Scaling of multicast trees

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 [3]. 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 L(m) ∝ m 0.8 . 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.