Dynamic Scheduling of Parallel Computations

Structures of parallel programs are usually modeled by task graphs in the scheduling literature. Such graphs are sometimes obtained while compiling the parallel programs. In many other cases, however, they can be determined only at run time. In this paper, we consider the scheduling of parallel computations whose task graphs are generated at run time. We analyze the case where the task graph has a random out-tree structure. When the number of offspring of a task has geometric distribution with a parameter which is decreasing and convex in the level, or the generation, then the breadth first policy stochastically minimizes the makespan. If, however, this parameter is increasing and concave, then the depth first policy stochastically minimizes the makespan.