We address the scheduling model of arbitrary speed-up curves and the broadcast scheduling model. The former occurs when jobs are scheduled in a multi-core system or on a cloud of machines. Here jobs can be sped up when given more processors or machines. However, the parallelizability of the jobs may vary and the algorithm is required to be oblivious of the parallelizability of a job. The latter model is natural in wireless and LAN networks where requests (or jobs) can be simultaneously satisfied together. Both settings are similar in that two schedules can do different amounts of work to satisfy all the jobs. We focus on optimizing the ℓk- norms of flow time. Recently, Gupta et al.  gave a (k + ɛ)-speed O(1)-competitive algorithm for the ℓk norms of flow time in both scheduling settings for fixed k. Inspired by this work, we give the first analysis of a scalable algorithm, i.e. (1 + ɛ)-speed O(1)-competitive, for all ℓk-norms of flow time in both settings for fixed k and 0 < ɛ ≤ 1. Both problems have a strong lower bound without resource augmentation, so this is the best result that can be shown in the worst case setting up to a constant factor in the competitive ratio.