From: tip-bot for Luca Abeni <tipbot@zytor.com>
To: linux-tip-commits@vger.kernel.org
Cc: torvalds@linux-foundation.org, mingo@kernel.org,
luca.abeni@unitn.it, tglx@linutronix.de, peterz@infradead.org,
linux-kernel@vger.kernel.org, hpa@zytor.com
Subject: [tip:sched/core] sched/dl/Documentation: Clarify indexing notation
Date: Tue, 19 May 2015 00:24:49 -0700 [thread overview]
Message-ID: <tip-c2a684930fce07f19d1a52d7bbe7474fe64fde31@git.kernel.org> (raw)
In-Reply-To: <1431954032-16473-6-git-send-email-luca.abeni@unitn.it>
Commit-ID: c2a684930fce07f19d1a52d7bbe7474fe64fde31
Gitweb: http://git.kernel.org/tip/c2a684930fce07f19d1a52d7bbe7474fe64fde31
Author: Luca Abeni <luca.abeni@unitn.it>
AuthorDate: Mon, 18 May 2015 15:00:28 +0200
Committer: Ingo Molnar <mingo@kernel.org>
CommitDate: Tue, 19 May 2015 08:39:20 +0200
sched/dl/Documentation: Clarify indexing notation
The "_i" index is used in this document to to denote a particular task,
so "sum_i", "max_i" and "min_i" might be confusing.
Signed-off-by: Luca Abeni <luca.abeni@unitn.it>
Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
Cc: Peter Zijlstra <peterz@infradead.org>
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: henrik@austad.us
Cc: juri.lelli@gmail.com
Cc: raistlin@linux.it
Link: http://lkml.kernel.org/r/1431954032-16473-6-git-send-email-luca.abeni@unitn.it
Signed-off-by: Ingo Molnar <mingo@kernel.org>
---
Documentation/scheduler/sched-deadline.txt | 10 +++++-----
1 file changed, 5 insertions(+), 5 deletions(-)
diff --git a/Documentation/scheduler/sched-deadline.txt b/Documentation/scheduler/sched-deadline.txt
index 73ef489..c794ebf 100644
--- a/Documentation/scheduler/sched-deadline.txt
+++ b/Documentation/scheduler/sched-deadline.txt
@@ -133,7 +133,7 @@ CONTENTS
arrival time r_j (the time when the job starts), an amount of computation
time c_j needed to finish the job, and a job absolute deadline d_j, which
is the time within which the job should be finished. The maximum execution
- time max_j{c_j} is called "Worst Case Execution Time" (WCET) for the task.
+ time max{c_j} is called "Worst Case Execution Time" (WCET) for the task.
A real-time task can be periodic with period P if r_{j+1} = r_j + P, or
sporadic with minimum inter-arrival time P is r_{j+1} >= r_j + P. Finally,
d_j = r_j + D, where D is the task's relative deadline.
@@ -141,7 +141,7 @@ CONTENTS
WCET and its period (or minimum inter-arrival time), and represents
the fraction of CPU time needed to execute the task.
- If the total utilization sum_i(WCET_i/P_i) is larger than M (with M equal
+ If the total utilization U=sum(WCET_i/P_i) is larger than M (with M equal
to the number of CPUs), then the scheduler is unable to respect all the
deadlines.
Note that total utilization is defined as the sum of the utilizations
@@ -159,8 +159,8 @@ CONTENTS
More precisely, it can be proven that using a global EDF scheduler the
maximum tardiness of each task is smaller or equal than
((M − 1) · WCET_max − WCET_min)/(M − (M − 2) · U_max) + WCET_max
- where WCET_max = max_i{WCET_i} is the maximum WCET, WCET_min=min_i{WCET_i}
- is the minimum WCET, and U_max = max_i{WCET_i/P_i} is the maximum utilization.
+ where WCET_max = max{WCET_i} is the maximum WCET, WCET_min=min{WCET_i}
+ is the minimum WCET, and U_max = max{WCET_i/P_i} is the maximum utilization.
