Modelling the blocking behaviour of Clos networks

The Clos network has been widely used for telecommunications and parallel computing systems. For this reason, it is important to have a thorough understanding of its performance. Several analytical models have been proposed to estimate the blocking probability of Clos networks but, due to the effect of approximations, a common problem has been that they may not be very accurate in some cases. In particular, the blocking probability in these models contradicts the well-known deterministic nonblocking condition for the Clos network. In this paper, we present an analytical model for the blocking probability of the three-stage Clos network. We analyze the blocking behavior of the network under both random routing and packing strategy. The proposed model can more accurately describe the blocking behavior of the network and is consistent with the deterministic non-blocking condition. Through simulations, we also demonstrate that the analytical model presented in this paper is consistent with the simulation results.