Library rt.model.schedule.uni.basic.platform_tdma
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
rt.model.schedule.uni.schedule.
Require Import rt.model.policy_tdma.
Module Platform_TDMA.
Import Job UniprocessorSchedule div.
Export PolicyTDMA.
(* In this section, we define properties of the processor platform for TDMA. *)
Section Properties.
Context {sporadic_task: eqType}.
Context {Job: eqType}.
Variable job_arrival: Job → time.
Variable job_cost: Job → time.
Variable job_deadline: Job → time.
Variable job_task: Job → sporadic_task.
(* Consider any job arrival sequence... *)
Variable arr_seq: arrival_sequence Job.
(* ..., any uniprocessor... *)
Variable sched: schedule Job.
(* ... and any sporadic task set. *)
Variable ts: {set sporadic_task}.
(* Consider any TDMA slot assignment... *)
Variable time_slot: TDMA_slot sporadic_task.
(* ... and any slot order. *)
Variable slot_order: TDMA_slot_order sporadic_task.
(* In order to characterize a TDMA policy, we first define whether a job is executing its TDMA slot at time t. *)
Let job_in_time_slot (job:Job) (t:instant):=
Task_in_time_slot ts slot_order (job_task job) time_slot t.
(* We say that a TDMA policy is respected by the schedule iff
1. when a job is scheduled at time t, then the corresponding task
is also in its own time slot... *)
Definition sched_implies_in_slot j t:=
(scheduled_at sched j t → job_in_time_slot j t).
(* 2. when a job is backlogged at time t,the corresponding task
isn't in its own time slot or another previous job of the same task is scheduled *)
Definition backlogged_implies_not_in_slot_or_other_job_sched j t:=
(backlogged job_arrival job_cost sched j t →
¬ job_in_time_slot j t ∨
(∃ j_other, arrives_in arr_seq j_other∧
job_arrival j_other < job_arrival j∧
job_task j = job_task j_other∧
scheduled_at sched j_other t)).
Definition Respects_TDMA_policy:=
∀ (j:Job) (t:time),
arrives_in arr_seq j →
sched_implies_in_slot j t ∧ backlogged_implies_not_in_slot_or_other_job_sched j t.
End Properties.
End Platform_TDMA.
Require Import rt.model.arrival.basic.task
rt.model.arrival.basic.job rt.model.priority
rt.model.arrival.basic.task_arrival
rt.model.schedule.uni.schedule.
Require Import rt.model.policy_tdma.
Module Platform_TDMA.
Import Job UniprocessorSchedule div.
Export PolicyTDMA.
(* In this section, we define properties of the processor platform for TDMA. *)
Section Properties.
Context {sporadic_task: eqType}.
Context {Job: eqType}.
Variable job_arrival: Job → time.
Variable job_cost: Job → time.
Variable job_deadline: Job → time.
Variable job_task: Job → sporadic_task.
(* Consider any job arrival sequence... *)
Variable arr_seq: arrival_sequence Job.
(* ..., any uniprocessor... *)
Variable sched: schedule Job.
(* ... and any sporadic task set. *)
Variable ts: {set sporadic_task}.
(* Consider any TDMA slot assignment... *)
Variable time_slot: TDMA_slot sporadic_task.
(* ... and any slot order. *)
Variable slot_order: TDMA_slot_order sporadic_task.
(* In order to characterize a TDMA policy, we first define whether a job is executing its TDMA slot at time t. *)
Let job_in_time_slot (job:Job) (t:instant):=
Task_in_time_slot ts slot_order (job_task job) time_slot t.
(* We say that a TDMA policy is respected by the schedule iff
1. when a job is scheduled at time t, then the corresponding task
is also in its own time slot... *)
Definition sched_implies_in_slot j t:=
(scheduled_at sched j t → job_in_time_slot j t).
(* 2. when a job is backlogged at time t,the corresponding task
isn't in its own time slot or another previous job of the same task is scheduled *)
Definition backlogged_implies_not_in_slot_or_other_job_sched j t:=
(backlogged job_arrival job_cost sched j t →
¬ job_in_time_slot j t ∨
(∃ j_other, arrives_in arr_seq j_other∧
job_arrival j_other < job_arrival j∧
job_task j = job_task j_other∧
scheduled_at sched j_other t)).
Definition Respects_TDMA_policy:=
∀ (j:Job) (t:time),
arrives_in arr_seq j →
sched_implies_in_slot j t ∧ backlogged_implies_not_in_slot_or_other_job_sched j t.
End Properties.
End Platform_TDMA.