Achieving 100% Throughput In An Input-Queued Switch

It is well known that head-of-line (HOL) blocking limits the throughput of an input-queued switch with FIFO queues. Under certain conditions, the throughput can be shown to be limited to approximately 58%. It is also known that if non-FIFO queueing policies are used, the throughput can be increased. However, it has not been previously shown that if a suitable queueing policy and scheduling algorithm are used then it is possible to achieve 100% throughput for all independent arrival processes. In this paper we prove this to be the case using a simple linear programming argument and quadratic Lyapunov function. In particular, we assume that each input maintains a separate FIFO queue for each output and that the switch is scheduled using a maximum weight bipartite matching algorithm.