In deriving the expression for the bandwidth of a crossbar system, we have assumed that all processors generate requests for memory modules during a given cycle. Derive a similar expression for the case whereby only a fraction of processors, f, generate requests during a given cycle. Consider the two cases whereby a processor generates a memory request with probability r in a given cycle and whereby a processor can request any memory module. 3. Consider the recursive expression developed for the bandwidth of a Delta MIN network consisting of stages of a ! b crossbar switches. Assuming that a 2, b 4, and ra 0.5, compute the bandwidth of such a network.