New Online Algorithm for Dynamic Speed Scaling with Sleep State

In this paper, we consider an energy-efficient scheduling problem where $n$ jobs $J_1, J_2, ..., J_n$ need to be executed such that the total energy usage of these jobs is minimized while ensuring that each job is finished within it's deadline. We work in an online setting where a job is known only at it's arrival time, along with it's processing volume and deadline. In such a setting, the currently best-known algorithm by Han et al. \cite{han} provides a competitive ratio max $\{4, 2 + {\alpha}^{\alpha}\}$ of energy usage. In this paper, we present a new online algorithm SqOA which provides a competitive ratio max $\{4, 2 + (2-1/{\alpha})^\alpha 2^{\alpha-1}\}$ of energy usage. For $\alpha \geq 3$, the competitive ratio of our algorithm is better than that of any other existing algorithms for this problem.