This research addresses the multiprocessor scheduling problem of hard real-time systems, and it especially focuses on optimal and global schedulers when practical constraints are taken into account. First, we propose an improvement of the optimal algorithm BF. We formally prove that our adaptation is (i) optimal, i.e., it always generates a feasible schedule as long as such a schedule exists, and (ii) valid, i.e., it complies with the all the requirements. We also show that it outperforms BF by providing a computing complexity of O(n), where n is the number of tasks to be scheduled. Next, we propose a schedulability analysis which indicates a priori whether the real-time application can be scheduled by our improvement of BF without missing any deadline. This analysis is, to the best of our knowledge, the first such test for multiprocessors that takes into account all the main overheads generated by the Operating System.