Probabilistic Analysis of the Optimal Efficiency of the Multi-Level Dynamic Load Balancing Scheme

This paper investigates the optimal efficiency of the multi-level dynamic load balancing scheme for ORparallel programs, using probability theory. In the single-level dynamic load balancing scheme, one processor divides a given task into a number of subtasks, which are distributed to other processors on demand and then executed independently. We introduce a formal model of the execution as a queuing system with several servers. And we investigate the optimal granularity of the subtasks to attain the maximal efficiency, taking account of dividing costs and load imbalance between the processors. Thus we obtain estimates of the maximal efficiency. We then apply these results to analysis of the efficiency of the multi-level dynamic load balancing scheme, which is the iterated application of the singlelevel scheme in a hierarchical manner. And we show how the scalability is thereby improved over the singlelevel scheme.