Commit 0c43c153 authored by Björn Brandenburg's avatar Björn Brandenburg

define notion of job progress / lack of progress

parent 2e447612
Require Export rt.restructuring.analysis.facts.behavior.service.
(** * Job Progress (or Lack Thereof) *)
(** In the following section, we define a notion of "job progress", and
conversely a notion of a lack of progress. *)
Section Progress.
(** Consider any type of jobs with a known cost... *)
Context {Job : JobType}.
Context `{JobCost Job}.
(** ... and any kind of schedule. *)
Context {PState : Type}.
Context `{ProcessorState Job PState}.
(** For a given job and a given schedule... *)
Variable sched : schedule PState.
Variable j : Job.
Section NotionsOfProgress.
(** ...and two ordered points in time... *)
Variable t1 t2 : nat.
Hypothesis H_t1_before_t2: t1 <= t2.
(** ... we say that the job has progressed between the two points iff its
total received service has increased. *)
Definition job_has_progressed := service sched j t1 < service sched j t2.
(** Conversely, if the accumulated service does not change, there is no
progress. *)
Definition no_progress := service sched j t1 == service sched j t2.
(** We note that the negation of the former is equivalent to the latter
definition. *)
Lemma no_progress_equiv: ~~ job_has_progressed <-> no_progress.
Proof.
rewrite /job_has_progressed /no_progress.
split.
{ rewrite -leqNgt leq_eqVlt => /orP [EQ|LT]; first by rewrite eq_sym.
exfalso.
have MONO: service sched j t1 <= service sched j t2
by apply service_monotonic.
have NOT_MONO: ~~ (service sched j t1 <= service sched j t2)
by apply /negPf; apply ltn_geF.
move: NOT_MONO => /negP NOT_MONO.
contradiction. }
{ move => /eqP ->.
rewrite -leqNgt.
by apply service_monotonic. }
Qed.
End NotionsOfProgress.
(** For convenience, we define a lack of progress also in terms of given
reference point [t] and the length of the preceding interval of
inactivity [delta], meaning that no progress has been made for at least
[delta] time units. *)
Definition no_progress_for (t : instant) (delta : duration) := no_progress (t - delta) t.
End Progress.
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