Return-Path: Received: (majordomo@vger.kernel.org) by vger.kernel.org via listexpand id S965022AbbDIJjV (ORCPT ); Thu, 9 Apr 2015 05:39:21 -0400 Received: from mail-lb0-f177.google.com ([209.85.217.177]:34408 "EHLO mail-lb0-f177.google.com" rhost-flags-OK-OK-OK-OK) by vger.kernel.org with ESMTP id S933620AbbDIJjN (ORCPT ); Thu, 9 Apr 2015 05:39:13 -0400 Date: Thu, 9 Apr 2015 11:39:08 +0200 From: Henrik Austad To: Luca Abeni Cc: peterz@infradead.org, juri.lelli@gmail.com, raistlin@linux.it, mingo@kernel.org, linux-kernel@vger.kernel.org, linux-doc@vger.kernel.org, Luca Abeni Subject: Re: [RFC 4/4] Documentation/scheduler/sched-deadline.txt: add some references Message-ID: <20150409093908.GB10954@sisyphus.home.austad.us> References: <1428494380-1917-1-git-send-email-luca.abeni@unitn.it> <1428494380-1917-5-git-send-email-luca.abeni@unitn.it> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Disposition: inline Content-Transfer-Encoding: 8bit In-Reply-To: <1428494380-1917-5-git-send-email-luca.abeni@unitn.it> User-Agent: Mutt/1.5.21 (2010-09-15) Sender: linux-kernel-owner@vger.kernel.org List-ID: X-Mailing-List: linux-kernel@vger.kernel.org Content-Length: 8490 Lines: 176 On Wed, Apr 08, 2015 at 01:59:40PM +0200, Luca Abeni wrote: > Add a description of the Dhall's effect, some discussion about > schedulability tests for global EDF, and references to real-time literature, > --- > Documentation/scheduler/sched-deadline.txt | 81 ++++++++++++++++++++++++---- > 1 file changed, 71 insertions(+), 10 deletions(-) > > diff --git a/Documentation/scheduler/sched-deadline.txt b/Documentation/scheduler/sched-deadline.txt > index ffaf95f..da5a8d7 100644 > --- a/Documentation/scheduler/sched-deadline.txt > +++ b/Documentation/scheduler/sched-deadline.txt > @@ -160,7 +160,8 @@ CONTENTS > 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. > + is the minimum WCET, and U_max = max_i{WCET_i/P_i} is the maximum > + utilisation[12]. > > 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 > @@ -202,15 +203,52 @@ CONTENTS > > 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 > - that the tardiness of real-time tasks 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 > - must be scheduled by setting: > + utilisations or densities: it can be shown that even if D_i = P_i task > + sets with utilisations slightly larger than 1 can miss deadlines regardless > + of the number of CPUs. + \newline (add som breathing space) > + For example, consider a M tasks {Task_1,...Task_M} scheduled on M - 1 Please consider rewriting this to "Consinder a set of M+1 tasks on a system with M CPUs [...]" As 'M' is normally used to denote the number of cores available and it is much easier to grasp the context of " + 1" rather than " + CPUs, with the first M - 1 tasks having a small worst case execution time > + WCET_i=e and period equal to relative deadline P_i=D_i=P-1. The last task Normally, 'e' is used to denote an _arbitrarily_ small value, and I suspect that this is indeed the case here as well (you're going to describe Dhall's effect, right?). Perhaps make that point explicit? T_i = {P_i, e, P_i} > + (Task_M) has period, relative deadline and worst case execution time > + equal to P: P_M=D_M=WCET_M=P. T_M = {P, P, P} > + If all the tasks activate at the > + same time t, global EDF schedules the first M - 1 tasks first (because > + their absolute deadlines are equal to t + P - 1, hence they are smaller > + than the absolute deadline of Task_M, which is t + P). As a result, Task_M > + can be scheduled only at time t + e, and will finish at time t + e + P, > + after its absolute deadline t + P. The total utilisation of the task set ^^^^^^ Drop this, the text is full of equations as it is. > + is (M - 1) · e / (P - 1) + P / P = (M - 1) · e / (P - 1) + 1, and for > + small values of e this can become very close to 1. This is known as "Dhall's > + effect"[7]. This gives the impression that 'e' must be constant, but all it really means is that e is an 'arbitrarily small value which can be *almost* 0' and that they will be picked _before_ the heavy task by EDF. > + More complex schedulability tests for global EDF have been developed in > + real-time literature[8,9], but they are not based on a simple comparison > + between total utilisation (or density) and a fixed constant. If all tasks > + have D_i = P_i, a sufficient schedulability condition can be expressed in > + a simple way: > + sum_i WCET_i / P_i <= M - (M - 1) · U_max sum_i; as stated in another comment, just juse 'sum' (IMHO) > + where U_max = max_i {WCET_i / P_i}[10]. Notice that for U_max = 1, > + M - (M - 1) · U_max becomes M - M + 1 = 1 and this schedulability condition > + just confirms the Dhall's effect. A more complete survey of the literature > + about schedulability tests for multi-processor real-time scheduling can be > + found in [11]. > + > + As seen, enforcing that the total utilisation is smaller than M does not > + guarantee that global EDF schedules the tasks without missing any deadline > + (in other words, global EDF is not an optimal scheduling algorithm). However, > + a total utilisation smaller than M is enough to guarantee that non real-time > + tasks are not starved and that the tardiness of real-time tasks has an upper > + bound[12] (as previously noticed). Different bounds on the maximum tardiness > + experienced by real-time tasks have been developed in various papers[13,14], > + but the theoretical result that is important for SCHED_DEADLINE is that if > + the total utilisation is smaller or equal than M then the response times of > + the tasks are limited. > + > + Finally, it is important to understand the relationship between the > + scheduling deadlines assigned by SCHED_DEADLINE and the tasks' deadlines > + described above (which represent the real temporal constraints of the task). What about simething like " Finally, it is important to understand the relationship between the scheduling deadlines assigned by SCHED_DEADLINE and the tasks' deadlines described above. The task itself supplies a _relative_ deadline, i.e. an offset after the release of the task at which point it must be complete whereas SCHED_DEADLINE assigns an _absolute_ deadline (a specific point in time) on the form D_i = r_i + d_i " Or somesuch? I may be overdoing this. > + If an admission test is used to guarantee that the scheduling deadlines are > + respected, then 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 must be scheduled by setting: > > - runtime >= WCET > - deadline = D > @@ -242,6 +280,29 @@ CONTENTS > Concerning the Preemptive Scheduling of Periodic Real-Time tasks on > One Processor. Real-Time Systems Journal, vol. 4, no. 2, pp 301-324, > 1990. > + 7 - S. J. Dhall and C. L. Liu. On a real-time scheduling problem. Operations > + research, vol. 26, no. 1, pp 127-140, 1978. > + 8 - T. Baker. Multiprocessor EDF and Deadline Monotonic Schedulability > + Analysis. Proceedings of the 24th IEEE Real-Time Systems Symposium, 2003. > + 9 - T. Baker. An Analysis of EDF Schedulability on a Multiprocessor. > + IEEE Transactions on Parallel and Distributed Systems, vol. 16, no. 8, > + pp 760-768, 2005. > + 10 - J. Goossens, S. Funk and S. Baruah, Priority-Driven Scheduling of > + Periodic Task Systems on Multiprocessors. Real-Time Systems Journal, > + vol. 25, no. 2–3, pp. 187–205, 2003. > + 11 - R. Davis and A. Burns. A Survey of Hard Real-Time Scheduling for > + Multiprocessor Systems. ACM Computing Surveys, vol. 43, no. 4, 2011. > + http://www-users.cs.york.ac.uk/~robdavis/papers/MPSurveyv5.0.pdf > + 12 - U. C. Devi and J. H. Anderson. Tardiness Bounds under Global EDF > + Scheduling on a Multiprocessor. Real-Time Systems Journal, vol. 32, > + no. 2, pp 133-189, 2008. > + 13 - P. Valente and G. Lipari. An Upper Bound to the Lateness of Soft > + Real-Time Tasks Scheduled by EDF on Multiprocessors. Proceedings of > + the 26th IEEE Real-Time Systems Symposium, 2005. > + 14 - J. Erickson, U. Devi and S. Baruah. Improved tardiness bounds for > + Global EDF. Proceedings of the 22nd Euromicro Conference on > + Real-Time Systems, 2010. > + > > 4. Bandwidth management > ======================= > -- > 1.7.9.5 > -- Henrik Austad -- To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to majordomo@vger.kernel.org More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/