Low-cost static performance prediction of parallel stochastic task compositions

Current analytic solutions to the execution time distribution of a parallel composition of tasks having stochastic execution times are computationally complex, except for a limited number of distributions. In this paper, we present an analytical solution based on approximating execution time distributions in terms of the first four statistical moments. This low-cost approach allows the parallel execution time distribution to be approximated at ultra-low solution complexity for a wide range of execution time distributions. The accuracy of our method is experimentally evaluated for synthetic distributions as well as for task execution time distributions found in real parallel programs and kernels (NAS-EP, SSSP, APSP, Splash2-Barnes, PSRS, and WATOR). Our experiments show that the prediction error of the mean value of the parallel execution time for N-ary parallel composition is in the order of percents, provided the task execution time distributions are sufficiently independent and unimodal.