Library prosa.classic.implementation.uni.jitter.fp_rta_example

Require Import prosa.classic.util.all.
Require Import prosa.classic.model.priority.
Require Import prosa.classic.model.arrival.basic.task.
Require Import prosa.classic.model.schedule.uni.schedulability.
Require Import prosa.classic.model.arrival.jitter.job.
Require Import prosa.classic.model.schedule.uni.jitter.schedule.
Require Import prosa.classic.analysis.uni.jitter.workload_bound_fp
               prosa.classic.analysis.uni.jitter.fp_rta_comp.
Require Import prosa.classic.implementation.uni.jitter.job
               prosa.classic.implementation.uni.jitter.task
               prosa.classic.implementation.uni.jitter.arrival_sequence
               prosa.classic.implementation.uni.jitter.schedule.
From mathcomp Require Import ssreflect ssrbool ssrnat eqtype seq bigop div.

Module ResponseTimeAnalysisFP.

  Import JobWithJitter UniprocessorScheduleWithJitter SporadicTaskset Priority Schedulability
         WorkloadBoundFP ResponseTimeIterationFP.
  Import ConcreteJob ConcreteTask ConcreteArrivalSequence ConcreteScheduler.

  Section ExampleRTA.

    Let tsk1 := {| task_id := 1; task_cost := 1; task_period := 5;
                                 task_deadline := 6; task_jitter := 1 |}.
    Let tsk2 := {| task_id := 2; task_cost := 1; task_period := 5;
                                 task_deadline := 6; task_jitter := 0|}.
    Let tsk3 := {| task_id := 3; task_cost := 1; task_period := 6;
                                 task_deadline := 6; task_jitter := 1|}.

    Program Let ts := Build_set [:: tsk1; tsk2; tsk3] _.

    Remark ts_has_positive_costs:
      ∀ tsk, tsk \in ts → task_cost tsk > 0.
    Remark ts_has_positive_periods:
      ∀ tsk, tsk \in ts → task_period tsk > 0.

    Let RTA_claimed_bounds :=
      fp_claimed_bounds task_cost task_period task_deadline task_jitter (RM task_period).
    Let schedulability_test :=
      fp_schedulable task_cost task_period task_deadline task_jitter (RM task_period).

    Fact RTA_yields_these_bounds :
      RTA_claimed_bounds ts = Some [:: (tsk1, 2); (tsk2, 2); (tsk3, 3)].

    Fact schedulability_test_succeeds :
      schedulability_test ts = true.


    Let arr_seq := periodic_arrival_sequence ts.

    Let higher_eq_priority := FP_to_JLDP job_task (RM task_period).

     Variable job_jitter: concrete_job → time.
     Hypothesis H_jitter_is_bounded:
       ∀ j,
         arrives_in arr_seq j →
         job_jitter_leq_task_jitter task_jitter job_jitter job_task j.

    Let sched := scheduler job_arrival job_cost job_jitter arr_seq higher_eq_priority.

    Let no_deadline_missed_by :=
      task_misses_no_deadline job_arrival job_cost job_deadline job_task arr_seq sched.

    Corollary ts_is_schedulable:
      ∀ tsk,
        tsk \in ts →
        no_deadline_missed_by tsk.

  End ExampleRTA.

End ResponseTimeAnalysisFP.