Before revision:  We assume 2 (essential) speeds in our proposed platform. We relax this assumption and consider many speedsin our energy considerations. This problem has been considered previously in the field of parallel computing and scheduling theory for the general case where multiprocessor platforms have K distinct speeds.
After revision:  Interestingly, this special case has not been studied in the field of parallel computing and scheduling theory for the general case where multiprocessor platforms have K distinct speeds.