Exact GPS simulation with logarithmic complexity, and its application to an optimally fair scheduler

Abstract

Generalized Processor Sharing (GPS) is a fluid scheduling policy providing perfect fairness. The minimum deviation (lead/lag) with respect to the GPS service achievable by a packet scheduler is one packet size. To the best of our knowledge, the only packet scheduler guaranteeing such minimum deviation is Worst-case Fair Weighted Fair Queueing (WF 2 Q), that requires on-line GPS simulation. Existing algorithms to perform GPS simulation have O ( N ) complexity per packet transmission ( N being the number of competing flows). Hence WF 2 Q has been charged for O ( N ) complexity too. Schedulers with lower complexity have been devised, but at the price of at least O ( N ) deviation from the GPS service, which has been shown to be detrimental for real-time adaptive applications and feedback based applications. Furthermore, it has been proven that the lower bound complexity to guarantee O (1) deviation is Ω(log N ), yet a scheduler achieving such result has remained elusive so far.In this paper we present an algorithm that performs exact GPS simulation with O (log N ) worst-case complexity and small constants. As such it improves the complexity of all the packet schedulers based on GPS simulation. In particular, using our algorithm within WF 2 Q, we achieve the minimum deviation from the GPS service with O (log N ) complexity, thus matching the aforementioned lower bound. Furthermore, we assess the effectiveness of the proposed solution by simulating real-world scenarios.