Scaling of Multicast Trees:
Comments on the Chuang-Sirbu scaling law 

Graham Phillips
USC/Information Sciences Institute
4676 Admiralty Way, Suite 1001
Marina del Rey, CA 90292
graham@isi.edu

Scott Shenker
International Computer Science Institute
1947 Center Street
Berkeley, CA 94704
shenker@icsi.berkeley.edu

Hongsuda Tangmunarunkit
USC/Information Sciences Institute
4676 Admiralty Way, Suite 1001
Marina del Rey, CA 90292
hongsuda@isi.edu

June 7, 1999

Abstract:

One of the many benefits of multicast, when compared to traditional unicast, is that multicast reduces the overall network load. While the importance of multicast is beyond dispute, there have been surprisingly few attempts to quantify multicast's reduction in overall network load. The only substantial and quantitative effort we are aware of is that of Chuang and Sirbu [sirbu]. They calculate the number of links L in a multicast delivery tree connecting a random source to m random and distinct network sites; extensive simulations over a range of networks suggest that . In this paper we examine the function L(m) in more detail and derive the asymptotic form for L(m) in k-ary trees. These results suggest one possible explanation for the universality of the Chuang-Sirbu scaling behavior.