An expanded stochastic model in DAG schemes

Previously, the second order moment of computation and communication times was taken into account in addition to their means in stochastic DAG schemes, in which the variation of computation and communication time caused by the heterogeneous distributed computing environment was considered. However, it is not optimal to consider only the variation caused by heterogeneous distributed computing environment. In this paper, it is proposed that the data placement policies of parallel program can also induce the variation of computation and communication time, and an expanded stochastic DAG is presented, in which the heterogeneity and the data placement policies of parallel program are considered together. Through the theoretic discursion of two matrix multiplying algorithms and experiments based on these two algorithms, the expanded definition has been validated. And the experiment results have been shown that a significant improvement in the parallel execution time of the expanded stochastic DAG can be achieved by optimizing the parallel algorithm, modifying the data placement policies and considering the heterogeneous environment.