## End-to-End Congestion Control for the Internet: Delay and Stability (2001)

### Cached

### Download Links

Citations: | 150 - 1 self |

### BibTeX

@MISC{Johari01end-to-endcongestion,

author = {Ramesh Johari and David Tan},

title = {End-to-End Congestion Control for the Internet: Delay and Stability},

year = {2001}

}

### Years of Citing Articles

### OpenURL

### Abstract

Under the assumption that queueing delays will eventually become small relative to propagation delays, we derive stability results for a fluid flow model of end-to-end Internet congestion control. The theoretical results of the paper are intended to be decentralized and locally implemented: each end system needs knowledge only of its own roundtrip delay. Criteria for local stability and rate of convergence are completely characterized for a single resource, single user system. Stability criteria are also described for networks where aH users share the same roundtrip delay. Numerical experiments investigate extensions to more general networks. Through simulations, we are able to evaluate the relative importance of queueing delays and propagation delays on network stability. Finally, we suggest how these results may be used to design network resources.

### Citations

5114 |
Matrix Analysis
- Horn, Johnson
- 1985
(Show Context)
Citation Context ...tions of κ (where κ may be vector valued). Then the maximum modulus of the roots λ of p λsκ , 0 is continuous in κ. Proof. The roots of any polynomial are continuous functions of the coefficients =-=[8]-=-. If the coefficients are continuous functions of κ, this immediately implies the conclusion of the lemma. - Lemma 2 For sufficiently small κ, equation (9) has all roots with modulus less than unity. ... |

2433 | Congestion avoidance and control
- Jacobson, Karels
- 1988
(Show Context)
Citation Context ...ffi Dr for all j r. As before, user r adjusts xr t to reach a target number of marks per unit time wr. The delay structure we have assumed here is very similar to the current operation of TCP =-=[9]-=-. In TCP, the sender transmits packets to a receiver; for every packet received, an acknowledgment is transmitted back to the sender. All packets make a round trip from sender to receiver, and back to... |

1525 |
Rate control in communication networks: shadow prices, proportional fairness and stability
- Kelly, Maullo, et al.
- 1998
(Show Context)
Citation Context ...lays experienced by all users. For this reason, we will instead consider a model which implements end-to-end congestion control, in response to simple congestion indication signals from resources. In =-=[11]-=-, Kelly et al. proposed two complementary congestion control algorithms. The FRFC algorithm is similar to the “dual algorithm” of [11]: it relies on the resource to implement the congestion control. I... |

877 | An Architecture for Differentiated Services - Blake, Black, et al. - 1998 |

682 | Tsitsiklis, Parallel and distributed computation: Numerical Methods - Bertsekas, N - 1989 |

617 | Applied Probabilities and Queues - Asmussen |

575 | Optimization Flow Control I: Basic Algorithm and Convergence - Low, Lapsley - 1999 |

356 | Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED - Misra, Gong, et al. - 2000 |

327 |
Fundamentals of Queueing Theory
- Gross, Harris
- 1998
(Show Context)
Citation Context ... these equations with the analysis of a (continuous-time) M/D/1 queue, examined at time points where individuals leave the queue; in that case, the queue length equation is Qt Qt 1 1 1 ) Yt =-=[6]-=-. We will suppose that, for each t, Yt is a Poisson random variable of parameter y 1, independent of the past history of the process. This makes Qt a discrete time Markov chain. We will try to compu... |

322 | Resource pricing and the evolution of congestion control
- Gibbens, Kelly
- 1969
(Show Context)
Citation Context ...a task handled primarily by the links in the network. 1 Which viewpoint should we adopt? Arguments have been made at an economic level regarding the fairness benefits of end system congestion control =-=[5]-=-: it is suggested that end users are best equipped to adjust their flows so as to maximize utility, and hence congestion control should be implemented by asking resources to convey information on inci... |

