Stochastic Prediction of Execution Time for Dynamic Bulk Synchronous Computations

We consider the problem of execution time prediction for non-deterministic multi-phase bulk synchronous computations in multiprocessors. We characterize the computations in two stochastic workload evolution models: additive and multiplicative. The additive model reflects the commutations in which the workload changes between phases are independent of processes' present workload. The multiplicative model becomes relevant when the workload change in a process is proportional to its load base. We take advantage of their salient features and show that conventional approaches based on central limit theorem in statistics are viable to predict the execution time for long run computations. By an elegant coordination of results from order statistics and convergence rates in the central limit theorem, we derive tighter bounds on execution time of short run computations, under some mild assumptions on their workload change distributions. Accuracy of the predictions is analyzed rigorously and verified by simulations.