Library prosa.model.priority.deadline_monotonic

Deadline-Monotonic Fixed-Priority Policy

We define the notion of deadline-monotonic task priorities, i.e., the classic FP policy in which tasks are prioritized in order of their relative deadlines.
#[export] Instance DM (Task : TaskType) `{TaskDeadline Task} : FP_policy Task :=
  hep_task (tsk1 tsk2 : Task) := task_deadline tsk1 task_deadline tsk2

In this section, we prove a few basic properties of the DM policy.
Section Properties.

Consider any kind of tasks with relative deadlines...
  Context {Task : TaskType}.
  Context `{TaskDeadline Task}.

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

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

DM is transitive.
  Lemma DM_is_transitive : transitive_task_priorities (DM Task).
  Proof. by movet y x z; apply: leq_trans. Qed.

DM is total.
  Lemma DM_is_total : total_task_priorities (DM 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.