# Library prosa.model.priority.rate_monotonic

Require Export prosa.model.priority.classes.
Require Export prosa.model.task.arrival.sporadic.

# 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).
#[export] Instance RM (Task : TaskType) `{SporadicModel Task} : FP_policy Task :=
{
hep_task (tsk1 tsk2 : Task) := task_min_inter_arrival_time tsk1 ≤ task_min_inter_arrival_time tsk2
}.
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
RM_is_reflexive
RM_is_transitive
RM_is_total
: basic_rt_facts.