A SCHEDULABILITY ANALYSIS OF AN IEC-61499 CONTROL APPLICATION

A SCHEDULABILITY ANALYSIS OF AN IEC-61499 CONTROL APPLICATION

Mohamed Khalgui, Xavier Rebeuf, Françoise Simonot-Lion

LORIA - INPL Campus S ientique, BP 239 54506 Vandoeuvre-lès-Nan y - Fran e {khalgui, rebeuf, simonot}loria.fr tel: +33 3 83 58 17 28, fax: +33 3 83 58 17 01

Abstra t: This paper deals with the temporal orre tness of ontrol appli ations designed using the omponent-based standard IEC 61499. In this standard, a fun tion blo k is dened as an event trigger omponent ontaining its own data. To validate the temporal behavior of an appli ation, we have to take into a

ount its s heduling on the exe ution support. We propose an abstra tion of the omponent behavior taking into a

ount all its possible exe utions. Moreover, we propose to verify the temporal orre tness of the appli ation with regard to global temporal properties (end to end delays). Thanks to su h hara terization, we show that it is possible to he k deadlines for the appli ation to ensure its orre tness. To rea h this goal, we transform the appli ation into a dependant tasks model(Copyright

2005 IFAC).

Keywords: Fun tion Blo ks, IEC 61499, Real Time, s hedulability analysis, oine s heduling.

1. INTRODUCTION

In the ontrol systems eld, the IEC 61499 standard (WG6 2003, WG6 2004) is a omponent-based methodology allowing to design appli ations as well

Industrial ontrol appli ations need to satisfy not only fun tional properties but also temporal ones. To validate a priori the orre tness of su h appli ations, one of the key issues is to model their temporal behaviors. To manage the design omplexity, several methods based on omponents have been proposed (Pe os 2005, holoblo 2005, Stewart et

al. 1997, Arti us 1996). In su h approa hes, evaluating temporal behavior requires also a model of the exe ution support.

as the exe ution support (Crnkovi and Larsson 2002). In the standard, the Fun tion Blo k is dened as an event trigger omponent (Lewis n.d.). It is a reusable fun tional unit of software owning data. A ontrol appli ation is spe ied by a fun tion blo ks network" whi h an be distributed on one or more devi es. Several omplex appli ations have been spe ied using fun tion blo ks (Ifak 2005). Moreover, reusable fun tion blo ks libraries already exist (holoblo 2005).

The standard allows to validate stati interoperabil-

(IEC61131-3 1993) for the Programmable Logi

ity between blo ks. Nevertheless, temporal behavior

Controllers. We an divide its des ription into two

depends on dynami data. Therefore, it is di ult

parts: the ar hite ture des ription and the blo k

to a priori validate temporal interoperability. We

behavior through the events sele tion me hanism.

propose an abstra tion of ea h blo k behavior taking into a

ount all its possible exe utions. Su h abstra tion allows to ompute an upper bound of

2.1 Ar hite ture des ription

the appli ation exe ution time. We show that it is possible to verify the temporal orre tness of the ap-

An appli ation fun tion blo k (FB) (gure 1) is

pli ation with regard to global temporal properties

a fun tional unit of software that supports some

(end to end delays).

fun tionalities of an appli ation. It is omposed by

To validate temporal interoperability, we propose a s hedulability analysis of a fun tion blo ks network distributed on one devi e. To perform su h analysis, we propose to transform the fun tion blo ks appli ation into a parti ular dependent tasks model in the order to take advantages of the results in this eld. Some

works

are

proposed

about

s hedulability

analysis of systems in one pro essor. In the nonpreemptive ase, (Cu u et al. 2002) presents an optimal algorithm to s hedule systems with pre eden e, periodi ity and laten y onstraints (end to end deadline). In addition, (Cu u and Sorel 2003) proves the existen e of a hyper-period

T

an interfa e and an implementation. The interfa e

ontains data/event inputs and outputs supporting the intera tion with the environment. Events are responsible for the a tivation of the fun tion blo k while data ontain valued information. The implementation onsists of a body and a head. The body is omposed of internal data and algorithms implementing the blo k fun tionalities. Ea h algorithm gets values in the input data hannel and produ es values in the output data ones. They are programmed in stru tured text (ST) language (IEC61131-3 1993).

for syn-

hronous systems allowing the proposed algorithm to nd a s hedule applying it from of from 0 to

∞.

