Impact of network delay variations on multicast sessions with TCP-like congestion control

We study the impact of random noise (queueing delay) on the performance of a multicast session. With a simple analytical model, we analyze the throughput degradation within a multicast (one-to-many) tree under TCP-like congestion and flow control. We use the (max, plus) formalism together with methods based on stochastic comparison (association and convex ordering) and on the theory of extremes (Lai and Robbins´ (1978) notion of maximal characteristics) to prove various properties of the throughput. We first prove that the throughput obtained from Golestani and Sabnani´s (1999) deterministic model is systematically optimistic. In presence of light tailed random noise, we show that the throughput decreases like the inverse of the logarithm of the number of receivers. We find analytically an upper and a lower bound for the throughput degradation. Within these bounds, we characterize the degradation which is obtained for various tree topologies. In particular, we observe that a class of trees commonly found in IP multicast sessions (which we call umbrella trees) is significantly more sensitive to network noise than other topologies