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    Subject[tip:sched/core] sched/dl/Documentation: Clarify indexing notation
    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).


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