Schedulers for BGW Tasks to Guarantee Quality of Service
of Embedded Real-time Systems
Mohamed Ould Sass and Maryline Chetto
IRCCyN Laboratory, University of Nantes, Nantes, France
Embedded, Real-time, Processor Overload, Fault-tolerance, Uniprocessor, Scheduling.
We present a new task model called BGW for preemptable, periodic task sets, scheduled on a uniprocessor
embedded platform. The tasks may be subject to faults and the processor may be overloaded. According to
BGW, any Black job has to execute a primary algorithm before deadline, any Grey job may execute either the
primary or the back-up algorithm and any White job may be discarded. We describe several Earliest Deadline
First (EDF) based scheduling frameworks suitable for this model. We also present and discuss the results of
experiments that compare the EDF scheduler applied to conventional Liu and Layland task sets to various
schedulers applied to BGW task sets. The Quality of Service is observed through metrics including ratio of
deadline success, preemption rate, etc.
We consider the problem of scheduling preemptable,
periodic real-time task systems with arbitrary rela-
tive deadlines, scheduled on a single processor by
an online scheduler. We focus our attention on firm
real-time systems for which producing no result be-
fore deadline can be accepted only under some pre-
specified conditions that depend on the application.
The problem of real-time scheduling has been studied
extensively from about forty years starting with the
famous research paper of Liu and Layland in 1973
(Liu and Layland, 1973). Most of these works (see
a survey in (Liu, 2000)) have focussed on hard real-
time systems and resulted in a number of fixed and
dynamic priority driven scheduling algorithms with
associated off-line schedulability tests.
In this paper, we propose to describe and evaluate
a new task model for answering requirements of firm
real-time systems that accept deadline violations due
to either occurrence of faults or/and processing over-
load. Overload conditions can be caused by a bad sys-
tem design, not anticipated simultaneous arrivals of
interrupts, hardware defects in data acquisition from
sensors, under-estimatedcomputational demands, op-
erating system exceptions, etc. Fault-tolerance tech-
niques intend to keep the system operational in the
presence of faults, even with producing degraded re-
sults. We will show how the BGW task model permits
to guarantee online graceful and controlled degrada-
tion of the Quality of Service in embedded real-time
2.1 Traditional Task Scheduling
Traditionally, a periodic task τ
is characterized by
two parameters at least: C
, worst case execution time
and T
, activation period. Every task periodically gen-
erates an infinite set of jobs for execution. The uti-
lization factor of a periodic task gives the ratio of ex-
ecution requirement per period: u
. As a conse-
quence, the total utilization factor of a task set com-
posed of n tasks is :
. The following EDF
schedulability test was established (Liu and Layland,
1 i.e. total utilization is at most one.
A task set is said to be feasible if there exists at least
one schedule where all jobs of all tasks complete by
their deadline at run time. Earliest Deadline First was
proved optimal and Deadline Monotonic was proved
the best one in the class of fixed priority schedulers
(Liu and Layland, 1973). However, EDF as well as
DM are suitable for under-loaded processing systems
where the processing demand is lower than the pro-
cessing capacity at every time. Such schedulers are
particularly adapted to a hard real-time context that
Ould Sass M. and Chetto M..
Schedulers for BGW Tasks to Guarantee Quality of Service of Embedded Real-time Systems.
DOI: 10.5220/0005181700530058
In Proceedings of the 5th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS-2015), pages 53-58
ISBN: 978-989-758-084-0
2015 SCITEPRESS (Science and Technology Publications, Lda.)
imposes underload conditions.
2.2 Fault-tolerant Scheduling
Redundancy is the foundation of fault tolerance tech-
niques. There are three types of redundancy: hard-
ware, software and temporal. Permanent faults are
generally dealt through hardware redundancy while
temporal redundancy techniques serve for transient
or intermittent faults. They consist in re-executing
a task which has failed with either the same cod-
ing version (pure temporal redundancy) or a differ-
ent version, currently a shorter one. We are interested
with the Deadline Mechanism (DL) model. Each task
has two independent software versions (Liestman and
Campbell, 1986). Firstly, a major version called pri-
mary produces results with high precision when it is
completely executedbefore deadline. Secondly, a ver-
sion called alternate or back-up with shorter execution
time has to run for producing a just acceptable result
whenever the primary fails in executing timely due to
a fault or processor overload.
