Optimal speed scaling under arbitrary power functions

This paper investigates the performance of online dynamic speed scaling algorithms for the objective of minimizing a linear combination of energy and response time. We prove that (SRPT, P−1(n)), which uses Shortest Remaining Processing Time (SRPT) scheduling and processes at speed such that the power used is equal to the queue length, is 2-competitive for a very wide class of power-speed tradeoff functions. Further, we prove that there exist tradeoff functions such that no online algorithm can attain a competitive ratio less than 2.