Blocking probability of bicast connections in a Clos network

Clos networks, which are ubiquitous in large capacity switches, have been widely studied for unicast connection requests. But most of the results for unicast do not hold when the switch has to support multicast connections. Our interest is specifically in bicast connections which are required for setting up backup protected circuits in optical backbone networks. In this work we have proposed two approximation methods to estimate the blocking probability of a switch that is not strictly non-blocking in the presence of bicast connections. We have considered two ways of realizing a bicast connection - by splitting the circuit at the outer stage or at the middle stage. We have also carried out simulations to be compared with our analytical results and found that they closely match. Furthermore, we have compared two routing strategies - one randomly selects an available middle stage block and the other selects one of the highly loaded ones, and found that the latter significantly reduces blocking.