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## On Power-Law Relationships of the Internet Topology (1999)

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Venue: | IN SIGCOMM |

Citations: | 1643 - 71 self |

### Citations

767 |
Routing of multipoint connections.
- Waxman
- 1998
(Show Context)
Citation Context ...e attention it has attracted recently. Paxson and Floyd consider this problem as a major reason \Why We Don't Know HowTo Simulate The Internet" [16]. Several graph-generator models have been proposed =-=[23]-=- [5] [27], but the problem of creating realistic topologies is not yet solved; the selection of several parameter values are left to the intuition and the experience of each researcher. As our primary... |

471 | Distance vector multicast routing protocol,” http:// ds.internic.net /rfc /rfc1075.html
- Waitzman, Partridge, et al.
(Show Context)
Citation Context ...e can estimate the number of edges from Lemma 2, and 6 Some protocols that employ broadcasting or ooding techniques are the link-state protocols OSPF and MOSPF [13], and the multicast protocols DVMRP =-=[22]-=-, QoSMIC [7], YAM [1].Year 1999 2000 2001 2002 Nodes 4389 5763 7137 8511 Edges 8256 12639 15301 18384 E ective diameter 4.26 4.39 4.61 4.78 Table 4: Internet prediction assuming linear node increase.... |

310 |
The Fractal Geometry of Nature, W.H
- Mandelbrot
- 1982
(Show Context)
Citation Context ...lieve that these power-laws characterize the dynamic equilibrium of the Internet growth in the same way power-laws appear to describe various natural networks such as the the human respiratory system =-=[12]-=-, and automobile networks [6]. At a more practical level, the regularities characterize the topology concisely during 1998. If this time period turns out to be a transition phase for the Internet, our... |

266 | A quantitative comparison of graph-based models for Internet topology
- Zegura, Calvert, et al.
- 1997
(Show Context)
Citation Context ...on it has attracted recently. Paxson and Floyd consider this problem as a major reason \Why We Don't Know HowTo Simulate The Internet" [16]. Several graph-generator models have been proposed [23] [5] =-=[27]-=-, but the problem of creating realistic topologies is not yet solved; the selection of several parameter values are left to the intuition and the experience of each researcher. As our primary contribu... |

183 | Self-similarity and heavy tails: structural modeling of network traffic
- Willinger, Paxson, et al.
- 1998
(Show Context)
Citation Context ...twork tra c and are both related to power-laws. Avariable X follows a heavy tail distribution if P [X >x]=k a x ,a L(x), where k 2< + and L(x)is a slowly varying function: limt!1[L(tx)=L(x)] = 1 [20] =-=[24]-=-. APareto distribution is a special case of a heavy tail distribution with P [X >x]=k a x ,a . It is easy to see that power-laws, Pareto and heavy-tailed distributions are intimately related. In a pio... |

177 | A better model for generating test networks
- Doar
- 1996
(Show Context)
Citation Context ...ention it has attracted recently. Paxson and Floyd consider this problem as a major reason \Why We Don't Know HowTo Simulate The Internet" [16]. Several graph-generator models have been proposed [23] =-=[5]-=- [27], but the problem of creating realistic topologies is not yet solved; the selection of several parameter values are left to the intuition and the experience of each researcher. As our primary con... |

162 | Beyond uniformity and independence: Analysis of R-trees using the concept of fractal dimension
- Faloutsos, Kamel
- 1994
(Show Context)
Citation Context ...aracterize the dynamic equilibrium of the Internet growth in the same way power-laws appear to describe various natural networks such as the the human respiratory system [12], and automobile networks =-=[6]-=-. At a more practical level, the regularities characterize the topology concisely during 1998. If this time period turns out to be a transition phase for the Internet, our observations will obviously ... |

144 |
Self-similarity through high variability: Statistical analysis of ethernet lan traffic at the source level
- Willinger, Taqqu, et al.
- 1995
(Show Context)
Citation Context ... the self-similar nature of Local Area Network (LAN) tra c. Second, Paxson and Floyd [15] provide evidence of self similarity in Wide Area Network (WAN) tra c. In modeling the tra c, Willinger et al. =-=[25]-=- provide structural models that describe LAN tra c as a collective e ect of simple heavytailed ON-OFF sources. Finally, Willinger et al. [24] bring all of the above together by describing LAN and WAN ... |

139 |
On routes and multicast trees in the internet
- Pansiot, Grad
- 1998
(Show Context)
Citation Context ...e subnetworks are called domains or autonomous systems 2 . This way, the topology of the Internet can be studied at two di erent granularities. At the router level, we represent each router by a node =-=[14]-=-. At the inter-domain level, each domain is represented by a single node [10] and each edge is an inter-domain interconnection. The study of the topology at both levels is equally important. The Inter... |

