(m,k)-firm constraints and DBP scheduling: impact of the initial k-sequence and exact schedulability test

In this paper we study the scheduling of (m, k)–firm synchronous periodic task systems using the Distance Based Priority (DBP) scheduler. We first show three phenomena: (i) choosing, for each task, the initial k-sequence 1k is not optimal, (ii) we can even start the scheduling from a (fictive) error state (in regard to the initial k-sequence) and (iii) the period of feasible DBP-schedules is not necessarily the task hyper-period. We then show that any feasible DBPschedule is periodic and we upper-bound the length of that period. Lastly, based on our periodicity result we provide an exact schedulability test.