Multicast traffic in input-queued switches: Optimal scheduling and maximum throughput

Abstract

Abstract-This paper studies input-queued packet switches loaded with both unicast and multicast traffic. The packet switch architecture is assumed to comprise a switching fabric with multicast (and broadcast) capabilities, operating in a synchronous slotted fashion. Fixed-size data units, called cells, are transferred from each switch input to any set of outputs in one time slot, according to the decisions of the switch scheduler, that identifies at each time slot a set of nonconflicting cells, i.e., cells neither coming from the same input, nor directed to the same output.First, multicast traffic admissibility conditions are discussed, and a simple counterexample showing intrinsic performance losses of input-queued with respect to output-queued switch architectures is presented. Second, the optimal scheduling discipline to transfer multicast packets from inputs to outputs is defined. This discipline is rather complex, requires a queuing architecture that probably is not implementable, and does not guarantee in-sequence delivery of data. However, from the definition of the optimal multicast scheduling discipline, the formal characterization of the sustainable multicast traffic region naturally follows. Then, several theorems showing intrinsic performance losses of input-queued with respect to output-queued switch architectures are proved. In particular, we prove that, when using per multicast flow FIFO queueing architectures, the internal speedup that guarantees 100% throughput under admissible traffic grows with the number of switch ports.

A Dynamic Frame Sizing Algorithm for CICQ Switches with 100% Throughput

“…Using this in (2) implies that the number of packets left at the end of the n th frame can only come from the new arrivals in that frame, i.e.,…”

“…It is known (see e.g., [2]) that an input-buffered switch (with an unbuffered crossbar) cannot achieve 100% throughput with multicast traffic, even when fanout splitting is allowed. The main objective of this section is to show that our dynamic frame sizing algorithm also achieves 100% throughput for CICQ switches with multicast traffic.…”

On the Speedup Required to Achieve 100% Throughput for Multicast Over Crossbar Switches

“…To avoid head of the line (HOL) blocking [6], we assume the presence of virtual output queueing (VOQ) at each input for every possible fanout set. Further, virtual output queueing at a per fanout set level is referred to as multicast virtual output queueing (MC-VOQ) in [2]. Note that in an n × n switch, for a given input, there exist 2 n − 1 possible fanout sets.…”

“…One of the main reasons for this is the difficulty of the task. Indeed, it was shown in [1] that "optimal scheduling" of multicast packets is NP-hard over a crossbar switch and in [2] it was proved that the resource speedup necessary to achieve 100% throughput for all admissible multicast traffic grows unbounded with increasing switch size. These results hold even when the crossbar switch is multicast capable, i.e., it is capable of connecting an input to multiple outputs.…”

“…These results hold even when the crossbar switch is multicast capable, i.e., it is capable of connecting an input to multiple outputs. It is also stated in [2] that "the numerical evaluation of the necessary speedup is prohibitive" and no scaling law has been given as to how the speedup scales with the switch size.…”