hes had a huge switch fabric, in order to spare money, a small blocking probability was accepted. For this reason, it is important to have a means to evaluate the blocking probability of a Clos switch fabric. Two approximations have been developed for this reason: the Lee or the Jacobaeus [14] approximations. In both cases, the starting assumption is that no rearrangements of existing connections is possible SO that when a new connection arrives to an input switch, the potential number of other active connections on the ingress and egress switches that can block the new con- nection request is - 1. In the Lee approximation, it is assumed that each internal link between stages is already occupied by a connection with a certain probability p, and that this is completely indepen- dent between different links. This overestimates the blocking probability, particularly for small r. The probability that a given internal link is busy is p=(n-1),9 (7.1) where q is the probability that an ingress or egress link is busy, that is related to the over- all traffic offered to the switch fabric. The probability that the path connecting an ingress switch to an egress switch via a particular middle stage switch is free is the probability that both links are free, that is, (1 - p)2. Hence, the probability P that this path is unavailable is P=1-(1-p)2 (7.2) The probability of blocking , that is, the probability that no path connecting the consid- ered ingress and egress ports via whatever middle stage is available, is r====== (7.3) Switching Systems: Architecture and Performances vinri D FIGURE 7.8 Example of rearrangement of a Clos switch fabric to eliminate a blocking situation: (a) the path between input and output ports labeled with E is blocked due to the configuration of the last element of the second stage; (b) the block is removed by rerouting the path between output and input D ports. Telecommunication Networks This is a very simple equation to use in practical cases, but especially for small values of r is a large upper bo