Library prosa.model.priority.rate_monotonic

Rate-Monotonic Fixed-Priority Policy

We define the notion of rate-monotonic task priorities for sporadic tasks, i.e., the classic FP policy in which sporadic tasks are prioritized in order of their minimum inter-arrival times (or periods).
In this section, we prove a few basic properties of the RM policy.
Section Properties.

Consider sporadic tasks...
  Context {Task : TaskType}.
  Context `{SporadicModel Task}.

...and jobs stemming from these tasks.
  Context {Job : JobType}.
  Context `{JobTask Job Task}.

RM is reflexive.
  Lemma RM_is_reflexive : reflexive_task_priorities (RM Task).
  Proof. by move⇒ ?; rewrite /hep_task /RM. Qed.

RM is transitive.
  Lemma RM_is_transitive : transitive_task_priorities (RM Task).
  Proof. by move⇒ ? ? ?; apply: leq_trans. Qed.

RM is total.
  Lemma RM_is_total : total_task_priorities (RM Task).
  Proof. by move⇒ ? ?; apply: leq_total. Qed.

End Properties.

We add the above lemmas into a "Hint Database" basic_rt_facts, so Coq will be able to apply them automatically.
Global Hint Resolve
  : basic_rt_facts.