Re: [PATCH 3/4] Documentation/scheduler/sched-deadline.txt: improve and clarify AC bits

From: Randy Dunlap
Date: Tue Aug 12 2014 - 14:11:12 EST

On 08/12/14 08:49, Juri Lelli wrote:
> From: Luca Abeni <luca.abeni@xxxxxxxx>
> Admission control is of key importance for SCHED_DEADLINE, since it guarantees
> system schedulability (or tells us something about the degree of guarantees
> we can provide to the user).
> This patch improves and clarifies bits and pieces regarding AC, both for UP
> and SMP systems.
> Signed-off-by: Luca Abeni <luca.abeni@xxxxxxxx>
> Signed-off-by: Juri Lelli <juri.lelli@xxxxxxx>
> Cc: Randy Dunlap <rdunlap@xxxxxxxxxxxxx>
> Cc: Peter Zijlstra <peterz@xxxxxxxxxxxxx>
> Cc: Ingo Molnar <mingo@xxxxxxxxxx>
> Cc: Henrik Austad <henrik@xxxxxxxxx>
> Cc: Dario Faggioli <raistlin@xxxxxxxx>
> Cc: Juri Lelli <juri.lelli@xxxxxxxxx>
> Cc: linux-doc@xxxxxxxxxxxxxxx
> Cc: linux-kernel@xxxxxxxxxxxxxxx
> ---
> Documentation/scheduler/sched-deadline.txt | 87 +++++++++++++++++++++++-----
> 1 file changed, 73 insertions(+), 14 deletions(-)
> diff --git a/Documentation/scheduler/sched-deadline.txt b/Documentation/scheduler/sched-deadline.txt
> index 4acba51..d056034 100644
> --- a/Documentation/scheduler/sched-deadline.txt
> +++ b/Documentation/scheduler/sched-deadline.txt

> @@ -134,6 +135,48 @@ CONTENTS
> 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.
> + The utilisation of a real-time task is defined as the ratio between its
> + wcet and its period (or minimum inter-arrival time), and represents

"wcet" seems to be used here without any explanation of what it means.

> + the fraction of CPU time needed to execute the task.
> +
> + If the total utilisation sum_i(WCET_i/P_i) (sum of the utilisations
> + WCET_i/P_i of all the tasks in the system - notice that when considering
> + multiple tasks, the parameters of the i-th one are indicated with the "_i"
> + suffix) is larger than M (with M equal to the number of CPUs), then the
> + system will surely not be able to respect all of the deadlines, and no
> + execution time is guaranteed for non real-time tasks, which risk to be
> + starved by real-time tasks.
> + If, instead, the total utilisation is smaller than M, then non real-time
> + tasks will not be starved and the system might be able to respect all the
> + deadlines.
> + As a matter of fact, in this case it is possible to provide an upper bound
> + for the tardiness (defined as the maximum between 0 and the difference
> + between the finishing time of a job and its absolute deadline).
> + More precisely, it can be proved 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.
> +
> + If M=1 (uniprocessor system), or in case of partitioned scheduling (each
> + real-time task is statically assigned to one and only one CPU), then it is
> + possible to formally check if all the deadlines are respected.
> + If D_i = P_i for all tasks, then EDF is able to respect all the deadlines
> + of all the tasks executing on a CPU if and only if the total utilisation
> + 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 C_i/min{D_i,T_i}, and EDF is able to respect all of the deadlines
> + of all the tasks running on a CPU if the sum sum_i C_i/min{D_i,T_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).
> +
> + On multiprocessor systems with global EDF scheduling (non partitioned
> + systems), a sufficient test for schedulability can not be based on the


> + utilisations (it can be shown that task sets with utilisations slightly
> + larger than 1 can miss deadlines regardless of the number of CPUs M).
> + However, as previously stated enforcing that the total utilisation is smaller
> + than M is enough to guarantee that non real-time tasks are not starved and
> + the real-time tasks tardiness has an upper bound.
> SCHED_DEADLINE can be used to schedule real-time tasks guaranteeing that
> the jobs' deadlines of a task are respected. In order to do this, a task

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