On the speedup required for a multicast parallel packet switch

A parallel packet switch (PPS) is a switch in which the memories run slower than the line rate. Arriving packets are load-balanced packet-by-packet over multiple lower speed center stage packet switches. It is known that, for unicast traffic, a PPS can precisely emulate a FCFS output-queued (OQ) switch with a speedup of two and an OQ switch with delay guarantees with a speedup of three. In this paper we ask: is it possible for a PPS to emulate the behavior of an OQ multicast switch? The main result is that for multicast traffic an N-port PPS can precisely emulate a FIFO OQ switch with a speedup of S>2√N+1, and a switch that provides delay guarantees with a speedup of S>2√(2N)+2