Multi-tree multicast with a backpressure algorithm

This paper addresses the problem of utility maximization of multicast sessions with multiple trees over static infrastructure networks. The utility functions are general concave functions. Inspired by the derivation of the unicast backpressure algorithms, we introduce a problem formulation with tree-flow conservation constraints and derive a multicast backpressure algorithm. The algorithm is much more distributed and local than previous algorithms. We provide a rigorous analysis of the performance including the primal optimality and the bound on real queue sizes using the Lyapunov optimization technique and the convex optimization techniques together.