Improved multi‐processor scheduling for flow time and energy

Energy usage has been an important concern in recent research on online scheduling. In this paper, we study the tradeoff between flow time and energy (Albers and Fujiwara 2007; Bansal et al. 2007b, Bansal et al. 2008; Lam et al. 2008b) in the multi‐processor setting. Our main result is an enhanced analysis of a simple non‐migratory online algorithm called CRR (classified round robin) on m≥2 processors, showing that its flow time plus energy is within O(1) times of the optimal non‐migratory offline algorithm, when the maximum allowable speed is slightly relaxed. The result still holds even if the comparison is made against the optimal migratory offline algorithm. This improves previous analysis that CRR is O(log P)‐competitive where P is the ratio of the maximum job size to the minimum job size.