When is a Work-Conserving Switch Not?

Crossbar-based switches are commonly used to implement routers with throughputs up to about 1 Tb/s. The advent of work-conserving crossbar scheduling algorithms now makes it possible to engineer systems that perform well, even under extreme traffic conditions. Unfortunately, all the published work-conservation results for crossbar scheduling apply only to systems that switch fixed-length cells, not variable length packets. Routers that use a cellbased crossbar with a nominally work-conserving scheduler to switch variable length packets can fail to be work-conserving at the external links, since the router cannot forward a packet until all of its constituent cells reach the output line card. Speedups as large as the number of inputs and outputs can be required to achieve work-conservation, using schedulers that operate only on cells. There appear to be fundamental obstacles to achieving practical workconservation for variable length packet switches based on unbuffered crossbars. However, we show that adding buffers to crossbars allows work-conservation to be achieved for variable length packet switching, using modest speedups. In particular we define packet versions of the Group by Virtual Output Queue (GVOQ) scheduler of Chuang et. al. and the Least Occupied Output First (LOOFA) scheduler of Krishna et. al. and show that they are both workconserving for speedups ≥2. Specific versions of both algorithms are also shown to be orderpreserving for speedups ≥2, meaning that they can exactly emulate an ideal, output queued switch. This work is supported by the National Science Foundation (grant #CNS-0325298).