Rate Quantization and the Speedup Required to Achieve 100% Throughput for Multicast Over Crossbar Switches

The problem of providing quality-of-service (QoS) guarantees for multicast traffic over crossbar switches has received limited attention despite the popularity of its counterpart for unicast traffic. Providing a 100% throughput to all admissible multicast traffic has been shown to be a very difficult task, and it requires a very high speedup in the switching fabric. In this paper, we introduce the concept of rate quantization and use rate quantization to show an analogy between packet scheduling in crossbar switches and circuit switching in three-stage Clos networks. We exploit the analogy to adopt circuit-switching algorithms in wide-sense and strict-sense nonblocking Clos networks in order to construct nonblocking packet schedulers for unicast and multicast traffic. We illustrate a simple multicast nonblocking packet scheduler, for which a speedup of 6logn/loglogn is sufficient to support 100% throughput for any admissible multicast traffic in an n×n crossbar switch. Moreover, we revisit some problems in unicast switch scheduling. We illustrate that the analogy provides useful perspectives, and we give a simple proof for a well-known result.