Require Import prosa.classic.util.all.
Require Import prosa.classic.model.arrival.basic.arrival_sequence prosa.classic.model.priority.
Require Import
Require Import
From mathcomp Require Import ssreflect ssrbool eqtype ssrnat seq fintype bigop.

Module InterferenceBoundJitter.

  Import ArrivalSequence WorkloadBoundJitter Priority Interference.

  Section Definitions.

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

    (* 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_jitter task_cost task_period task_jitter tsk_other R_other delta)
             (delta - task_cost tsk + 1).

    End PerTask.

  End Definitions.

End InterferenceBoundJitter.