Library prosa.model.priority.deadline_monotonic

Require Export prosa.model.priority.classes.

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.

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_priorities.
Proof. by move⇒ ?; rewrite /hep_job_at /JLFP_to_JLDP /hep_job /FP_to_JLFP /hep_task /DM. Qed.

DM is transitive.

Lemma DM_is_transitive : transitive_priorities.
Proof. by intros t y x z; apply leq_trans. Qed.

DM is total.

Lemma DM_is_total : total_priorities.
Proof. by move⇒ t j1 j2; apply leq_total. Qed.

End Properties.

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

Hint Resolve
     DM_is_reflexive
     DM_is_transitive
     DM_is_total
  : basic_facts.