e written (7.40) In order to evaluate the real blocking probability, it is also needed that at least one output toward the correct direction does exist in some other SP. This brings to the following equa- tion for the overall OXC blocking probability, that we have to remember is conditioned to the fact that the OXC was not blocked at the arrival of the new connection request (N,S)=SP(N)[1-Ps(N)s-1] (7.41) where N takes into account the possibility of blocking on N-independent directions. The blocking probability is shown in Figure 7.37 for N=4 and different values of S. From the figure (take into account the log scale) it results that there is an abrupt transition for a threshold value of the traffic intensity between a regime of low blocking probability to a regime of high blocking probability, where the OXC functionality is greatly degraded. In order to maintain the probability of blocking low it is needed to maintain low Tine that can be done by increasing the OXC dimension. Thus, a network level trade-off should be needed to correctly fix all the OXC parameters. The need of this kind of trade-off and the fact that blocking always can occur has limited the diffusion of this solution with respect to the solution based on an electronic switch fabric, even if it is effective in terms of power consumption and footprint. In order to alleviate the blocking problem without using architectures with very low val- ues of S, several solutions have been proposed; one of them is based on the idea of adding FIGURE 7.37 Blocking probability of an opaque OXC with a switch fabric segmented in switch- ing planes versus the offered traffic intensity for different number of switch planes and different OXC cardinality (i.e., number of input/output Traffic intensity (Tin) directions). Telecommunication Networks 11 Switch 12 Switch 13 Switch Local Local channels channels FIGURE 7.38 Alternative architectural scheme of an opaque OXC with a switch fabric segmented in switching planes (SPs) with an inter-SPs connectivity to reduce the 