Rate quantization and service quality over single crossbar switches

We study the provision of deterministic rate guarantees over single crossbar switches. Birkhoff decomposition yields a general approach for this problem, but the required complexity can be very high and the quality of service can be unsatisfactory for practical traffic sources. We develop a method called rate quantization which works with any resource speedup greater than 1 to convert the set of desired rates into a certain discrete set in such a way that the complexity and the quality of service guarantees can be greatly improved over a Birkhoff switch. Moreover, quantization enables us to develop a Slepian-Duguid-like algorithm that enables the switch to both adapt to dynamically varying traffic and simplify switch scheduling significantly.