Two distinct scheduling frameworks may be im-
plemented for the DL mechanism (Chetto and Chetto,
1989) (Chetto and Chetto, 1991). Firstly, according
to the First Chance (FC) technique the alternate ver-
sion of any job executes completely first before the
primary version of the same job starts execution. If
the primary version finishes before deadline, its re-
sults are used in preference to those of the alternate.
Secondly, the Last Chance (LC) technique attempts to
execute first the primary version. Nevertheless suffi-
cient processing time intervals have to be reserved to
guarantee feasible execution of the alternate version
if the primary fails. Consequently, success of any pri-
mary leads to discard the corresponding alternate and
recover processing time since the result of the alter-
nate becomes no longer necessary. In this strategy, the
scheduler has to suspend any running primary when-
ever an alternate requires to be executed so as to meet
its deadline. Theoretical and simulation studies estab-
lished that the LC strategy outperforms the FC strat-
egy (Chetto and Chetto, 1989) (Chetto and Chetto,
2.3 Scheduling with Overload
Any scheduling algorithm should aim at minimizing
the overall damage to the system performance when-
ever a processing overload occurs. This can be per-
formed by dynamically changing some timing param-
eters of the tasks (e.g. execution time or period), using
importance values attached to the tasks or skipping
some jobs of recurring tasks. In that work, we opt for
the Skip-Over (SO) model (Koren and Shasha, 1995).
Each periodic task is characterized by a value called
skip factor denoted by s
, (2 s
) signifying that
among s
successive jobs, at most one can be skipped.
Every job of a task has one of the two colours: red or
blue. A red job has to complete before deadline while
a blue one can be aborted at any time. Moreover, af-
ter a deadline missing, at least (s
1) jobs are red and
must be executed timely. Several scheduling schemes
have been proposed and analysed for the SO model
such as RTO (Red Tasks Only) or BWP (Blue When
Possible). Red jobs are scheduled as soon as possible
according to the EDF (Earliest Deadline First) rule
while blue ones are always rejected (that is never exe-
cuted). The BWP scheme is an improvement of RTO.
BWP schedules blue jobs whenever their execution
does not prevent the red ones from completing within
their deadlines. In other words, blue jobs are served
in background relatively to red jobs.
BGW (Black GreyWhite) is a noveltask model which
uses time redundancy to cope with both transient pro-
cessor overload and faults (Sass et al., 2013). The
BGW model derives from:
the DL Model where each periodic task has two
independent versions for fault-tolerance and over-
load management.
and the SO model where each periodic task has a
skip parameter for overload management.
Every job generated by a periodic task takes at every
time instant one of the three following colours :
Black if the job has to imperatively produce a re-
sult through the primary version,
Grey if the job has to produce a result through at
least one version, but in preference the primary
White if the job may be dropped i.e. the job has
no execution requirement even if it is preferable
to execute one of the two versions.
Formally, a BGW task set τ = {τ
} is com-
posed of n periodic tasks where each task τ
is charac-
terized by its conventional timing parameters and two
additional QoS parameters (n
). Let us define the
term ”distance” as a number of requests. n
the maximum distance allowed between two consecu-
tive successful executions of the primary version. l
the maximum distance allowed between two consecu-
tive successful executions of a job (whatever primary
or alternate).
We have introduced this model to guarantee the
stability of computer-based control systems. As the
processor may sometimes be overloaded, this model
will permit us to determine online the algorithm (pri-
mary or alternate) that has to be executed for every
task. Control may be realized through two kinds of
algorithm: one which returns very precise results but
require high processor utilization (primary executed
by a black job or a grey job) and one which returns
just acceptable results with very short execution time.
As a consequence, at a given time instant for a given
task, the scheduler has to execute a job which may be
either a black job, or a grey job or it may execute no
job at all. The choice depends first on the algorithms
(primary or alternate) that have been executed in the
past and second on the parameters n
and l
of the task.
Any scheduling scheme for BGW-tasks should :
guarantee that the requirements of the BGW tasks
are satisfied. At least one primary version over
successive jobs has to be executed timely, and
one alternate version over l
successive jobs has to
be executed timely. In other words, the scheduler
should timely execute the primary version of each
Black job and either the primary version or the
alternate version of each Grey job.
maximize the number of successful primary exe-
minimize the number of unsuccessful jobs i.e jobs
which are either discarded or not completed be-
fore deadline.
