 an NxN crossbar, a 2N X 2N fabric can be built with four NxN elements, a 3N X 3N fabric can be built using nine NxN building blocks, and SO on. This construction is shown in Figure 7.5. Since the path through the fabric from an input to an output port is not unique and there is no automatic routing algorithm, the algorithm used by the external controller to set up the signal path when a new connection between input and output is required is an impor- tant aspect of the crossbar working. This is important in particular in dynamic applications, when the input of the switch fabric is generally constituted by the output of a set of queues, where the arriving switch- ing requests are accumulated (see Figure 7.2) and fast switching based on the priorities of the incoming requests is the key to achieve high performances. As shown in Figure 7.6, the route connecting an input port with a selected output is not unique, and in the worst case (when the signal enters from a port at the edge of the switch and has to exit from the port at the corresponding edge on the exit side) there are two com- pletely disjoined paths between the input and the output. Telecommunication Networks FIGURE 7.5 Example of the procedure to build a 2N X 2N switch fabric starting from four N X N crossbar elements. Independent paths between input 1 and output 4 Path 1 Path 2 FIGURE 7.6 Example of the multiple routes connecting Input selected input and output ports in a crossbar switch fabric. Output This means that the failure of a crosspoint in the switch fabric can create block- ing patterns, that is correspondences between input and output that cannot be set, but not necessarily destroy the existing configuration, especially if a large number of ports is free. From a performance point of view, the crossbar switch fabric is a good solution; unfor- tunately, it is not easy to scale it to a large switch dimension. As a matter of fact, the number of elementary 2x2 switches required by a crossbar with N = 2M input/output ports is M², SO that the cost o