Scheduling of an input-queued switch to achieve maximal throughput

Achieving high throughput in input-queued switches has been found to be difficult, especially when traffic is nonuniform in the sense that different inputs have very different cell generation rates. We show that for general arrival processes, 100% throughput can be achieved with a simple algorithm that is very easy to implement. We consider a switch in which in each time slot, at most one cell may be transmitted from each input, and at most one cell may be received at each output. Cells that are destined for output j arrive at input i according to a stationary and ergodic process, and arrivals are queued at the input. The problem is to decide which inputs are to transmit to which outputs in each time slot in order to maximize throughput. Necessary conditions for stability are that the total arrival rate to each input must be less than i, and the total arrival rate destined to each output must be less than i. We propose a simple scheduling algorithm and show that with this algorithm the necessary conditions for stability are also sufficient.