(m,k)-firm constraints and DBP: counter-intuitive phenomena and exact feasibility 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 (counter-intuitive) phenomena: (i) choosing, for each task, the initial k -sequence 1k is not optimal, (ii) even less intuitive, but not contradictory, 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 DBP-schedule is periodic and we upper-bound the length of that period. Lastly, based on our periodicity result we provide an exact feasibility test.