137 | An Analysis of Internet Inter-Domain Topology and Route Stability
- Govindan, Reddy
- 1997
(Show Context)
Citation Context ...logy of the Internet can be studied at two di erent granularities. At the router level, we represent each router by a node [14]. At the inter-domain level, each domain is represented by a single node =-=[10]-=- and each edge is an inter-domain interconnection. The study of the topology at both levels is equally important. The Internet community develops and employs di erent protocols inside a domain and bet... |

132 |
Multicast routing extensions for OSPF
- Moy
- 1994
(Show Context)
Citation Context ... a hypothesis for the number of nodes, we can estimate the number of edges from Lemma 2, and 6 Some protocols that employ broadcasting or ooding techniques are the link-state protocols OSPF and MOSPF =-=[13]-=-, and the multicast protocols DVMRP [22], QoSMIC [7], YAM [1].Year 1999 2000 2001 2002 Nodes 4389 5763 7137 8511 Edges 8256 12639 15301 18384 E ective diameter 4.26 4.39 4.61 4.78 Table 4: Internet p... |

114 | Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law
- Philips, Shenker, et al.
- 1999
(Show Context)
Citation Context ...d characteristics of the human-computer interaction. Recently, Chuang and Sirbu [2] use a power-law to estimate the size of multicast distribution trees. Note that in a follow-up work, Philips et al. =-=[17]-=- verify the reasonable accuracy of the Chuang-Sirbu scaling law for practical purposes, but they also propose an estimate that does not follow apower-law. 3 Internet Instances In this section, we pres... |

81 | Building Shared Trees Using a One-to-Many Joining Mechanism
- Carlberg, Crowcroft
- 1997
(Show Context)
Citation Context ...emma 3 The number of pairs within h hops is P (h) = ch H ; N 2 ; where c = N +2E to satisfy initial conditions. h h In networks, we often need to reach a target without knowing its exact position [7] =-=[1]-=-. In these cases, selecting the extent ofour broadcast or search is an issue. On the one hand, a small broadcast will not reach our target. On the other hand, an extended broadcast creates too many me... |

63 |
Wide-area tra c: The failure of poisson modeling
- Paxson, Floyd
- 1995
(Show Context)
Citation Context ...r-laws, Pareto and heavy-tailed distributions are intimately related. In a pioneering work, Leland et al. [11] show the self-similar nature of Local Area Network (LAN) tra c. Second, Paxson and Floyd =-=[15]-=- provide evidence of self similarity in Wide Area Network (WAN) tra c. In modeling the tra c, Willinger et al. [25] provide structural models that describe LAN tra c as a collective e ect of simple he... |

47 |
Sirbu “Pricing multicast communication: A cost based approach
- Chuang, M
- 1998
(Show Context)
Citation Context ...d behavior of the tra c to the heavy-tailed distribution of the size of the transmitted data les, and to the heavy-tailed characteristics of the human-computer interaction. Recently, Chuang and Sirbu =-=[2]-=- use a power-law to estimate the size of multicast distribution trees. Note that in a follow-up work, Philips et al. [17] verify the reasonable accuracy of the Chuang-Sirbu scaling law for practical p... |

40 |
On the self-similar nature of Ethernet tra
- Leland, Taqqu, et al.
- 1994
(Show Context)
Citation Context ...special case of a heavy tail distribution with P [X >x]=k a x ,a . It is easy to see that power-laws, Pareto and heavy-tailed distributions are intimately related. In a pioneering work, Leland et al. =-=[11]-=- show the self-similar nature of Local Area Network (LAN) tra c. Second, Paxson and Floyd [15] provide evidence of self similarity in Wide Area Network (WAN) tra c. In modeling the tra c, Willinger et... |

26 |
A Border Gateway Protocol 4 (BGP-4)", Internet Request for Comments 1771, http//ds.internic.net/rfc/rfc 1771.txt
- Rekhter, Li
- 1995
(Show Context)
Citation Context ... di erent instances of an evolving network. Although we focus on the Internet topology at the interdomain level, we also examine an instance at the router 4 BGP stands for the Border Gateway Protocol =-=[19]-=-, and it is the inter-domain routing protocol. level. The graph represents the topology of the routers of the Internet in 1995, and was tediously collected by Pansiot and Grad [14]. Rout-95: the route... |

