Library prosa.analysis.facts.model.workload

Require Export prosa.model.aggregate.workload.
Require Export prosa.analysis.facts.behavior.arrivals.

Lemmas about Workload of Sets of Jobs

In this file, we establish basic facts about the workload of sets of jobs.
Section WorkloadFacts.

Consider any type of tasks ...
  Context {Task : TaskType}.
  Context `{TaskCost Task}.

... and any type of jobs associated with these tasks.
  Context {Job : JobType}.
  Context `{JobTask Job Task}.
  Context `{JobArrival Job}.
  Context `{JobCost Job}.

Consider any job arrival sequence.
  Variable arr_seq : arrival_sequence Job.

For simplicity, let's define a local name.
  Let arrivals_between := arrivals_between arr_seq.

We prove that workload can be split into two parts.
  Lemma workload_of_jobs_cat:
    ∀ t t1 t2 P,
      t1 ≤ t ≤ t2 →
      workload_of_jobs P (arrivals_between t1 t2) =
      workload_of_jobs P (arrivals_between t1 t)
      + workload_of_jobs P (arrivals_between t t2).
  Proof.
    move ⇒ t t1 t2 P /andP [GE LE].
    rewrite /workload_of_jobs /arrivals_between.
      by rewrite (arrivals_between_cat _ _ t) // big_cat.
  Qed.

End WorkloadFacts.