Online scheduling of splittable tasks

We consider online scheduling of splittable tasks on parallel machines, where the goal is to minimize the last completion time (the makespan). In our model, each task can be split into a limited number of parts, that can then be scheduled independently and in parallel. We consider both the case where the machines are identical and the case where some subset of the machines have a (fixed) higher speed than the others. We design a class of algorithms that allows us to give tight bounds for a large class of cases where tasks may be split into relatively many parts. For identical machines, we also improve upon the natural greedy algorithm in other classes of cases.