s a free input of an ingress switch, and this has to be connected to a free output on a particular egress switch. In the worst case, n - 1 other connections are active on the considered ingress switch, and n - 1 other connections are active on the con- sidered egress switch. Let us also assume, in the worst case, that each of these connections passes through a different middle stage switch. Hence, in the worst case, 2n - 2 of the middle stage switches are unable to carry the new connection. Therefore, to ensure strictly nonblocking opera- tion, another middle stage switch is required, making a total of at least 2n - 1. Telecommunication Networks 7.2.2.2 Rearrangeable Nonblocking Clos Networks If m > n, the Clos network is rearrangeable nonblocking, which means that an unused input on an ingress switch can always be connected to an unused output on an egress switch, but to do that, existing connections may have to be rearranged by assigning them to different center stage switches in the Clos network. To prove this property is out of this brief summary, but an example is shown in Figure 7.8 utilizing a Clos switch fabric with r=n=m=4 that results rearrangeable nonblocking. Let us imagine receiving the set of connection requests that are shown in Figure 7.8a, where the input and output ports to be connected are identified with the same letter, and let us imagine that the connections arrive SO that the letters are in alphabetical order. First arrives connection A and it is routed, then B, C, D, and all are routed, when connection E arrives, it is blocked. In order to route connection E, connection D has to be rerouted SO to free the central stage switch. After D is rerouted (see Figure 7.8b) connection E can be routed, thus removing the situation of removable block that was created by the request of connection E. 7.2.2.3 Blocking Clos Networks If m < n, the Clos network is blocking. For a long time, blocking Clos networks have found a large application in telephone switches. As a matter of fact, since telephone switc