0

to

T,

instead

On another side, (Jeay et al. 1991)

gives a s hedulability ondition for a set of periodi and sporadi operations with arbitrary release times. (Howell and k. Venkatrao 1995) studies the omplexity for the problem of non-preemptively s heduling of periodi and sporadi tasks on one pro essor using inserted idle times. Using part of this result, we show that it is possible to generate a safe o-line s heduling for a fun tion blo ks network. Moreover,

Figure 1. An IEC 61499 fun tion blo k

the proposed s hedulability analysis allows to dene a strategy for a fun tion blo k to adapt its internal

The blo k head is onne ted to event ows. It sele ts

behavior a

ording to the s heduling.

the sequen e of algorithms to exe ute with regard to

In the next se tion 2, we briey present the IEC 61499 standard. Then we present our behavior hara terization of an appli ation. The se tion 4 deals with its transformation into a tasks model. In the se tion 5, we propose a generation of tasks dead-

an input event o

urren e. The sele tion me hanism of an event o

urren e is en oded in a state ma hine

alled the Exe ution Control Chart (ECC). At the end of the algorithms exe ution, the ECC sends the

orresponding output event o

urren es.

lines a

ording to the appli ation delays. Finally,

In the standard, a fun tion blo ks network denes

we present a s hedulability analysis based on the

the fun tional ar hite ture of a ontrol appli ation.

generated deadlines.

Ea h fun tion blo k event input (resp. output) is linked to an event output (resp. input) by a hannel. Otherwise, it orresponds to a global appli ation

2. THE IEC 61499 STANDARD

input (resp. output). Data inputs and outputs follow the same rules (gure 2).

We present the main on epts of the IEC 61499

The exe ution support ar hite ture (i.e. the indus-

Fun tion Blo ks standard (WG6 2003, WG6 2004).

trial ontrol system) is dened by a devi es net-

This standard is an extension of the IEC 61131.3

work. A devi e is omposed of one pro essing unit,

sensors, a tuators and network interfa es. In order to manage intera tions with a given physi al pro esses, a devi e ontains several resour es. A resour e ontains FBs networks intera ting with a physi al pro ess. Considered as a logi exe ution unit orresponding to time slots of the pro essing unit, the resour e provides s heduling fun tion for its lo al FBs networks. The operational ar hite ture orresponds to a distribution of the appli ation fun tion blo ks over the

Figure 3. The ECC behavior

dierent resour es of the exe ution support ar hite -

* It a tivates the algorithms sequen e orresponding

ture. The advantage of su h approa h is to take into

to the sele ted event. Then, it waits for the resour e

a

ount hardware as well as software omponents.

s heduler to exe ute this sequen e.

For sake of simpli ity, we onsider in this paper only one fun tion blo ks network distributed on a single resour e of a devi e. Running Example. For all the ontinuation, we

onsider the following running example of a ontrol appli ation lo ated in a resour e of a devi e. This

ontrol appli ation is omposed by four FBs supporting its fun tionalities (gure 2).

* When the exe ution ends, it emits orresponding output events o

urren es. We note that an algorithms sequen e is atomi . Moreover, the resour e s heduling fun tion applies only non preemptive poli ies. On the other hand, the poli y of events priorities in the ECC is not spe ied in the standard. Therefore, it is up to the designer to x su h priority for ea h fun tion blo k (Khalgui et

al. 2004). Note that the ECC is spe ied as a state ma hine where ea h tra e is omposed by a waiting of an input event, invo ations of algorithms, sending of output events. Running Example. we present the ECC behavior

of the fun tion blo k

F B1

(gure 4). The sele tion

me hanism is performed thanks to a state variable ′ ′ a of F B1.

ie1 o

urren e, it asks (!ex_fb) the pro essor to perform the orresponding When the ECC sele ts an

algorithms sequen e. When the exe ution is nished

F B1 state variables, F B4 or simultaneously oe2 F B3 and F B2 .

