Library prosa.implementation.priority.edf

Require Export prosa.model.priority.edf.

EDF Priority Policy

We introduce the classic EDF priority policy, under which jobs are scheduled in order of their urgency, i.e., jobs are ordered according to their absolute deadlines. The EDF policy belongs to the class of JLFP policies.

#[local] Instance EDF (Job : JobType) `{JobDeadline Job} : JLFP_policy Job :=
{
hep_job (j1 j2 : Job) := job_deadline j1 ≤ job_deadline j2
}.

In this section, we prove a few properties about EDF policy.

Section PropertiesOfEDF.

Consider any type of jobs with deadlines.

Context {Job : JobType}.
Context `{JobDeadline Job}.

Consider any arrival sequence.

Variable arr_seq : arrival_sequence Job.

Under the concrete EDF implementation, hep_job is exactly deadline order.

  Fact EDF_hep_job :
    ∀ j1 j2,
      @hep_job Job (EDF Job) j1 j2
      = (job_deadline j1 ≤ job_deadline j2 ).
  Proof. by []. Qed.

EDF is reflexive.

Fact EDF_is_reflexive : reflexive_job_priorities (EDF Job).
Proof. by move⇒ j; apply:leqnn. Qed.

EDF is transitive.

Fact EDF_is_transitive : transitive_job_priorities (EDF Job).
Proof. by move⇒ y x z; apply: leq_trans. Qed.

EDF is total.

Fact EDF_is_total : total_job_priorities (EDF Job).
Proof. by move⇒ j1 j2; apply: leq_total. Qed.

The concrete EDF implementation is indeed an EDF policy.

  Fact EDF_is_EDF_policy :
    policy_is_EDF (EDF Job).
  Proof.
    repeat split.
    - by move⇒ j1 j2; rewrite EDF_hep_job.
    - exact: EDF_is_reflexive.
    - exact: EDF_is_transitive.
    - exact: EDF_is_total.
  Qed.

End PropertiesOfEDF.

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

Global Hint Resolve
     EDF_is_EDF_policy
     EDF_is_reflexive
     EDF_is_transitive
     EDF_is_total
  : basic_rt_facts.