Probabilistic analysis of a crossbar switch

This paper presents a probabilistic analysis of a crossbar switch interconnection network. A crossbar switch can be used to interconnect various combinations of computer subsystems. In the analysis below it is assumed, without loss of generality, that the crossbar is being used to connect N processors to M memories. The crossbar is termed an N-M crossbar (read “N to M crossbar”). General expressions are developed for a variety of performance figures for an N-M crossbar including: the probability of a memory request being accepted (i.e. not being blocked by another request to the same memory), the expected bandwidth of the crossbar, and the average wait time of a request before it is accepted. Closed form solutions to these expressions are given for the uniform request case and for the favorite memory case (i.e. where processor i requests memory i with a higher probability than others memories). The closed form solutions are tested against simulations.