Skip to content
GitLab
Menu
Projects
Groups
Snippets
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Menu
Open sidebar
Marco Maida
PROSA  Formally Proven Schedulability Analysis
Commits
f9c453b8
Commit
f9c453b8
authored
Jan 14, 2016
by
Felipe Cerqueira
Browse files
Fix small issues with naming
parent
32197425
Changes
1
Hide whitespace changes
Inline
Sidebyside
interference_bound_edf.v
View file @
f9c453b8
...
...
@@ 151,15 +151,15 @@ Module EDFSpecificBound.
Let
p_k
:
=
task_period
tsk_k
.
Let
n_k
:
=
div_floor
D_i
p_k
.
(* Let's give a simpler name to job interference. *)
Let
interference_caused_by
:
=
job_interference
job_cost
sched
j_i
.
(* Identify the subset of jobs that actually cause interference *)
Let
interfering_jobs
:
=
filter
(
fun
(
x
:
JobIn
arr_seq
)
=>
(
job_task
x
==
tsk_k
)
&&
(
job_
interference
job_cost
sched
j_i
x
t1
t2
!=
0
))
(
job_task
x
==
tsk_k
)
&&
(
interference
_caused_by
x
t1
t2
!=
0
))
(
jobs_scheduled_between
sched
t1
t2
).
(* Let's give a simpler name to job interference. *)
Let
interference_caused_by
:
=
job_interference
job_cost
sched
j_i
.
(* Now, consider the list of interfering jobs sorted by arrival time. *)
Let
order
:
=
fun
(
x
y
:
JobIn
arr_seq
)
=>
job_arrival
x
<=
job_arrival
y
.
...
...
@@ 188,7 +188,7 @@ Module EDFSpecificBound.
rewrite
big_mkcond
;
rewrite
[
\
sum_
(
_
<
_

_
)
_
]
big_mkcond
/=.
apply
eq_bigr
;
intros
i
_;
clear

i
.
destruct
(
job_task
i
==
tsk_k
)
;
rewrite
?andTb
?andFb
;
last
by
done
.
destruct
(
job_
interference
job_cost
sched
j_i
i
t1
t2
!=
0
)
eqn
:
DIFF
;
first
by
done
.
destruct
(
interference
_caused_by
i
t1
t2
!=
0
)
eqn
:
DIFF
;
first
by
done
.
by
apply
negbT
in
DIFF
;
rewrite
negbK
in
DIFF
;
apply
/
eqP
.
Qed
.
...
...
@@ 235,11 +235,12 @@ Module EDFSpecificBound.
(* Also, for any job of task tsk_k, the interference is bounded by the task cost. *)
Lemma
interference_bound_edf_interference_le_task_cost
:
forall
j
(
INi
:
j
\
in
interfering_jobs
),
forall
j
,
j
\
in
interfering_jobs
>
interference_caused_by
j
t1
t2
<=
task_cost
tsk_k
.
Proof
.
rename
H_valid_job_parameters
into
PARAMS
.
intros
j
;
rewrite
mem_filter
;
move
=>
/
andP
[/
andP
[/
eqP
JOBj
_
]
_
].
intros
j
INi
;
rewrite
mem_filter
;
move
=>
/
andP
[/
andP
[/
eqP
JOBj
_
]
_
].
specialize
(
PARAMS
j
)
;
des
.
apply
leq_trans
with
(
n
:
=
service_during
sched
j
t1
t2
)
;
first
by
apply
job_interference_le_service
.
...
...
@@ 381,7 +382,7 @@ Module EDFSpecificBound.
End
FactsAboutFirstJob
.
(* Now, let's prove the interference bound for the particular case of a single job.
This case must be solved separately because the single job can s
y
multaneously
This case must be solved separately because the single job can s
i
multaneously
be carryin and carryout job, so its response time is not necessarily
bounded by R_k (from the hypothesis H_all_previous_jobs_completed_on_time). *)
Section
InterferenceSingleJob
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment