Library prosa.classic.implementation.uni.susp.dynamic.oblivious.fp_rta_example

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

Module ResponseTimeAnalysisFP.

  Import Job UniprocessorSchedule SporadicTaskset Priority Schedulability
         SuspensionIntervals SuspensionObliviousFP WorkloadBoundFP.
  Import ConcreteJob ConcreteTask ConcreteArrivalSequence ConcreteScheduler.

  Section ExampleRTA.

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

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

    Fact ts_has_valid_parameters:
      valid_sporadic_taskset task_cost task_period task_deadline ts.

    Let inflated_cost := inflated_task_cost task_cost task_suspension_bound.

    Fact inflated_cost_le_deadline_and_period:
      ∀ tsk,
        tsk \in ts →
          inflated_cost tsk ≤ task_deadline tsk ∧
          inflated_cost tsk ≤ task_period tsk.

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

    Fact RTA_yields_these_bounds :
      RTA_claimed_bounds ts = Some [:: (tsk1, 3); (tsk2, 3); (tsk3, 5)].

    Fact schedulability_test_succeeds :
      schedulability_test ts = true.


    Let arr_seq := periodic_arrival_sequence ts.

     Variable next_suspension: job_suspension concrete_job_eqType.
     Hypothesis H_dynamic_suspensions:
       dynamic_suspension_model job_cost job_task next_suspension task_suspension_bound.

    Let higher_eq_priority := FP_to_JLDP job_task (RM task_period).

    Let sched := scheduler job_arrival job_cost arr_seq next_suspension 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.