Optimal Scheduling of Periodic Gang Tasks

The gang scheduling of parallel implicit-deadline periodic task systems upon identical multiprocessor platforms is considered. In this scheduling problem, parallel tasks use several processors simultaneously. We propose two DPFAIR (deadline partitioning) algorithms that schedule all jobs in every interval of time delimited by two subsequent deadlines. These algorithms define a static schedule pattern that is stretched at run-time in every interval of the DPFAIR schedule. The first algorithm is based on linear programming and is the first one to be proved  optimal for the considered gang scheduling problem. Furthermore, it runs in polynomial time for a fixed number m of processors and an efficient implementation is fully detailed. The second algorithm is an approximation algorithm based on a fixed-priority rule that is competitive under resource augmentation analysis in order to compute an optimal schedule pattern. Precisely, its speedup factor is bounded by (2-1/m). Both algorithms are also evaluated through intensive numerical experiments.