Modeling the blocking behavior of Clos networks

The Clos network has been widely used for data communications and parallel computing systems. 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 with those widely-used models 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 a new analytical model assuming a random routing strategy for the blocking probability of the three-stage Clos network. The new model can more accurately describe the blocking behavior of the network and is consistent with the deterministic nonblocking condition. We also extend our model to incorporate a packing strategy. Finally through simulations we demonstrate that the analytical model presented in this paper is consistent with the simulation results under both random routing and packing strategies.