A packet having a crossbar architecture with M inputs and N outputs is considered. Following earlier work, the theoretical capacity of such a switch is found in terms of the throughput of a closed queueing network. A state-dependent server model that approximates the rate at which the switch is transferring packets as a function of the work backlog (the number of packets queued at the switch inputs) is then developed. In this way, the model reflects the fact that such a switch tends to function more efficiently as the work backlog increases. This model yields an accurate method for approximating the entire distribution of the work backlog, as well as mean queue lengths and waiting times.>