Multiprocessor scheduling problem with probabilistic execution costs

In this paper, we propose a method for tolerating an inaccuracy of the estimated execution cost of tasks that is usually assumed to be accurate in static multiprocessor scheduling algorithms. In the proposed method, tasks are assigned onto processors in such a way to minimize the maximum expected execution cost rather than the worst case or best case execution costs. A detailed analysis of the proposed method is given, and it is shown that (1) there is an instance for which the algorithm is not optimal, and (2) for a class of instances, the algorithm generates an optimal solution.