Re: [PATCH v2 3/4] Documentation/scheduler/sched-deadline.txt: improve and clarify AC bits

[Ingo Molnar <mingo@kernel.org>]

some speling fixes:

* Juri Lelli <juri.lelli@arm.com> wrote:

> From: Luca Abeni <luca.abeni@unitn.it>
> 
> 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@unitn.it>
> Signed-off-by: Juri Lelli <juri.lelli@arm.com>
> Cc: Randy Dunlap <rdunlap@infradead.org>
> Cc: Peter Zijlstra <peterz@infradead.org>
> Cc: Ingo Molnar <mingo@redhat.com>
> Cc: Henrik Austad <henrik@austad.us>
> Cc: Dario Faggioli <raistlin@linux.it>
> Cc: Juri Lelli <juri.lelli@gmail.com>
> Cc: linux-doc@vger.kernel.org
> Cc: linux-kernel@vger.kernel.org
> ---
>  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 8372c3d..10fc4c4 100644
> --- a/Documentation/scheduler/sched-deadline.txt
> +++ b/Documentation/scheduler/sched-deadline.txt
> @@ -38,16 +38,17 @@ CONTENTS
>  ==================
>  
>   SCHED_DEADLINE uses three parameters, named "runtime", "period", and
> - "deadline" to schedule tasks. A SCHED_DEADLINE task is guaranteed to receive
> + "deadline" to schedule tasks. A SCHED_DEADLINE task should receive

Comma before 'to'?

>   "runtime" microseconds of execution time every "period" microseconds, and
>   these "runtime" microseconds are available within "deadline" microseconds
>   from the beginning of the period.  In order to implement this behaviour,
>   every time the task wakes up, the scheduler computes a "scheduling deadline"
>   consistent with the guarantee (using the CBS[2,3] algorithm). Tasks are then
>   scheduled using EDF[1] on these scheduling deadlines (the task with the
> - closest scheduling deadline is selected for execution). Notice that this
> - guaranteed is respected if a proper "admission control" strategy (see Section
> - "4. Bandwidth management") is used.
> + closest scheduling deadline is selected for execution). Notice that the
> + task actually receives "runtime" time units within "deadline" if a proper
> + "admission control" strategy (see Section "4. Bandwidth management") is used
> + (clearly, if the system is overloaded this guarantee cannot be respected).
>  
>   Summing up, the CBS[2,3] algorithms assigns scheduling deadlines to tasks so
>   that each task runs for at most its runtime every period, avoiding any
> @@ -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
> + 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.

The last part doesn't really parse as correct English for me - 
maybe also split this overly long sentence into two or three 
sentences, to make it easier to understand?

> + 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).

s/the tardiness/tardiness ?

> + More precisely, it can be proved that using a global EDF scheduler the

s/proved/proven

> + 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 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.

s/then it is possible/it is possible ?
 
> + 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

s/all of the deadlines/all 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

Comma after 'stated'.

> + than M is enough to guarantee that non real-time tasks are not starved and
> + the real-time tasks tardiness has an upper bound.
>

s/and the real-time/and that the real-time

s/the real-time tasks tardiness/the tardiness of real-time tasks

>   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
> @@ -163,14 +206,22 @@ CONTENTS
>  4. Bandwidth management
>  =======================
>  
> - In order for the -deadline scheduling to be effective and useful, it is
> - important to have some method to keep the allocation of the available CPU
> - bandwidth to the tasks under control. This is usually called "admission
> - control" and if it is not performed at all, no guarantee can be given on
> - the actual scheduling of the -deadline tasks.
> -
> - The interface used to control the fraction of CPU bandwidth that can be
> - allocated to -deadline tasks is similar to the one already used for -rt
> + As previously mentioned, in order for the -deadline scheduling to be

s/the -deadline scheduling/-deadline scheduling

> + effective and useful (that is, to be able to provide "runtime" time units
> + within "deadline"), it is important to have some method to keep the allocation
> + of the available fractions of CPU time to the various tasks under control.
> + This is usually called "admission control" and if it is not performed, then
> + no guarantee can be given on the actual scheduling of the -deadline tasks.
> +
> + As already stated in Section 3, a necessary condition to be respected to
> + correctly schedule a set of real-time tasks is that the total utilisation
> + is smaller than M. When talking about -deadline tasks, this requires to
> + impose that the sum of the ratio between runtime and period for all tasks
> + is smaller than M. Notice that the ratio runtime/period is equivalent to
> + the utilisation of a "traditional" real-time task, and is also often
> + referred as "bandwidth".

s/referred as/referred to as ?

Thanks,

	Ingo