(?end_ex) and depending on the ECC sends and Figure 2. A ontrol appli ation

f bn.

oe3

oe1

to

to respe tively

ie5 o

urren e, it waits the pro essor to exe ute the orresponding algorithms When the ECC sele ts an

oe7 to F B3 depending on the internal variables.

sequen e. When it is nished, it sends 2.2 Events sele tion me hanism

or

oe8

to

F B2

Let turn to the internal des ription of a fun tion blo k. Note that only algorithms exe ution spends

3. BEHAVIOR CHARACTERIZATION

time. In a given fun tion blo k, the ECC is said idle if there is no algorithm to exe ute. Otherwise, the

To hara terize temporal behavior of a fun tion

ECC is busy (gure 4).

blo k, we have to take into a

ount the exe ution

A

ording to the standard (WG6 2004), the FB

ontains an internal buer for input o

urren es. The ECC behavior is devised into three steps:

of the ECC. Indeed, the ECC de ides not only algorithms to exe ute but also the output events to send. Nevertheless, the sele tion of transitions inside the ECC may depend on internal state variables.

* First, it sele ts one input event o

urren e a

ord-

Then we propose to dene sets of output events

ing to priority rules dened in the resour e.

orresponding to all possible exe utions.

f ollow(f b1 , ie1 ) = {{oe1 }, {oe2 , oe3 }} f ollow(f b1 , ie5 ) = {{oe7 }, {oe8 }} f ollow(f b4 , ie4 ) = {{oe4 }} 3.2

f bn

temporal onstraint

A real time appli ation must often respe t temporal

onstraints as end to end delays. To asso iate su h delay to the fun tion blo ks network, we need to rst formalize the omposition between fun tion blo ks. Figure 4. The ECC behavior of

F B1

We propose a fun tion

cause

that spe ies ausali-

To validate the temporal orre tness of the appli a-

ties between an event input of a fun tion blo k and

tion, we propose to dene end to end delays orre-

an output of another one a

ording to the fun tion

sponding to time onstraints imposed by the prob-

blo ks network. Note that

lem spe i ation. In this se tion, we rst present the

site fun tion that asso iates to an output event the

abstra tion of the fun tion blo k behavior. Then we

input event target of the sent o

urren es.

propose a formalization for end to end delays. For all the ontinuation, we denote by

f bn

a fun tion

blo ks network.

Running example. From the link between

and

F B4,

cause(ie4 ) = oe1 ef f ect(oe1) = ie4

We propose to ompute an abstra tion of the fun tion blo k behavior. The di ulty is to identify the output events sent orresponding to an input event

We dene

state ma hine. Nevertheless, ring a transition in the ECC an depend on internal variables of the blo k. Therefore, we propose to identify the supersets of

inputs

set of input (resp output) events of a fun tion blo k

F B. tr

be a tra e in

ECCF B ,

we denote by

• IE(tr) the input event o

urring in tr • OE(tr) the set of output events o

urring in tr We propose a fun tion input event

ie ∈ IEF B ,

f ollow

asso iating to an

the sets of simultaneous

is

outputs = {oe ∈ OE/ef f ect(oe) ∈ / IE} Running example. We have the following sets :

inputs = {ie1 , ie5 } outputs = {oe4 , oe5 , oe6 , oe9 , oe10 }

sible exe ution), we asso iate a superset gathering

IE (resp OE ) the set of input (output) f bn. Let onsider IEF B (resp OEF B ) the

of

inputs = {ie ∈ IE/cause(ie) ∈ / OE}

For ea h tra e of the ECC automaton (i.e. ea h pos-

Let onsider

outputs) the set f bn whi h

not linked to another event.

output events possibly o

urring simultaneously.

all the output event o

urring in this tra e.

(respe tively

input (respe tively output) events in

o

urren e. Su h asso iation is spe ied in the ECC

Let

F B1

one an dedu e :

3.1 Fun tion blo k behavior

events of

ef f ect spe ies the oppo-

We propose the fun tion end to end delays for

delay that en odes all the f bn. delay(ie, oe) denotes

the maximum duration that an take the exe ution

ie ∈ inputs oe ∈ outputs one.

between the re eive of an and the sent of an

o

urren e

Running Example. delay(ie1 , oe4 ) spe ies the maximum duration for the treatment of the ie1 and ie4 algorithms sequen e. Let suppose the following

delay(ie1 , oe4 ) = delay(ie1 , oe5 ) = delay(ie1 , oe6 ) = 10ms and delay(ie5 , oe9 ) = delay(ie5 , oe10 ) = 17.

onstraints :

output events.

f ollow(f b, ie) = {OE(tr)/ie = IE(tr), tr ∈ ECCF B }

4. TRANSFORMATION INTO A TASKS MODEL

Running Example. For example, we asso iate to

ie5

two sets of output events orresponding to the

two tra es in the ECC starting from the transition triggered by

?ie5 .

