some direct consequences of the above definition. Consider a stochastic differential equation driven ¥ by independent Poisson ; ?>%>Ž>Ž3; $ Counters : n "k• Þ " J Þ We have the following “Itô rule”. âEãwD $]ä If function, then ; " Bmš =D $ > - B- - 1998 |