With the advent of high-speed networks, various switch architectures have been proposed to meet the increasingly stringent performance requirements being placed on the underlying switching systems. In general, the performance analysis of such a switch architecture is a difficult task mainly due to the fact that a switch consists of a large number of queues which interact with each other in a fairly complicated manner. In this paper, we analyze a crossbar switch with input queueing in terms of maximum throughput, and formalize the phenomenon that virtual queues formed by the head-of-line cells become decoupled as the switch size grows unboundedly large. We also establish various properties of the limiting queue size processes so obtained.