Library prosa.classic.analysis.apa.interference_bound

Require Import prosa.classic.util.all.
Require Import prosa.classic.model.schedule.global.basic.schedule.
Require Import prosa.classic.analysis.apa.workload_bound.
From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq fintype bigop.

Module InterferenceBoundGeneric.

  Section Definitions.

    Import Schedule WorkloadBound.

    Context {sporadic_task: eqType}.
    Variable task_cost: sporadic_task → time.
    Variable task_period: sporadic_task → time.
    Variable task_deadline: sporadic_task → time.

    Variable num_cpus: nat.

    (* Let tsk be the task to be analyzed. *)
    Variable tsk: sporadic_task.

    Let task_with_response_time := (sporadic_task × time)%type.

    (* Assume a known response-time bound for each interfering task ... *)
    Variable R_prev: seq task_with_response_time.

    (* ... and an interval length delta. *)
    Variable delta: time.

    Section PerTask.

      Variable tsk_R: task_with_response_time.
      Let tsk_other := fst tsk_R.
      Let R_other := snd tsk_R.

      (* Based on the workload bound, Bertogna and Cirinei define the
         following interference bound for a task. *)
      Definition interference_bound_generic :=
        minn (W task_cost task_period tsk_other R_other delta) (delta - (task_cost tsk) + 1).

    End PerTask.

  End Definitions.

End InterferenceBoundGeneric.