314 | Mathematical Statistics and Data Analysis - Rice - 1995 |

242 | On traffic phase effects in packet-switched gateways
- Floyd, Jacobson
- 1992
(Show Context)
Citation Context ...ge oscillations; however, as we will discover, these oscillations are not independent of one another. Instead, when all users share the same roundtrip delay, their rates tend to become “phase-locked” =-=[4]-=-: all rates oscillate exactly in phase with each other. One such example is presented in Figure 5. The parameters for the simulation are D 5000, and κr κ < D for all r R. All other parameter... |

200 |
Differential-Difference Equations
- Bellman, Cooke
- 1963
(Show Context)
Citation Context ... stable point. In this section, we consider this problem, via the theory of differential-difference equations. For convenience, we restate here a result due to Hayes [7] taken from Bellman and Cooke (=-=[1]-=-, Theorem 13.8). Lemma 4 (Hayes) All the roots of beλ c λeλ 0, where b and c are real, have negative real parts if and only if: (1) b 1; and (2) b B c DC a21 b2, where a1 is the root of a... |

191 | Introduction to Dynamic Systems : theory, models, and applications, chapter Analysis of Nonlinear Systems - Luenberger - 1979 |

117 | Feedback Control of Congestion in Packet Switching Networks: The Case of a Single Congested Node - Benmohamed, Meerkov - 1993 |

102 | Models for a self-managed Internet - Kelly - 2000 |

62 | A Theoretical Analysis of Feedback Flow Control - Shenker - 1990 |

27 |
Roots of the transcendental equation associated with a certain differential difference equation
- Hayes
- 1950
(Show Context)
Citation Context ...o study rate of convergence to the stable point. In this section, we consider this problem, via the theory of differential-difference equations. For convenience, we restate here a result due to Hayes =-=[7]-=- taken from Bellman and Cooke ([1], Theorem 13.8). Lemma 4 (Hayes) All the roots of beλ c λeλ 0, where b and c are real, have negative real parts if and only if: (1) b 1; and (2) b B c DC a... |

18 | Analysis of a rate-based feedback control strategy for long haul data transport,” Performance Evaluation - Fendick, Rodrigues, et al. - 1992 |

12 | Designing stable abr flow control with rate feedback and open loop control:first-order control case. Performance Evaluation
- Chong, Nagarajan, et al.
- 1998
(Show Context)
Citation Context ... hand, resources would be required to estimate the delays experienced by each flow passing through them—a very difficult problem in a network on the scale of the Internet. The work of Chong et al. in =-=[2, 3]-=- is related to this point. In [2, 3], Chong et al. analyzed the equilibrium and stability of their proposed first-order rate-based flow control (FRFC) algorithm for a single bottleneck resource of mul... |

12 | Mathematical models of rate control for communication networks - Tan - 1999 |

8 | Dynamical Behavior of Rate Based Flow Control Systems - Bolot, Shankar - 1990 |

5 | control of congestion in packet switching networks: The case of multiple congested node - “Feedback - 1997 |

4 |
First-order rate-based flow control with dynamic queue threshold for high-speed wide-area ATM networks
- Chong, Nagarajan, et al.
- 1998
(Show Context)
Citation Context ... hand, resources would be required to estimate the delays experienced by each flow passing through them—a very difficult problem in a network on the scale of the Internet. The work of Chong et al. in =-=[2, 3]-=- is related to this point. In [2, 3], Chong et al. analyzed the equilibrium and stability of their proposed first-order rate-based flow control (FRFC) algorithm for a single bottleneck resource of mul... |

2 | Adaptive algorithms for feedback based flow control in highspeed, wide-area networks - Bonomi, Seery - 1995 |

1 |
Models for a self-managed Internet. To appear in
- Kelly
- 2000
(Show Context)
Citation Context ...by data waiting to be served at resources within the network. We will work from the assumption that, in the future, queueing delays will become small relative to propagation delay, as Kelly argues in =-=[10]-=-. Router hardware and network capacity continue to improve rapidly, reducing queueing delays; on the other hand, propagation delays are fixed by the distances between nodes on the network, and the spe... |

1 | rate-based flow control with dynamic queue threshold for high-speed wide-area ATM networks - “First-order - 1998 |