Performance characteristics of multicast flows on random trees

We consider a flow of data packets from one source to many destinations in a communication network represented by a random oriented tree. Multicast transmission is characterized by the ability of some tree vertices to replicate received packets depending on the number of destinations downstream. We are interested in characteristics of multicast flows on Galton-Watson trees and trees generated by point aggregates of a Poisson process. Such stochastic settings are intended to represent tree shapes arising in the Internet and in some ad hoc networks. The main result in the branching process case is a functional equation for the joint probability generating function of flow volumes through a given vertex and in the whole tree. We provide conditions for the existence and uniqueness of solution and a method to compute it using Picard iterations. In the point process case, we provide bounds on flow volumes using the technique of stochastic comparison from the theory of continuous percolation. We use these results to derive a number of random trees' characteristics and discuss their applications to analytical evaluation of the load induced on a network by a multicast session.