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(** * Sequential Readiness Model *)

(** In this module, we define the notion of sequential task readiness.
    This notion is similar to the classic Liu & Layland model without
    jitter or self-suspensions. However, an important difference is
    that in the sequential task readiness model only the earliest
    pending job of a task is ready. *)

Section SequentialTasksReadiness.

  (** Consider any type of job associated with any type of tasks... *)
  Context {Job : JobType}.
  Context {Task : TaskType}.
  Context `{JobTask Job Task}.
  Context `{JobArrival Job}.
  Context `{JobCost Job}.

  (** ... and any kind of processor state. *)
  Context {PState : ProcessorState Job}.

  (** Consider any job arrival sequence ... *)
  Variable arr_seq : arrival_sequence Job.

  (** A job [j] is ready at a time instant [t] iff all jobs from task
     [job_task j] that arrived earlier than job [j] are already
     completed by time [t]. *)
  #[local,program] Instance sequential_ready_instance : JobReady Job PState :=
  {
    job_ready sched j t := pending sched j t &&
                             prior_jobs_complete arr_seq sched j t
  }.
  
Job: JobType
Task: TaskType
H: JobTask Job Task
H0: JobArrival Job
H1: JobCost Job
PState: ProcessorState Job
arr_seq: arrival_sequence Job
sched: schedule PState
j: Job
t: instant
H2: pending sched j t &&
prior_jobs_complete arr_seq sched j t
pending sched j t
 by move: H2 => /andP[]. Qed.

End SequentialTasksReadiness.