Extending the Birkhoff-von Neumann switching strategy for multicast - On the use of optical splitting in switches

The Birkhoff-von Neumann (BVN) strategy for single-stage input-queued crossbar switches does not support multicast, as it considers only permutation-based switch configurations. This paper extends the BVN strategy to multicast switching, where an input can simultaneously transmit to multiple outputs. Knowledge of the average rates of flows is used to compute an offline schedule. We begin by considering a system in which the fanout of each flow is split in a predecided manner. We call this static splitting (as opposed to dynamic splitting where no such constraint is imposed), and we study the rate region of the switch under this restriction. We provide a graph-theoretic formulation of the rate region.