Library prosa.classic.implementation.global.parallel.bertogna_fp_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.global.schedulability.
Require Import prosa.classic.model.schedule.global.basic.schedule prosa.classic.model.schedule.global.basic.platform
               prosa.classic.model.schedule.global.basic.interference.
Require Import prosa.classic.analysis.global.parallel.workload_bound
               prosa.classic.analysis.global.parallel.interference_bound_fp
               prosa.classic.analysis.global.parallel.bertogna_fp_comp.
Require Import prosa.classic.implementation.job prosa.classic.implementation.task
               prosa.classic.implementation.arrival_sequence.
Require Import prosa.classic.implementation.global.basic.schedule. From mathcomp Require Import ssreflect ssrbool ssrnat eqtype seq bigop div.

Module ResponseTimeAnalysisFP.

  Import Job Schedule SporadicTaskset Priority Schedulability Platform
         Interference InterferenceBoundFP WorkloadBound
         ResponseTimeIterationFP.
  Import ConcreteJob ConcreteTask ConcreteArrivalSequence ConcreteScheduler.

  Section ExampleRTA.

    Let tsk1 := {| task_id := 1; task_cost := 2; task_period := 6; task_deadline := 6|}.
    Let tsk2 := {| task_id := 2; task_cost := 3; task_period := 8; task_deadline := 6|}.
    Let tsk3 := {| task_id := 3; task_cost := 2; task_period := 12; task_deadline := 12|}.

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

    Section FactsAboutTaskset.

      Fact ts_has_valid_parameters:
        valid_sporadic_taskset task_cost task_period task_deadline ts.

      Fact ts_has_constrained_deadlines:
        ∀ tsk,
          tsk \in ts →
          task_deadline tsk ≤ task_period tsk.

    End FactsAboutTaskset.

    Let num_cpus := 2.

    Let schedulability_test :=
      fp_schedulable task_cost task_period task_deadline num_cpus.

    Fact schedulability_test_succeeds :
      schedulability_test ts = true.

    Let arr_seq := periodic_arrival_sequence ts.

    Let higher_priority := FP_to_JLDP job_task (RM task_period).

    Section FactsAboutPriorityOrder.

      Lemma ts_has_unique_priorities :
        FP_is_antisymmetric_over_task_set (RM task_period) ts.

      Lemma priority_is_total :
        FP_is_total_over_task_set (RM task_period) ts.

    End FactsAboutPriorityOrder.

    Let sched := scheduler job_arrival job_cost num_cpus arr_seq higher_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.