A more accurate analytical model on blocking probability of multicast networks

Multicast communication is one of the most important collective communication operations and is highly demanded in telecommunication environments and scalable parallel and distributed computing systems. In this paper, we consider the issue of supporting multicast in the widely used a three-stage Clos network or υ(m,n,r) network. We improve a previously proposed analytical model (Yang and Wang 1998) for the blocking probability of the υ(m,n,r) multicast network by introducing more reasonable assumptions based on the properties of multicast communication and the Clos network. We also compare the improved analytical model with the simulation results under three typical routing control strategies. As can be seen, the improved model matches better with the simulation results and further confirms that a υ(m,n,r) network with a comparable cost to a permutation network is almost nonblocking for multicast connections.