Multicast scheduling for input-queued switches

We design a scheduler for an M/spl times/N input-queued multicast switch. It is assumed that: 1) each input maintains a single queue for arriving multicast cells and 2) only the cell at the head of line (HOL) can be observed and scheduled at one time. The scheduler needs to be: 1) work-conserving (no output port may be idle as long as there is an input cell destined to it) and 2) fair (which means that no input cell may be held at HOL for more than a fixed number of cell times). The aim is to find a work-conserving, fair policy that delivers maximum throughput and minimizes input queue latency, and yet is simple to implement. When a scheduling policy decides which cells to schedule, contention may require that it leave a residue of cells to be scheduled in the next cell time. The selection of where to place the residue uniquely defines the scheduling policy. Subject to a fairness constraint, we argue that a policy which always concentrates the residue on as few inputs as possible generally outperforms all other policies. We find that there is a tradeoff among concentration of residue (for high throughput), strictness of fairness (to prevent starvation), and implementational simplicity (for the design of high-speed switches). By mapping the general multicast switching problem onto a variation of the popular block-packing game Tetris, we are able to analyze various scheduling policies which possess these attributes in different proportions. We present a novel scheduling policy, called TATRA, which performs extremely well and is strict in fairness. We also present a simple weight-based algorithm, called WBA.