Modelling the blocking behavior of multicast Clos networks

This paper considers three-stage switching networks able to support multicast traffic, i.e. connections in which one inlet is connected to more than one output at the same time. The nonblocking conditions for this network are studied under the assumption of absence of any optimized routing of the connections inside the structure (the so-called strict-sense nonblocking networks). An analytical model is developed here that provides not only the nonblocking conditions of three-stage multicast networks, but also the evaluation of the blocking probability when such conditions are not satisfied. Unlike previous well-known approaches, our model takes into account the correlation between occupancy events in link's belonging to different interstage patterns. The results being found also provide a more stringent condition of network nonblocking for multicast traffic which disproves some of the claimed results recently published in the technical literature.