Commit c2a68493 authored by Luca Abeni's avatar Luca Abeni Committed by Ingo Molnar

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: default avatarLuca Abeni <luca.abeni@unitn.it>
Signed-off-by: default avatarPeter 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.itSigned-off-by: default avatarIngo Molnar <mingo@kernel.org>
parent 48355c47
...@@ -133,7 +133,7 @@ CONTENTS ...@@ -133,7 +133,7 @@ CONTENTS
arrival time r_j (the time when the job starts), an amount of computation 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 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 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 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, 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. d_j = r_j + D, where D is the task's relative deadline.
...@@ -141,7 +141,7 @@ CONTENTS ...@@ -141,7 +141,7 @@ CONTENTS
WCET and its period (or minimum inter-arrival time), and represents WCET and its period (or minimum inter-arrival time), and represents
the fraction of CPU time needed to execute the task. 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 to the number of CPUs), then the scheduler is unable to respect all the
deadlines. deadlines.
Note that total utilization is defined as the sum of the utilizations Note that total utilization is defined as the sum of the utilizations
...@@ -159,8 +159,8 @@ CONTENTS ...@@ -159,8 +159,8 @@ CONTENTS
More precisely, it can be proven that using a global EDF scheduler the More precisely, it can be proven that using a global EDF scheduler the
maximum tardiness of each task is smaller or equal than maximum tardiness of each task is smaller or equal than
((M − 1) · WCET_max − WCET_min)/(M − (M − 2) · U_max) + WCET_max ((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} where WCET_max = max{WCET_i} is the maximum WCET, WCET_min=min{WCET_i}
is the minimum WCET, and U_max = max_i{WCET_i/P_i} is the maximum utilization. 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 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 real-time task is statically assigned to one and only one CPU), it is
...@@ -170,7 +170,7 @@ CONTENTS ...@@ -170,7 +170,7 @@ CONTENTS
of the tasks running on such a CPU is smaller or equal than 1. 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 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 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 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). (notice that this condition is only sufficient, and not necessary).
......
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