G. Philips and S. Shenker. Scaling of multicast trees: comments on the Chuang-Sirbu scaling law. In Proceedings of ACM SIGCOMM'99, pages 41--51, Sept. 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in communication networks. First, power laws have been observed in network trac [56] 30] 46] 13] In addition, the topology of the World Wide Web [4, 28] can be described by power laws. Furthermore, power laws describe the topology of peer to peer networks [39] and properties of multicast trees [12, 47, 57, 37]. Among these properties, the Chuang Sirbu law states that the size of the multicast tree follows a power law with respect to the number of group members with exponent 0.8. Our initial work [20] on power laws has generated signi cant follow up work. Various researchers veri ed our observations ....

....and Multi topology respectively. Unfortunately, four points is a rather small number to verify or disprove a linearity hypothesis experimentally. However, even this rough approximation has several useful applications as we show later in this section. It is worth mentioning that Philips et al. [47] state that the neighborhood growth is exponential and not a power law. In gure 6, we plot again the number of pairs in log lin for the Multi topology. We approximate the rst four hops and found a correlation coecient of 0:918 which is much lower than the previous correlation. From this, it seems ....

G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of mul11 ticast trees: Comments on the chuang-sirbu scaling law. ACM SIGCOMM, Sep 1999.

....the root to a randomly selected client. I. INTRODUCTION There are several inhibitors to the commercial use of multicast protocols. While it is clear that multicast is beneficial for transmitting the same information to large groups, its exact gain over unicast has not yet been determined [1] [2], 3] Network suppliers lack a fast and efficient way to estimate the size of large multicast groups, and the research community lacks reliable tree models. We present here a thorough investigation we performed on the structure and characteristics of multicast trees cut from generated power law ....

....routing. For example, IP packets are forwarded based on the reverse shortest path, and multicast routing protocols such as Source Specific Multicast [19] deliver packets along the shortest path route. In addition, we assume that client distribution in the tree is uniform, as has been shown by [2], 3] B. Tree Characteristics 1) Degree Rank and Size Rank Power Laws: Our results show that trees cut from a power law topology obey a similar power law. Specifically, we compared the degree frequency power law found by [4] Figure 1 shows in log log scale the degree frequency plot for Name ....

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G. Philips, S. Shenker, and H. Tangmunarunkit, "Scaling of multicast trees: Comments on the chuang-sirbu scaling law," in ACM SIGCOMM'99, Cambridge, Massachusetts, USA, 1999.

....has not yet been a comprehensive study of the Internet topology at the router level. In contrast, the interdomain level has been studied lately [15] In a parallel tangent, several people have studied topological properties indirectly, through the study of scaling of multicast trees in Internet [2, 12, 17]. Recently, Albert et al. [1] and Tauro and Faloutsos [15] studied the fault tolerance of the Internet at the interdomain level. Recall that our work here focuses at the router level of the Internet. Assumptions and limitations. The router level Internet graph contains communication links ....

G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. A CM SIGCOMM, September 1999.

....C.2.1 [Communication Networks] Architecture and Design topology General Terms Measurement 1. INTRODUCTION Realistic Internet topologies are of considerable importance to network researchers. Topology influences the dynamics of routing protocols [2, 10] the scalability of multicast [17], the efficacy of proposals for denial of service tracing and response [16, 11, 21, 22] and other aspects of protocol performance [18] Sadly, real topologies are not publicly available because ISPs generally regard their router level topologies as confidential. Some ISPs publish simplified ....

G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. In ACM SIGCOMM, August 1999.

....distribution; i.e, how often we tend to have very small groups or very large groups. Factor (5) has been not discussed above, but clearly it is very important as well. Several models are described in [12] where factors (1) and (2) are considered. The terms of affinity and disaffinity are used in [7] to describe the clustering and spreading out tendencies of members within a group. In our work, we use the node weighted framework which incorporates the difference among network nodes (factor (3) In this framework, each node is assigned a weight representing the probability for that node to ....

G. Philips and S. Shenker. Scaling of multicast trees: comments on the chuang-sirbu scaling law. In Proceedings of ACM SIGCOMM'99, pages 41--51, September 1999.

