On the computational complexity of maintaining GPS clock in packet scheduling

Packet scheduling is an important mechanism to provide QoS guarantees in data networks. A scheduling algorithm generally consists of two functions: one estimates how the GPS (general processor sharing) clock progresses with respect to the real time; the other decides the order of serving packets based on an estimation of their GPS start/finish times. In this work, we answer important open questions concerning the computational complexity of performing the first function. We systematically study the complexity of computing the GPS virtual start/finish times of the packets, which has long been believed to be Ω(n) per packet but has never been either proved or refuted. We also answer several other related questions such as "whether the complexity can be lower if the only thing that needs to be computed is the relative order of the GPS finish times of the packets rather than their exact values?".