Average-Case Performance Analysis of Online Non-clairvoyant Scheduling of Parallel Tasks with Precedence Constraints

We evaluate the average-case performance of three approximation algorithms for online non-clairvoyant scheduling of parallel tasks with precedence constraints. We show that for a class of wide task graphs, when task sizes are uniformly distributed in the range [1..C], the online non-clairvoyant scheduling algorithm LL-SIMPLE has an asymptotic average-case performance bound of M/(M-(3-(1+1/C)^C+1)C-1), where M is the number of processors. For arbitrary probability distributions of task sizes, we present numerical and simulation data to demonstrate the accuracy of our general asymptotic average-case performance bound. We also report extensive experimental results on the average-case performance of online non-clairvoyant scheduling algorithms LL-GREEDY and LS. Algorithm LL-GREEDY has better performance than LL-SIMPLE by using an improved algorithm to schedule independent tasks in the same level. Algorithm LS produces even better schedules due to break of boundaries among levels.