23 | Alternate Path Routing and Pinning for Interdo- main Multicast Routing
- Zappala, Estrin, et al.
- 1997
(Show Context)
Citation Context ...nditions. The average neighborhood is a commonly used parameter in the performance of network protocols. Our estimate is an improvement over the commonly used estimate that uses the average outdegree =-=[26]-=- [7] which we call averageoutdegree estimate: NN 0 (h) =d (d , 1) h,1 In gure 9, we plot the actual and both estimates of the average neighborhood size versus the number of hops for the Int-12-98 grap... |

14 |
Self-Similarity in World Wide Web Tra c: Evidence and Possible Causes
- Crovella, Bestavros
- 1997
(Show Context)
Citation Context ...scopic level of WANs with the heavy-tailed behavior at the microscopic level of individual sources. In addition, Crovella and Bestavros use power-laws to describe tra c patterns in the World Wide Web =-=[3]-=-. At an intuitive level, the previous works seem to attribute the heavy-tailed behavior of the tra c to the heavy-tailed distribution of the size of the transmitted data les, and to the heavy-tailed c... |

14 |
Laws: Minutes From an In
- Schroeder, Fractals, et al.
- 1991
(Show Context)
Citation Context ... open the oodgates to discovering many additional power-laws of the Internet topology. Our optimism is based on two facts: (a) power-laws are intimately related to fractals, chaos and self-similarity =-=[21]-=- and (b) there is overwhelming evidence that self-similarity appears in a large number of settings, ranging from tra c patterns in networks [24], to biological and economical systems [12]. ACKNOWLEDGM... |

11 |
Designing QoSMIC: a QoS Multicast Internet protocol. Internet Draft: draft-banerjea-qosmic-OO.[ps,txt], available from ftp://ftp.ietf.org/internet-drafts
- Banerjea, Faloutsos, et al.
- 1998
(Show Context)
Citation Context ...n. Lemma 3 The number of pairs within h hops is P (h) = ch H ; N 2 ; where c = N +2E to satisfy initial conditions. h h In networks, we often need to reach a target without knowing its exact position =-=[7]-=- [1]. In these cases, selecting the extent ofour broadcast or search is an issue. On the one hand, a small broadcast will not reach our target. On the other hand, an extended broadcast creates too man... |

8 |
Power-laws and the internet topology
- Siganos, Faloutsos, et al.
(Show Context)
Citation Context ... properties such as the diameter, the number of edges, the number of spanning trees, the number of connected components, and the number of walks of a certain length between vertices, as we can see in =-=[8]-=- and [4]. All of the above suggest that the eigenvalues intimately relate to topological properties of graphs. We plot the eigenvalue i versus i in log-log scale for the rst 20 eigenvalues. Recall tha... |

8 |
Why we don't know howtosimulate the internet
- Paxson, Floyd
- 1997
(Show Context)
Citation Context ...ernet topology 1 is an important open problem despite the attention it has attracted recently. Paxson and Floyd consider this problem as a major reason \Why We Don't Know HowTo Simulate The Internet" =-=[16]-=-. Several graph-generator models have been proposed [23] [5] [27], but the problem of creating realistic topologies is not yet solved; the selection of several parameter values are left to the intuiti... |

7 |
Spectra ofGraphs
- Cvetkovic, Doob, et al.
- 1980
(Show Context)
Citation Context ...ies such as the diameter, the number of edges, the number of spanning trees, the number of connected components, and the number of walks of a certain length between vertices, as we can see in [8] and =-=[4]-=-. All of the above suggest that the eigenvalues intimately relate to topological properties of graphs. We plot the eigenvalue i versus i in log-log scale for the rst 20 eigenvalues. Recall that i is t... |

5 |
Heavy tailed modelling and teletra c data
- Resnick
- 1997
(Show Context)
Citation Context ...in network tra c and are both related to power-laws. Avariable X follows a heavy tail distribution if P [X >x]=k a x ,a L(x), where k 2< + and L(x)is a slowly varying function: limt!1[L(tx)=L(x)] = 1 =-=[20]-=- [24]. APareto distribution is a special case of a heavy tail distribution with P [X >x]=k a x ,a . It is easy to see that power-laws, Pareto and heavy-tailed distributions are intimately related. In ... |

3 |
Behavior and Principle of Least E ort: An Introduction to Human Ecology
- Human
(Show Context)
Citation Context ...ith an exponent of1:6. Second, power-laws are obeyed in diverse settings, like income distribution (the \Pareto law"), and the frequency distribution of words in natural text (the \Zipf distribution" =-=[28]-=-). 6 Conclusions Our main contribution is a novel way to study the Internet topology, namely through power-laws. These powerlaws capture concisely the highly skewed distributions of the graph properti... |