Abstract

concerning the computational complexity for packet scheduling algorithms to achieve tight end-to-end delay bounds. We rst focus on the dierence between the time a packet nishes service in a scheduling algorithm and its virtual nish time under a GPS (General Processor Sharing) scheduler, called GPS-relative delay. We prove that, under a slightly restrictive but reasonable computational model, the lower bound computational complexity of any scheduling algorithm that guarantees O(1) GPS-relative delay bound is log2n) (widely believed as a \folklore theorem" but never proved). We also discover that, surprisingly, the complexity lower bound remains the same even if the delay bound is relaxed to O(n ) for 0 < a < 1. This implies that the delaycomplexity tradeo curve is \at" in the \interval" [O(1), O(n)). We later extend both complexity results (for O(1) ) delay) to a much stronger computational model. Finally, we show that the same complexity lower bounds are conditionally applicable to guaranteeing tight end-to-end delay bounds. This is done by untangling the relationship between the GPS-relative delay bound and the end-to-end delay bound.

Citations