On the Computational Complexity of Maintaining GPS Clock and Providing Tight Delay Bounds in Packet Schedule

Abstract

Packet scheduling is an important mechanism for providing QoS guarantees in data networks. A scheduling algorithm in general consists of two functions: one estimates how the GPS (General Processor Sharing) clock progresses with respect to the real time, and the other decides the order of serving the packets based on the estimation of their GPS start/finish times. In this work, we answer important open questions concerning the computational complexity of performing both functions. The first part of our work systematically studies the complexity of computing the GPS virtual start/finish times of the packets, which is long believed to be Ω(n) per packet but has never been proved or explicitly refuted. It also answers several other related open questions such as “whether the complexity can be lower if we only want to compute the relative order of the GPS finish times of the packets rather than their exact values?” The second part of our work studies the inherent complexity for scheduling algorithms to guarantee tight delay bounds. We extend the prior work by Xu and Lipton to a stronger and more practical computational model and explore related issues. We show rigorously that existing methodologies used in prior work will not be suitable for establishing lower bound results under the new model.