Probabilistic Runtime Guarantees for Statically Scheduled Taskgraphs with Stochastic Task Runtimes

Abstract

Tasks with stochastic runtimes and dependencies are frequently met in multicore applications, but static schedulers need deterministic task runtimes as input. We first demonstrate by scheduling experiments that both for binomially and geometrically distributed task runtimes, which are often found in taskgraphs, choice of average task runtime as scheduler input is sufficient to obtain schedules with good average makespan, i.e. that inserting runtime buffers depending on the standard deviation of task runtimes is not helpful in the majority of cases. Furthermore, we compute discretized makespan distributions for schedules with binomially and geometrically distributed runtimes as frequently occuring distributions. Thus, applications where probabilistic makespan guarantees with quantiles (vs. worst case execution times) are usable can profit from our analysis by starting with sampling their makespan distribution to approximate mean and standard deviation, and using our tool to compute the makespan distribution. As a side effect, we see that the rule of thumb “makespan is below average plus three (one) standard deviations in 99% of cases for binomially (geometrically) distributed runtimes” still apply, although makespans are not binomially or geometrically distributed but exhibit heavy tails. We also show how to mathematically derive makespan distribution for taskgraphs with stochastic task runtimes for different distributions, if stronger guarantees are needed.