In this paper, we report the results of a simulation
study where the performance of three EDF based
schedulers is analyzed.
We apply the FC technique where every alternate ex-
ecutes entirely and systematically for producing a re-
sult with just acceptable precision. After the corre-
sponding primary is authorized to start execution for
producing a result with a better precision but never-
theless with a longer execution time. By definition of
the Black colour, only the primary version is executed
for black jobs. Either the alternate version or the pri-
mary one has to be executed timely for every grey job.
The white job can be aborted.
The FC technique applied to the the BGW model
can be implemented through different scheduling
variants. We analyse here three EDF based schedul-
ing strategies, each one defined by a specific ordering
of versions. Let X > Y express that job with type
X should be executed with a higher priority than any
job with type Y. Any scheduling framework uses at
most five ordered lists which are respectively BP (BA
does not exist by definition of black colour), GA, GP,
WA and WP. This can be easily implemented in any
real-time operating system with only one list of jobs
that contains five ordered sub-lists. We assume in that
work that all the lists are ordered according to the ear-
liest deadline first rule. Our simulation results will
concern scheduling frameworks based on the follow-
ing priority ordering:
1. BP > GA > GP > WA > WP: Both the alternate
and the primary versions of any grey job should
be executed with a higher priority than the white
jobs. As a consequence this schedulingpolicy will
be denoted by GbWA (Grey before White Alter-
2. BP > GA > GP > WP: Both the alternate and
the primary versions of any grey job should be
executed with a higher priority than the primary
versions of the white jobs. In that policy, alter-
nate versions of white jobs are never executed. As
a consequence this scheduling policy will be de-
noted by GbWP (Grey before White Primary),
3. BP > GA > WA > GP > WP: The alternate ver-
sions of all grey jobs and white jobs should be
executed with a higher priority than the primary
versions of all grey jobs and white jobs. As a con-
sequence this scheduling policy will be denoted
by AbP (Alternate before Primary)
5.1 Simulation Environment
We developed a task set generator that outputs BGW-
schedulable task sets. The task generation proce-
dure was parameterized so thattask sets exhibitdiffer-
ent degrees of scheduling difficulty and consequently
allows us to provide an objective evaluation of the
BGW mechanism. The generator has the following
input parameters: number of tasks (n), Least Com-
mon Multiple of the periods (P), worst case alternate
load (U
), worst case primary load (U
), (n
) and (l
In all simulations reported in this paper, parame-
ters n and P take constant values 22 and 3360 respec-
tively. We considered 14 values for Up which uni-
formly vary from 0.8 to 2.2. U
is a linear function of
with U
= 0.2U
and n
= 7,l
= 4.
Outputs are the timing parameters of tasks (i.e. pe-
riod, relative deadline, worst case alternate execution
time and worst case primary execution time. More
precisely, for a given alternate load U
, C
and C
are proportional to T
) with a minimal value
equal to 1. The task sets which result from the dif-
ferent combinations of U
and U
were scheduled ac-
cording to BGW and EDF successively.
5.2 Metrics
We measure the resulting Quality of Service of the
system under the BGW mechanism by the ratio of
primary versions which are executed timely over the
total number of jobs (NPJ) and the ratio of jobs (pri-
maries and alternates) which are executed timely over
the total number of jobs (NSJ). Scheduling tasks in
overloaded conditions implies to discard some un-
completed jobs. Consequently, as processor time can
be wasted, we measure the wasted time ratio (WTR)
i.e. the percentage of time used by the processor for
producing no result or useless results.
The EDF scheduling strategy wastes time because
of uncompleted primaries. Under the BGW strategy,
time is wasted when both primaries and alternates are
uncompleted and white jobs do not execute.There are
also some processing time lost in preemptions and
context switches. So we measured the relative pre-
emption cost (RPC) i.e. the number of preemptions
per the total number of jobs within a time reference
5.3 NSJ Analysis
We analyse NSJ which gives the number of jobs
which are executed timely (either by primary or alter-
nate versions) over the total number of jobs. We com-
pare it for the three different BGW strategies in addi-
tion to the classical EDF scheduling algorithm (where
every job has only one version i.e. the primary one).
Fig.1 shows variation of NSJ by making vary the
primary load,U
, (and consequently the alternate load
). As shown by the four graphs, for high load, AbP
and GbWA strategies outperform GbWP and EDF.
