Commit bbefd14d authored by Maxime Lesourd's avatar Maxime Lesourd Committed by Björn Brandenburg

define preemptive work-conserving and priority-based schedules

Add model definitions for work-conserving and priority-based preemptive schedules.
parent d34bd413
From rt.restructuring.behavior Require Export schedule arrival_sequence.
From rt.restructuring.model Require Export priorities.
(* We now define what it means for a schedule to respect a priority *)
(* We only define it for a JLDP policy since the definitions for JLDP and JLFP are the same
and can be used through the conversions *)
Section Priority.
Context {Job: JobType} {Task: TaskType}.
Context `{JobCost Job} `{JobArrival Job}.
Context `{JLDP_policy Job}.
Variable arr_seq : arrival_sequence Job.
Context {PState : Type}.
Context `{ProcessorState Job PState}.
Variable sched : schedule PState.
Definition respects_preemptive_priorities :=
forall j j_hp t,
arrives_in arr_seq j ->
backlogged sched j t ->
scheduled_at sched j_hp t ->
hep_job_at t j_hp j.
End Priority.
From rt.restructuring.model Require Export task.
From rt.util Require Export list.
From mathcomp Require Export seq.
(* Definitions of FP, JLFP and JLDP priority relations. *)
(* In the following, "hep" means "higher or equal priority". We define an FP
policy as a relation among tasks, ... *)
Class FP_policy (Task: TaskType) := hep_task : rel Task.
(* ... a JLFP policy as a relation among jobs, a ... *)
Class JLFP_policy (Job: JobType) := hep_job : rel Job.
(* ... a JLDP policy as a relation among jobs that may vary over time. *)
Class JLDP_policy (Job: JobType) := hep_job_at : instant -> rel Job.
(* Since FP policies are also JLFP and JLDP policies, we define
conversions that express the generalization. *)
Instance FP_to_JLFP (Job: JobType) (Task: TaskType)
`{JobTask Job Task} `{FP_policy Task} : JLFP_policy Job :=
fun j1 j2 => hep_task (job_task j1) (job_task j2).
Instance JLFP_to_JLDP (Job: JobType) `{JLFP_policy Job} : JLDP_policy Job :=
fun _ j1 j2 => hep_job j1 j2.
Section Priorities.
Context {Job: eqType}.
Section JLDP.
(* Consider any JLDP policy. *)
Context `{JLDP_policy Job}.
(* We define common properties of the policy. Note that these definitions
can also be used for JLFP and FP policies *)
Definition reflexive_priorities := forall t, reflexive (hep_job_at t).
Definition transitive_priorities := forall t, transitive (hep_job_at t).
Definition total_priorities := forall t, total (hep_job_at t).
Section FP.
(* Consider any FP policy. *)
Context {Task : TaskType}.
Context `{FP_policy Task}.
(* We define whether the policy is antisymmetric over a taskset ts. *)
Definition antisymmetric_over_taskset (ts : seq Task) :=
antisymmetric_over_list hep_task ts.
End FP.
End Priorities.
From rt.restructuring.model Require Export schedule.tdma.
From rt.restructuring.model Require Export tdma.
From rt.util Require Import all.
(** In this section, we define the properties of TDMA and prove some basic lemmas. *)
From rt.restructuring.behavior Require Export schedule arrival_sequence.
(* In this file, we introduce a restrictive definition of work conserving
uniprocessor schedules. The definition is restrictive because it does not
allow for effects such as jitter or self-suspensions that affect whether a
job can be scheduled at a given point in time. A more general notion of work
conservation that is "readiness-aware", as well as a variant that covers
global scheduling, is TBD. *)
Section WorkConserving.
(* Consider any type of job associated with any type of tasks... *)
Context {Job: JobType}.
(* ... with arrival times and costs ... *)
Context `{JobArrival Job}.
Context `{JobCost Job}.
(* ... and any kind of processor state model. *)
Context {PState: Type}.
Context `{ProcessorState Job PState}.
(* Given an arrival sequence and a schedule ... *)
Variable arr_seq : arrival_sequence Job.
Variable sched: schedule PState.
(* We say that a scheduler is work-conserving iff whenever a job j
is backlogged, the processor is always busy with another job. *)
Definition work_conserving :=
forall j t,
arrives_in arr_seq j ->
backlogged sched j t ->
exists j_other, scheduled_at sched j_other t.
End WorkConserving.
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