Statistical analysis of stability of multicast trees in cumulative layered multicast

In this paper, we consider the stability of a multicast (one-to-many) tree in cumulative layered multicast, which is traditionally realized by dropping a layer when congestion is detected. First, we define a stability index to evaluate and quantify tree's stability. Then, for obtaining the general expression of the stability index, we develop a simple statistical model, which is based on the link-dependent model and the dependency-degree model in [X. Zhang et al., 2001]. We show that even in the case of lower link-marking probability, the stability of multicast tree is significantly more sensitive to network congestion when dependency between different links becomes smaller, indicating that more links will leave the tree when congestion occurs.