[PATCH 4/8] Documentation/scheduler/sched-deadline.txt: remove _i from sum, max and min

From: Luca Abeni
Date: Fri Apr 10 2015 - 06:22:06 EST

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.
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 39341d9..c52e635 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 utilisation sum_i(WCET_i/P_i) is larger than M (with M equal
+ If the total utilisation 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
Note that total utilisation is defined as the sum of the utilisations
@@ -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 â 1) Â WCET_max â WCET_min)/(M â (M â 2) Â 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 utilisation.
+ 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 utilisation.

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).


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