Periodic - aperiodic jobs scheduling on a single machine environment

Many control applications require both types of processes, periodic and aperiodic, which differ for their criticality. Periodic jobs usually have hard deadlines whereas aperiodic jobs usually have soft deadlines or no deadlines at all. In this paper we study the scheduling problem on a single machine environment in presence of both periodic and aperiodic jobs. The objective is to find a schedule with minimum of the makespan of the aperiodic jobs while respecting the time constraints of all periodic jobs. We first prove that the problem is NP-Hard and then propose a heuristic algorithm which evolves from classical LPT (Longest Processing Time) order. The performance of the proposed algorithm will be shown with experimental results.