STATIC ASSIGNMENT OF STOCHASTIC TASKS USING MAJORIZATION

We consider the problem of statically assigning many tasks to a (small er) system of homogeneous processors, where a task's structure is mode led as a branching process, all tasks are assumed to have identical be havior, and the tasks may synchronize frequently. We show how the theo ry of majorization can be used to obtain a partial order among possibl e task assignments. We show that if the vector of numbers of tasks ass igned to each processor under one mapping is majorized by that of anot her mapping, then the former mapping is better than the latter with re spect to a large number of objective functions. In particular, we show how the metrics of finishing time, the space-time product, and reliab ility are all captured. We also apply majorization to the problem of p artitioning a pool of processors for distribution among parallelizable tasks. Limitations of the approach, which include the static nature o f the assignment, are also discussed.