Analysis of scheduling algorithms that provide 100 % throughput in input - queued switches

Internet routers frequently use a crossbar switch to interconnect linecards. The crossbar switch is scheduled using an algorithm that picks a new crossbar configuration every cycle. Several scheduling algorithms have been shown to guarantee 100% throughput under a variety of traffic patterns. The first such algorithm was the maximum weight matching (MWM) algorithm in which the weight is the sum of the occupan-cies of the queues. We explore whether alternative weight functions, such as using the sum of the square of the occupancies, leads to stronger or weaker stability. The first result of this paper is that a broad class of weight functions give rise to strong stability, including the sum of the squares, the sum of the cubes and so on. A counter-intuitive result, indicating a limitation of the Lyapunov method, is that the sum of the square root of the occupancies is not included in this class, even though simulation suggests that the resulting average delay is lower than for the other functions. We also consider the simpler , , randomized scheduling algorithm (TASS) proposed by Tassiulas. We show similar results for different weight functions as for MWM. We finally show that TASS gives 100% throughput when the weights are noisy, or out-of-date.