ll blocking probability is (7.5) The probability PB can be expressed with a more explicit formula substituting to gi and fi a binomial distribution. After a difficult simplification, the final expression of the blocking probability results to be (7.6) m!(2n-m-2)! 7.2.2.4 Control of a Clos Switch Since a Clos switch is composed by a collection of suitably connected crossbar switches, it is also composed of a set of independently driven 2x2 switches. From the point of view of the switch control, it is somehow equivalent to the crossbar switch. Switching Systems: Architecture and Performances The route finding algorithm for a nonblocking Clos switch fabric can be formulated in several different ways. The most intuitive are probably the following: Individuate in the input stage the number of the switch from where the connection to be set up has to start; let us call it k. Staring from the first switch of the central stage, individuate the first central switch with the kth port free; let us call its number in the middle stage h. Switch the crossbar from where the signal comes in and the hth crossbar in the middle stage SO as to transfer the connection request at the kth output port of the middle stage. Move the signal to the kth output port of the middle stage. Transfer the signal to the kth switch of the third stage. Transfer the signal to the correct output port. The only thing to be noted is that, in the assumption of strictly nonblocking structure, there surely does exist a switch in the central stage having the kth input port free. Much more complicated algorithms have been introduced both in order to reduce as much as possible the calculation complexity and to be able to manage rearrangeable non- blocking and blocking Clos networks. A good set of starting information is contained in [4,15,16]. 7.2.2.5 Dimensions and Power Consumption Let us imagine the need for a strictly nonblocking switch fabric with N input and output ports. To implement this switch fabric with a Clos architecture, we have to satisfy the foll