In this part, we propose to transform system

S

f bn to

a tasks

with pre eden e onstraints (Babanov et

al. 2003). The purpose is to exploit the results on

f irst = {T ∈ T ask/T.pred ∈ / T ask}

this topi to perform the s hedulability analysis of

f bn.

last = {T ∈ T ask/∀s ∈ T.succ, ∀Tj ∈ s, Tj ∈ / T ask}

In this se tion, we dene the task hara terization in the system

S.

A task orresponds to one exe ution

of a fun tion blo k. Then, we dene a tra e as a

4.2 Tra e denition

ausality sequen e of tasks.

To spe ify a ausality sequen e of tasks, we dene

4.1 Task denition starting from a FB network An appli ation task

T

in

We dene the fun tion

generate(ie) that

ie.

onstru ts

ie the orresponding task T . Note is_generated_by(T ) is the opposite fun tion of generate. We denote by T ask the tasks set of S . setOE be a set of output events. We dene target(setOE ) that asso iates for setOE

fun tion

• T0 ∈ f irst • Tn−1 ∈ last • ∀i ∈]1, n − 1], Ti−1 = Ti .pred

the

Thanks to su h tra es prin iple, it is possible to

the

he k the appli ation end to end delays. Let

following set of tasks,

be the tra es set in

target(setOE ) = {T ∈ T ask/∃oe ∈ setOE , oe = cause(is_generated_by(T ))} is hara terized as follows,

We denote by

the rst task of the tra e

tr.

T race f irst(tr)

In this paper, we

onsider the ase of not reentry tra es (Klein et

al. 1993, Liu 2000) : the exe ution of the exe ution end of the

k − th

(k − 1) − th instan e of

the last

task. Otherwise the system is not feasible.

su h as,

Running Example. We distinguish ve tra es in

• W CET :

the worst ase exe ution time of the

algorithms sequen e orresponding to

ie. It an

be evaluated using the ode and the hara teristi s of the exe ution support. The task that must be exe uted before

the exe ution of

T.

It orresponds to the exe-

ution of the FB produ ing

• succ:

S.

instan e of the rst task must not start before the

T = {W CET, pred, succ}

• pred:

as a Tasks sequen e,

su h as,

that

T

tr

tr = T0 , T1 , ....., Tn−1

for an input event

A task

a tra e

orresponds to the exe ution

of a FB a tivated by an input event o

urren e

Let

S

cause(ie).

a set of tasks sets. All the elements of

a set orrespond to tasks to exe ute on e the exe ution of

T

tr1 = T1 , T2 ; tr2 = T1 , T3 tr4 = T5 , T6 and tr5 = T5 , T7 . Ea h a tasks sequen e in f bn.

this ontrol appli ation : ;

tr3 = T1 , T4

tra e spe ies

;

Note that we an lassi ally dene an operation

op(T )

in

S

as the set of tra es having the same

root. It orresponds to all possible exe utions of when

T

f bn

is a tivated (the orresponding input event

o

urs)

is nished. Note that ea h set

op(T ) = {tr ∈ T race/f irst(tr) = T }

orresponds to a possible exe ution s enario. (i.e. one tra e in the

ECC )

T.succ = {setT /setT ⊂ T ask, ∃setOE ∈ f ollow(f b, is_generated_by(T )), setT = target(setOE )} Running example. We generate the prede essor of

T4

and the su

essors of

T1

as follows,

T4 .pred = T1 T1 .succ = {{T2 , T3 }; {T4}} T1 exe ution is nished, two s enarios are possible : Either we exe ute T2 and T3 or we exe ute T4 . When the

We dene

f irst

(resp

last)

the tasks set that they

have not a prede essor (resp su

essor). These sets

orrespond to the

inputs

and

outputs

sets,

5. TASKS DEADLINES GENERATION

delay(tr) as the end to end tr ∈ T race. This temporal

onstraint orresponds to the delay(ie, oe) where ie

orresponds to the f irst(tr) and oe orresponds to an event produ ing by the last task of tr. We lassi ally dene deadline of a tra e

d(T ) the deadline of the task T ∈ tr. d(T ) has to take into a

ount the time for exe uting all the su

essors belonging to a same set of T.succ

We dene

before their respe tive deadlines. We hara terize

If

d(T )as

follows,

T ∈ last, d(T ) = delay(tr)