The AbP strategy exhibits a higher NSJ in com-
parison to the GbWA strategy, which in turn, is bet-
ter than GbWP. Indeed, under low alternate load (U
compared to primary load (U
), there are additional
chances of executing alternate versions of grey and
white jobs, when they have a higher priority in the
job execution order.
The basic EDF scheduler causes more jobs to fail
compared to the three scheduling strategies applied to
BGW-tasksets. Only primary versions are executed
under classical EDF, thus requiring large processing
time. These observations confirm the effectiveness of
our specific task model for overload control. For all
Figure 1: Percentage of successful jobs as a function of
BGW strategies, the number of deadline misses in-
creases asU
increases. High value ofU
causes more
processor time consumption by alternate version of
grey jobs, thus leading to higher deadline misses for
grey primaries. Clearly, the priority of alternate ver-
sions in the job execution order significantly impacts
the BGW performance in terms of global success.
This confirms usefulness of AbP and GbWA strate-
From U
= 100%, NSJ highly decreases until
reaching 50% for U
= 200% under the EDF algo-
rithm, and 40% under the GbWP strategy. For AbP
and GbWA, the decreasing is insignificant and in-
dependent from the primary load, until U
= 210%
where NSJ visibly starts decreasing. AbP and GbWA
have similar NSJ until U
reaches 170% where a
small difference between the two strategies can be ob-
Under higher load, the ratio of deadline misses
for EDF algorithm is approximately ten times higher
than for the AbP strategy. This observation outlines
why both the BGW model and specific scheduling
strategies improve significantly the resulting Quality
of Service of embedded systems under transient pro-
cessor overload. NSJ appears to have the highest val-
ues for the AbP and GbWA strategies, when the GA
list respectively WA list has higher priority than the
GP list respectively the WP list.
The GbWP policy behaves like EDF when the
primary load (U
) is increasing. Therefore, execut-
ing WP jobs before WA jobs leads to a significant
decrease in global success for GbWP relatively to
GbWA because primaries have a higher execution
time in comparison to alternates.
Let us note that 1/(n
+ 1) = 14.28% and 1/(l
1) = 71.72% that respectively represent the ratio of
black jobs and grey jobs which have to meet dead-
lines. When the primary load Up is high, all the
BGW policies execute the lowest number of black
jobs which is permitted by distance parameters. In
that situation, the BGW and EDF policies behave
identically in terms of success ratio. Nevertheless,
there is no control on which job fails under classical
EDF in contrast to BGW policies.
5.4 NPJ Analysis
Fig.2 depicts variation of NPJ i.e. the ratio of suc-
cessful primaries by making vary U
(primary load).
For all values of U
, GbWA outperforms EDF. GbWP
and EDF strategies offer the best performance since,
for the former strategy, the highest priorities are af-
fected to the GP and WP jobs. Whereas, for the latter
strategy, there is no execution of the two versions of
grey and white jobs by re-executing the primary ver-
sion after executing the alternate one. NPJ is greater
for the GbWP strategy, compared to the GbWA strat-
egy which is in turn, greater than the AbP algorithm.
With the small difference observed between the
EDF algorithm and the GbWP strategy in term of
successful primaries, we can state that, the BGW
strategies have a comparable performance if priorities
given to GP and WP jobs are greater compared to pri-
orities given to the WA jobs. It is very interesting to
note that NPJ, the percentage of successful primaries
remains greater than or equal to 14.28%, that is the
smallest ratio of primary versions to be executed in
accordance with the requirement of the BGW model.
At least 1/(n
) jobs have to execute their primary
version. In this study we have (n
= 7). As a con-
sequence, at least 1/7 = 14.28% primaries must be
executed timely. This explains why we can continue
the simulation experiment until U
= 700% and we
observe that NPJ is decreasing under 14.28%. It is
also observed that NPJ for EDF decrease rapidly as
grows, until it stands comparison to the AbP and
GbWA policies.
In fact, at higher values of the utilization factorU
in particular between U
= 210% and U
= 220%, we
observe that all schedulers behave identically when
observing NPJ i.e. the ratio of successful primaries.
Figure 2: Percentage of successful primaries as a function
of load.
