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sched/dl/Documentation: Clarify indexing notation

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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>
This commit is contained in:
Luca Abeni 2015-05-18 15:00:28 +02:00 committed by Ingo Molnar
parent 48355c4775
commit c2a684930f
1 changed files with 5 additions and 5 deletions
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10
Documentation/scheduler/sched-deadline.txt
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@ -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).