Leap Forward Virtual Clock: an O(log Log N) Fair Queuing Scheme with Guaranteed Delays and Throughput Fairness an O(log Log N) Fair Queuing Scheme with Guaranteed Delays and Throughput Fairness

We describe an eecient fair queuing scheme, Leap Forward Virtual Clock, that provides end-to-end delay bounds similar to PGPS, along with throughput fairness. Our scheme can be implemented with a worst-case time O(log log N) per packet (inclusive of sorting costs), which improves upon all previously known schemes that guarantee delay and throughput fairness similar to PGPS. Interestingly , both the classical virtual clock and the Self-Clocked Fair Queuing schemes can be thought of as special cases of our scheme, by setting the leap forward parameter appropriately. We use Zhang's virtual clock as a point of departure. We modify the original virtual clock scheme, which does not give throughput fairness, using two simple ideas: a quarantine mechanism that temporarily takes oversubscribed ows ooine, and a leap forward mechanism that advances the server clock forward when all ows are oversubscribed. These two mechanisms keep the server clock from lagging too far behind the packet tags. We prove that our scheme guarantees a fair share of the available bandwidth to each of the backlogged users, while precisely matching the delay bounds of PGPS schemes. In fact, by the worst-case fairness measure, our scheme is comparable to Worst-case Weighted Fair Queuing|the burstiness shown by PGPS does not occur in our scheme. In order to improve computational eeciency, we introduce a \coarsened" version of our scheme in which all tags assume values from a set of O(N) integers. We then use \approximate sorting" and a nite-universe priority queue to achieve O(log log N) processing time per packet. We can show that the coarsening of tags increases the delay bound by a very small additive constant.