mwalk - Anatomy

On the Anatomy of Inter-Domain Multicast Trees

Little previous research has focused on how multicast trees are really shaped. Intuitively, it seems that most inter-domain multicast trees should have a similar shape since most receivers are necessarily in different domains than the source. Therefore, the distribution tree must take a number of hops to traverse the sources own domain, cross the backbone and then the domains of each receiver. This should result in tall trees where most of the branching occurs at a limited number of peering points within the backbone and at edge routers near the receivers.

In our study, we focus on this branching and where it occurs within the tree. When we're talking about branching, however, we are really looking at each nodes out-degree. Work done by Faloutsos et al.('99) showed that the degree frequencies of Internet routers follow a skewed distribution; only a few routers have a high degree while most have a very low degree. The graph in the next column shows a similar effect for inter-domain multicast trees. We found that nearly 80% of the routers had an out-degree of one. This results in long chains of relay nodes that simply pass the packets along a single path.

But this still doesn't tell us where in the tree the branching occurs. The graph to the left shows the total average out-degree (in green) which grows with the number of receivers in the multicast group. If we separate the degrees into two components, however, more details emerge.

internal degree (blue) - the number of edges connecting two routers
leaf degree (red) - the number of links directly connecting receivers

It is clear, that the growth seen in the total out-degree is dominated by the leaf-degree as the number of receivers grows. In fact, the average internal degree tapers off quickly around 1.5. This means that the body of the multicast tree is fairly well behaved. The range of available links soon become used and new receivers are added to already connected subnets.

It seems that are intuition is correct. Most inter-domain multicast trees have a similar shape since the underlying network topology constrains the possible range of tree topologies.

updated 05.01.01