Commit bffcc219 authored by Björn Brandenburg's avatar Björn Brandenburg

note two simple facts about job deadlines

parent 8e762b51
......@@ -3,3 +3,4 @@ Require Export rt.restructuring.behavior.facts.completion.
Require Export rt.restructuring.behavior.facts.ideal_schedule.
Require Export rt.restructuring.behavior.facts.sequential.
Require Export rt.restructuring.behavior.facts.arrivals.
Require Export rt.restructuring.behavior.facts.deadlines.
From rt.restructuring.behavior Require Export schedule facts.service facts.completion.
(** In this file, we observe basic properties of the behavioral job
model w.r.t. deadlines. *)
Section DeadlineFacts.
(* Consider any given type of jobs with costs and deadlines... *)
Context {Job : JobType} `{JobCost Job} `{JobDeadline Job}.
(* ... any given type of processor states. *)
Context {PState: eqType}.
Context `{ProcessorState Job PState}.
(** We begin with schedules / processor models in which scheduled jobs
always receive service. *)
Section IdealProgressSchedules.
(* Consider a given reference schedule... *)
Variable sched: schedule PState.
(* ...in which complete jobs don't execute... *)
Hypothesis H_completed_jobs: completed_jobs_dont_execute sched.
(* ...and scheduled jobs always receive service. *)
Hypothesis H_scheduled_implies_serviced: ideal_progress_proc_model.
(* We observe that, if a job is known to meet its deadline, then
its deadline must be later than any point at which it is
scheduled. That is, if a job that meets its deadline is
scheduled at time t, we may conclude that its deadline is at a
time later than t. *)
Lemma scheduled_at_implies_later_deadline:
forall j t,
job_meets_deadline sched j ->
scheduled_at sched j t ->
t < job_deadline j.
Proof.
move=> j t.
rewrite /job_meets_deadline => COMP SCHED.
case: (boolP (t < job_deadline j)) => //.
rewrite -leqNgt => AFTER_DL.
apply completion_monotonic with (t' := t) in COMP => //.
apply scheduled_implies_not_completed in SCHED => //.
move/negP in SCHED. contradiction.
Qed.
End IdealProgressSchedules.
(** In the following section, we observe that it is sufficient to
establish that service is invariant across two schedules at a
job's deadline to establish that it either meets its deadline in
both schedules or none. *)
Section EqualProgress.
(* Consider any two schedules [sched] and [sched']. *)
Variable sched sched': schedule PState.
(* We observe that, if the service is invariant at the time of a
job's absolute deadline, and if the job meets its deadline in one of the schedules,
then it meets its deadline also in the other schedule. *)
Lemma service_invariant_implies_deadline_met:
forall j,
service sched j (job_deadline j) = service sched' j (job_deadline j) ->
(job_meets_deadline sched j <-> job_meets_deadline sched' j).
Proof.
move=> j SERVICE.
split;
by rewrite /job_meets_deadline /completed_by -SERVICE.
Qed.
End EqualProgress.
End DeadlineFacts.
\ No newline at end of file
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