....any ATM ABR rate allocation scheme to fairly accommodate multiple sources. 1 Introduction Multipoint communication is the exchange of information among multiple senders and multiple receivers. The basic advantage of multicast is that it allows economies of scale, especially after tree saturation [4, 19]. Multipoint support in Asynchronous Transfer Mode (ATM) networks is essential for efficient duplication and synchronization of data. Examples of multipoint applications include audio and video conferencing, and server and replicated database synchronization (see figure 1) Multipoint to point ....

....a pre determined weight with respect to that of a sender in a multicast session. This technique adds more flexibility at the expense of complexity in RM cells and processing. Weight assignment is also very difficult. Multicast pricing in the context of the Internet has recently been studied in [4, 19]. These studies quantify the cost of multicast relative to unicast, and find that the normalized cost of the multicast tree is where is the multicast group size and is the economies of scale factor, experimentally determined to be approximately 0.8 before tree saturation. Recent studies on ....

Philips, Shenker, and Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. In Proceedings of the ACM SIGCOMM, 1999. http://www.acm.org/sigcomm/sigcomm99/papers/session2-1.html.

....has not yet been a comprehensive study of the Internet topology at the router level. In contrast, the interdomain level has been studied lately [15] In a parallel tangent, several people have studied topological properties indirectly, through the study of scaling of multicast trees in Internet [2, 12, 17]. Recently, Albert et al. [1] and Tauro and Faloutsos [15] studied the fault tolerance of the Internet at the interdomain level. Recall that our work here focuses at the router level of the Internet. Assumptions and limitations. The router level Internet graph contains communication links ....

G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. ACM SIGCOMM, September 1999.

....to the heavy tailed distribution of the size of the transmitted data files, 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 purposes, but they also propose an estimate that does not follow a power law. 3 Internet Instances In this section, we present the Internet instances we acquired and we study their evolution in time. We examine the ....

....5 We define the eigen exponent, E, to be the slope of the plot of the sorted eigenvalues versus their order in log log scale. 5 Note that our results focus on relatively small neighborhoods compared to the diameter h ffi. Other experimental studies focus on neighborhoods of larger radius [17]. 1 10 100 1 10 971108.internet.svals exp(3.57926) x ( 0.471327 ) 1 10 100 1 10 980410.svals exp(3.69981) x ( 0.502062 ) a) Int 11 97 (b) Int 04 98 Figure 10: The eigenvalue plots: Log log plot of eigenvalues in decreasing order. 1 10 100 1 10 981205.svals exp(3.77292) x ....

G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the chuang-sirbu scaling law. ACM SIGCOMM. Computer Communication Review., Sep 1999.

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G. Philips and S. Shenker. Scaling of multicast trees: comments on the Chuang-Sirbu scaling law. In Proceedings of ACM SIGCOMM'99, pages 41--51, Sept. 1999.

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G. Philips and S. Shenker. Scaling of multicast trees: comments on the Chuang-Sirbu scaling law. In Proceedings of ACM SIGCOMM'99, pages 41--51, Sept. 1999.

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G. Philips and S. Shenker, Scaling of Multicast Trees: Comments on the Chuang-Sirbu Scaling Law, ACM SIGCOMM, 1999.

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G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. In ACM SIGCOMM, Aug. 1999.

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G. Philips and S. Shenker, "Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law," presented at the ACM SIGCOMM, Cambridge, MA, 1999.

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G. Philips and S. Shenker. Scaling of multicast trees: comments on the Chuang-Sirbu scaling law. In Proceedings of ACM SIGCOMM'99, pages 41--51, Sept. 1999.

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G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. In ACM SIGCOMM, Aug. 1999.

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G. Philips and S. Shenker. Scaling of multicast trees: comments on the Chuang-Sirbu scaling law. In Proceedings of ACM SIGCOMM'99, pages 41--51, Sept. 1999.

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G. Philips, S. Shenker, and H. Tangmunarunkit. Scaling of multicast trees: Comments on the Chuang-Sirbu scaling law. In ACM SIGCOMM'99, Cambridge, MA, USA, 1999.

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Graham Philips and Scott Shenker, Scaling of Multicast Trees: Comments on the Chuang-Sirbu scaling law, Proceedings of ACM SIGCOMM '99.

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G. Philips, S.Shenker, and H.Tangmunarunkit. Scaling of multicast trees: Comments on the chuang-sirbu scaling law. In Proceedings of ACM SIGCOMM'99, Aug 1999.

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