Donate to e Foundation | Murena handsets with /e/OS | Own a part of Murena! Learn more

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

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.it


Signed-off-by: default avatarIngo Molnar <mingo@kernel.org>
parent 48355c47
Loading
Loading
Loading
Loading
+5 −5
Original line number Diff line number Diff line
@@ -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).