und. The Jacobaeus approximation is more accurate since it is based on the observation that a connection between a free ingress port of the kth first stage switch and a free egress port of the hth third stage switch is blocked if and only if there is no middle stage available to accept the connection from the kth input port to transfer it to the hth output port (compare as an example with the routing performed in Figure 7.8). Let us assume that some particular mapping of connections entering the Clos network (input connections) already exists onto middle stage switches. This reflects the fact that only the relative configurations of ingress switches and egress switches is of relevance. Let us imagine that a new connection request between free input and output ports arrives. There are i input connections entering via the same ingress switch of the new request, and there are j connections leaving the Clos network (output connections) via the same egress switch. Hence, Oiu, and Oj u, being U=N 1. Let us call A the number of ways of assigning the j output connections to the m middle stage switches and B the number of these assignments which result in blocking. Then the number of cases in which the remaining m - j middle stage switches coincide with m - j of the i input connections to be inaccessible for the blocked connection is exactly B. Looking at the same phenomenon in another way, we can see that B is the number of configurations of the i input connections generating m - j input connections engaging the middle stage switches that remain free after the routing of the j output connections. In this way, j middle stage switches are blocked by the output connections and m - are blocked by a subset of input connections and the newly arrived connection request is blocked. Then the probability of blocking in the considered situation is (7.4) If fi is the probability that i other calls are already active on the ingress switch, and 8j is the probability that j other calls are already active on the egress switch, the overa