Considering the jobs execution order under BGW
scheduling strategies, we notice that when the compu-
tation times of GA jobs and WA jobs tend to zero, all
BGW scheduling policies tend to behave as the EDF
We note also that, the lower the priority is given to
WA jobs, the more similar are the behaviours of BGW
and EDF policies in terms of successful primaries ra-
tio. When the primary load U
becomes very high
(more than 210%), all the BGW policies execute only
primaries of the black jobs and so BGW and EDF
policies have similar NPJ. We can draw the same con-
clusion when the alternate load is roughly equal to the
primary load.
5.5 WTR Analysis
The wasted time ratio (WTR) is the percentage of
time used by the processor for producing useless re-
sults (notably jobs which are aborted). The EDF
scheduling strategy leads to waste processing time
when primaries are aborted before completion be-
cause of time starvation. Generally, wasted time
comes from the execution of primary grey jobs and
all versions of white jobs in the BGW policies.
Fig.3 shows the variation of WTR.
The best performance regarding WTR is given by
the GbWA algorithm for all load conditions. In under-
load conditions, WTR is equal to zero for EDF be-
cause only the primary versions are executed, and
EDF is optimal if there is no overload. For GbWP,
WTR is also equal to zero until U
= 110% and in-
creases slowly untilU
= 130%. Then, it continues to
increase with large values until 21% at U
= 220%.
Figure 3: Percentage of wasted time as a function of load.
Both the increase in the number of lost jobs and
the increase in computation time of alternate and pri-
mary versions lead to the increase in wasted time.
Indeed, abortion of any primary or alternate version
will create large unusable processing time. As U
creases, the ratio of lost jobs under EDF increases
more than the AbP and GbWA strategies. Hence,
WTR under EDF is greater than under AbP and
GbWA strategies when U
is very high.
5.6 RPC Analysis
It is interesting to compare the number of preemptions
generated by the different scheduling strategies, so as
to evaluate correctly the relative overhead. In fact, the
previous performance evaluation may have no signif-
icance if some schedulers exhibit unacceptable over-
head at runtime due to context switches.Fig.4 shows
RPC i.e. the preemption ratio.
In under-load conditions, we notice a light dif-
ference between the different algorithms. Globally,
RPC is approximately constant at 19% for the AbP
and GbWA strategies. We also observe similarity be-
tween GbWP and EDF with different values of al-
ternate loads. RPC for AbP and GbWA strategies is
greater than for GbWP and EDF algorithms. Con-
sequently, the number of selected WA, GP and WP
jobs to be executed for AbP and GbWA strategies in-
creases, which increases the preemption ratios.
Figure 4: Preemption Rate as a function of load.
Under all load conditions, the GbWP strategy of-
fers the best performance in terms of RPC compared
to the other BGW strategies. It is always less than
10% aboveU
= 110%. We observe small differences
between GbWP and EDF policies. EDF gives high
RPC in under-load conditions and decreases in over-
load conditions between 100% and 150%. RPC starts
to increase from U
= 150% for EDF until it reaches
the same level as AbP and GbWA.
Globally, RPC is stable for AbP and GbWA poli-
cies unlike GbWP and EDF strategies. RPC for BGW
policies, particularly for AbP and GbWA is higher
than for the EDF scheduler applied to jobs which are
all primary versions. When the primary version load
is high, the probability to execute timely the GP jobs
decreases. Thus, neither the execution of WA nor WP
jobs is achieved, hence, the decrease in RPC for the
GbWA strategy. According to jobs execution order
under BGW strategies, for example for GbWA when
the computation time of GA and WA jobs tends to be
close to ones of the GP and WP jobs, the BGW poli-
cies tends to behave as EDF in terms of RPC.
The contribution of this paper was twofold.
We described a new approach for modelling Qual-
ity of Service (QoS) requirements of periodic task
systems which may be the object of both tran-
sient faults and processor overloads. This ap-
proach consists in integrating the Deadline Mech-
anism and the Skip-Over model in a unified task
model, namely BGW. We have shown how BGW
permits to provide an acceptable quality of service
through adequate task scheduling.
We evaluated several scheduling schemes for
BGW-task sets with experiments. The simula-
tion demonstrates the merits of our proposed task
model compared to the classical Liu and Layland
task model. Simulations show the improvement
of specific scheduling frameworks for the BGW
model achievedin terms of ratio of successful jobs
and efficiency of processor usage which alleviates
the performance degradation under overload con-
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