Multicast routing in internetworks and extended LANs
SIGCOMM '88 Symposium proceedings on Communications architectures and protocols
Multicast routing in datagram internetworks and extended LANs
ACM Transactions on Computer Systems (TOCS)
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Scaling of multicast trees: comments on the Chuang-Sirbu scaling law
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Average Case Analysis of Algorithms on Sequences
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On the power-law random graph model of massive data networks
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WWIC '07 Proceedings of the 5th international conference on Wired/Wireless Internet Communications
Small-world characteristics of Internet topologies and implications on multicast scaling
Computer Networks: The International Journal of Computer and Telecommunications Networking
An analytical evaluation of autocorrelations in TCP traffic
AINTEC'05 Proceedings of the First Asian Internet Engineering conference on Technologies for Advanced Heterogeneous Networks
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One of the main benefits of multicast communication is the overall reduction of network load. To quantify this reduction, when compared to traditional unicast, experimental studies by Chuang and Sirbu indicated the so called power law which asserts that the ratio R(n) of the average number of links in a multicast delivery tree connecting n sites to the average number of links in a unicast path is Θ(n0.8). Our goal is to explain theoretically this behavior. Claiming that the essence of the phenomenon lies in the geometry of the internet and its modeling assumptions, we introduce the model of self-similar trees with similarity factor 0 ≤ θ R(n) and prove that it is Θ(n1-θ). We also discuss some experimental results of real networks that confirm the power law and show that these networks have the self similar profile. In particular, we find experimentally that the power law holds with θexp ≈ 0.12. Our theoretical findings are established by analytical techniques of the precise analysis of algorithms such as Mellin transform and complex asymptotics.