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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 usageof these jobs is minimized while ensuring that each job is finished within it'sdeadline. We work in an online setting where a job is known only at it'sarrival time, along with it's processing volume and deadline. In such asetting, the currently best-known algorithm by Han et al. \cite{han} provides acompetitive ratio max $\{4, 2 + {\alpha}^{\alpha}\}$ of energy usage. In thispaper, we present a new online algorithm SqOA which provides a competitiveratio 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 ofany other existing algorithms for this problem.

New Online Algorithm for Dynamic Speed Scaling with Sleep State