Library rt.restructuring.model.readiness.jitter

From mathcomp Require Export ssreflect ssrnat ssrbool eqtype fintype bigop.
Require Export rt.restructuring.behavior.all.

Require Import rt.util.nat.

We define the readiness indicator function for models with release jitter (and no self-suspensions).
Definition of a generic type of release jitter parameter.
Class JobJitter (Job : JobType) := job_jitter : Job → duration.

Section ReadinessOfJitteryJobs.
Consider any kind of jobs...
  Context {Job : JobType}.

... and any kind of processor state.
  Context {PState : Type}.
  Context `{ProcessorState Job PState}.

Supose jobs have an arrival time, a cost, and a release jitter bound.
  Context `{JobArrival Job} `{JobCost Job} `{JobJitter Job}.

We say that a job is released at a time after its arrival if the job's release jitter has passed.
  Definition is_released (j : Job) (t : instant) := job_arrival j + job_jitter j ≤ t.

A job that experiences jitter is ready only when the jitter-induced delay has passed after its arrival and if it is not yet complete.
  Global Program Instance jitter_ready_instance : JobReady Job PState :=
    {
      job_ready sched j t := is_released j t && ~~ completed_by sched j t
    }.
  Next Obligation.
    move: H3 ⇒ /andP [REL UNFINISHED].
    rewrite /pending. apply /andP. split ⇒ //.
    move: REL. rewrite /is_released /has_arrived.
    by apply leq_addk.
  Defined.

End ReadinessOfJitteryJobs.