# Library prosa.model.readiness.jitter

Require Export prosa.behavior.all.
Require Import prosa.util.nat.

# Job Model Parameter for Jobs Exhibiting Release Jitter

If a job exhibits release jitter, it is not immediately available for execution upon arrival, and can be scheduled only after its release, which occurs some (bounded) time after its arrival. We model this with the job_jitter parameter, which maps each job to its jitter duration.
Class JobJitter (Job : JobType) := { job_jitter : Job → duration }.

# Readiness of Jobs with Release Jitter

Based on the job model's jitter parameter, we define the readiness predicate for jogs with release jitter (and no self-suspensions).
Section ReadinessOfJitteryJobs.
Consider any kind of jobs...
Context {Job : JobType}.
... and any kind of processor state.
Context {PState : ProcessorState Job}.
Suppose jobs have an arrival time, a cost, and exhibit release jitter.
Context `{JobArrival Job} `{JobCost Job} `{JobJitter Job}.
We say that a job is released at a time t 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.
Based on the predicate is_released, it is easy to state the notion of readiness for jobs subject to release jitter: a job is ready only if it is released and not yet complete.
#[local,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⇒ sched j t /andP[REL UNFINISHED].
rewrite /pending. apply /andP. split ⇒ //.
move: REL. rewrite /is_released /has_arrived.
by apply: leq_trans; rewrite leq_addr.
Qed.
End ReadinessOfJitteryJobs.