If M=1 (uniprocessor system), or in case of partitioned scheduling (each
real-time task is statically assigned to one and only one CPU), it is
@@ -170,7 +170,7 @@ CONTENTS
of the tasks running on such a CPU is smaller or equal than 1.
If D_i != P_i for some task, then it is possible to define the density of
a task as WCET_i/min{D_i,P_i}, and EDF is able to respect all the deadlines
- of all the tasks running on a CPU if the sum sum_i WCET_i/min{D_i,P_i} of the
+ of all the tasks running on a CPU if the sum sum(WCET_i/min{D_i,P_i}) of the
densities of the tasks running on such a CPU is smaller or equal than 1
(notice that this condition is only sufficient, and not necessary).
next prev parent reply other threads:[~2015-05-19 7:25 UTC|newest]
Thread overview: 20+ messages / expand[flat|nested] mbox.gz Atom feed top
2015-05-18 13:00 [PATCH 0/9] SCHED_DEADLINE documentation update Luca Abeni
2015-05-18 13:00 ` [PATCH 1/9] Documentation/scheduler/sched-deadline.txt: correct definition of density as C_i/min{D_i,P_i} Luca Abeni
2015-05-19 7:23 ` [tip:sched/core] sched/dl/Documentation: Correct the " tip-bot for Zhiqiang Zhang
2015-05-18 13:00 ` [PATCH 2/9] Documentation/scheduler/sched-deadline.txt: switch to American English Luca Abeni
2015-05-19 7:23 ` [tip:sched/core] sched/dl/Documentation: Switch " tip-bot for Luca Abeni
2015-05-18 13:00 ` [PATCH 3/9] Documentation/scheduler/sched-deadline.txt: fix typos Luca Abeni
2015-05-19 7:24 ` [tip:sched/core] sched/dl/Documentation: Fix typos tip-bot for Luca Abeni
2015-05-18 13:00 ` [PATCH 4/9] Documentation/scheduler/sched-deadline.txt: use consistent namings Luca Abeni
2015-05-19 7:24 ` [tip:sched/core] sched/dl/Documentation: Use consistent naming tip-bot for Luca Abeni
2015-05-18 13:00 ` [PATCH 5/9] Documentation/scheduler/sched-deadline.txt: remove _i from sum, max and min Luca Abeni
2015-05-19 7:24 ` tip-bot for Luca Abeni [this message]
2015-05-18 13:00 ` [PATCH 6/9] Documentation/scheduler/sched-deadline.txt: Some notes on EDF schedulability Luca Abeni
2015-05-19 7:25 ` [tip:sched/core] sched/dl/Documentation: Add some " tip-bot for Luca Abeni
2015-05-18 13:00 ` [PATCH 7/9] Documentation/scheduler/sched-deadline.txt: add some references Luca Abeni
2015-05-19 7:25 ` [tip:sched/core] sched/dl/Documentation: Add " tip-bot for Luca Abeni
2015-05-18 13:00 ` [PATCH 8/9] Documentation/scheduler/sched-deadline.txt: relationship between tasks' deadlines and scheduling deadlines Luca Abeni
2015-05-19 7:25 ` [tip:sched/core] sched/dl/Documentation: Clarify the relationship between tasks' deadlines and absolute " tip-bot for Luca Abeni
2015-05-18 13:00 ` [PATCH 9/9] Documentation/scheduler/sched-deadline.txt: Split Section 3 Luca Abeni
2015-05-19 7:26 ` [tip:sched/core] sched/dl/Documentation: " tip-bot for Luca Abeni
2015-05-19 13:26 ` [PATCH 0/9] SCHED_DEADLINE documentation update Henrik Austad
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=tip-c2a684930fce07f19d1a52d7bbe7474fe64fde31@git.kernel.org \
--to=tipbot@zytor.com \
--cc=hpa@zytor.com \
--cc=linux-kernel@vger.kernel.org \
--cc=linux-tip-commits@vger.kernel.org \
--cc=luca.abeni@unitn.it \
--cc=mingo@kernel.org \
--cc=peterz@infradead.org \
--cc=tglx@linutronix.de \
--cc=torvalds@linux-foundation.org \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).