Library rt.model.schedule.global.basic.interference_edf

Require Import rt.util.all.
Require Import rt.model.arrival.basic.task rt.model.arrival.basic.job rt.model.priority rt.model.arrival.basic.task_arrival.
Require Import rt.model.schedule.global.basic.schedule rt.model.schedule.global.basic.interference
               rt.model.schedule.global.basic.platform.

Module InterferenceEDF.

  Import Schedule Priority Platform Interference Priority.

  Section Lemmas.

    Context {Job: eqType}.
    Variable job_arrival: Job → time.
    Variable job_cost: Job → time.
    Variable job_deadline: Job → time.

    (* Assume any job arrival sequence... *)
    Context {arr_seq: arrival_sequence Job}.

    (* Consider any schedule. *)
    Variable num_cpus: nat.
    Variable sched: schedule Job num_cpus.

    (* Assume that the schedule satisfies the global scheduling invariant
       for EDF, i.e., if any job of tsk is backlogged, every processor
       must be busy with jobs with no larger absolute deadline. *)
    Hypothesis H_scheduler_uses_EDF:
      respects_JLFP_policy job_arrival job_cost arr_seq sched (EDF job_arrival job_deadline).

    (* Under EDF scheduling, a job only causes interference if its deadline
       is not larger than the deadline of the analyzed job. *)
    Lemma interference_under_edf_implies_shorter_deadlines :
      ∀ j j' t1 t2,
        arrives_in arr_seq j →
        arrives_in arr_seq j' →
        job_interference job_arrival job_cost sched j' j t1 t2 != 0 →
        job_arrival j + job_deadline j ≤ job_arrival j' + job_deadline j'.

  End Lemmas.

End InterferenceEDF.