Analysis of Real-Time Scheduling Problems by Single Step and Maximal Step Semantics for Time Petri Net Models

One of the most intricate problem in the synthesis of hard real-time systems is the scheduling. There are two general approaches for scheduling tasks in real-time systems: runtime or pre-runtime scheduling. However, there are situations where the runtime approach does not find a feasible schedule even if such a schedule exists. This situation generally occurs when the task model imposes arbitrary intertask relations, such as precedence and exclusion relations. However, finding a feasible schedule is not trivial, because this problem is NP-Hard in its general form. The approach proposed in this paper models real-time systems using time Petri nets, and finds a pre-runtime scheduling, provided that one exists, using a depth-first search method adopting two kinds of firing rules: single and maximal step semantics. The main aim of this paper is to compare both semantics in the context of embedded hard real-time pre-runtime scheduling.