Non-preemptive multiprocessor static scheduling for systems with precedence and strict periodicity constraints

In this paper we propose a greedy heuristic to solve the non preemptive multiprocessor static scheduling problem with precedence and strict periodicity constraints. The system of periodic tasks is described by a graph where dependent tasks are connected by precedence constraints. First, each task is repeated within the LCM of all periods of tasks (hyper-period) allowing to unroll the graph over the hyper-period. We propose an algorithm adding some missing edges. Then, the tasks of the new graph are classified by their periods and assigned to the processors. Finally, we propose an extension of the SynDEx heuristic which already allocates and schedules tasks graph with precedence constraints, but tasks have the same period equal to the execution time of the complete graph. We apply this extended heuristic on the unrolled graph in order to allocate and schedule the periodic tasks onto the multiprocessor. We compute the complexity of the proposed heuristic, and perform a performance comparison which shows its effectiveness.