Otherwise ,

the s hedulability analysis of asyn hronous systems (Leung and Whitehead 1982). By analogy with

d(T ) = mins∈T.succ {minTi ∈s {d(Ti ) − Pd(Tj )≤d(Ti ) Tj .W CET }} Tj ∈s Running

[rmin +

our ase, the analysis may be done in

jmin , rmax + jmax + 2.lcm].

Example. We onstru t the dierent

deadlines of the dierent tasks. For the operation

op1 , we ompute rst of T2 , T3 and T4 .

all the deadlines of the tasks

• d(T2 ) = delay(tr1 ) = 10 • d(T3 ) = delay(tr2 ) = 10 • d(T4 ) = delay(tr3 ) = 10 We ompute then the deadline of

6.1 A

essibility graph generation Let

state

be the a

essibility graph orresponding to

C

of

G

Where,

• S • T

d(T4 ) − T4 .W CET }

a tasks set to exe ute, a sele ted task to exe ute between all the

S . We apply the EDF

a tivated tasks of

Therefore,

poli y

to perform su h sele tion.

• t

d(T1 ) = min{10 − 3 − 4, 10 − 1} = 3

S

be the tasks

system.

S

is s hedulable if its temporal behavior

is orre t. The s hedulability riterion is the respe t of the deadline for ea h task. To perform the s hedulability analysis of

S,

we propose to onstru t an

s heduling traje tories. Ea h traje tory represents a possible exe ution s enario of the appli ation. Therefore, several tra es are used to onstru t a

EDF

algorithm during

ea h traje tory onstru tion to verify end to end delays of the orresponding tra es. We present a temporal hara terization of

G.

[rmin + jmin , rmax + jmax + 2.lcm]. We present the following steps to

onstru t G. The rst step lets to onstru t the rst tasks state C0 .

Sin e

f bn are periodi , then ea h task T belonging to f irst is a tivated periodi ally. We

hara terize su h task by a release time r, a period p and a jitter j (the maximum deviation of the

all input events of

period).

be the rst state in

belonging to rst.

S0 = f irst We generate then step by step the dierent tasks states in the dierent

G

where

traje tories as follows,

Ci = {Ti , Si , ti } be a state Ti = {W CETi , predi , succi }

in the graph

Ti ∈ / last

Let suppose that

succi

ontains

k

tasks sets.

Ti .succ = {ts1 , ..., tsk } We onstru t

Ci

k

tasks states

C0 , ...., Ck−1

target of

as follows,

∀j ∈ [0, k − 1], Sj = (Si \{Ti })∪tsj if

Ti ∈ last tr

periods.

Let

Let Tmax = {rmax , pmax , jmax } and Tmin = {rmin , pmin , jmin } be two tasks of f irst su h as,

We onstru t

∀Ti ∈ f irst, rmin + jmin ≤ ri + ji ≤ rmax + jmax

G

Step: Let

T = {r, p, j} be the least ommon multiple of the tasks

C0 = {S0 , Tmin , tmin = rmin + G. S0 ontains the tasks

First step: Let

jmin }

if

S.

exe ution.

tions s enarios in the interval

a

essibility graph. The a

essibility graph is a set of

traje tory. We apply the

T

We apply su h algorithm to analyze all the exe u-

In this part, we propose a s hedulability analysis of an IEC 61499 ontrol appli ation. Let

the start time of the

We present the following algorithm to onstru t

6. SCHEDULABILITY ANALYSIS

lcm

We dene a tasks

C = {S, T, t}

min{d(T2 ) − T2 .W CET − T3 .W CET ;

Let

S.

as follows :

T1 .

d(T1 ) =

The system

G

the s hedulability analysis of

be the tra e ontaining

Cj

target of

Ci

Ti .

as follows

Sj = (Si \{Ti }) ∪{f irst(tr)} Thanks to this graph onstru tion, we dedu e that

As we treat only not reentry tra es, we an ex-

the appli ation is not s hedulable if one deadline of

ploit the result on the hyper period proposed for

a task belonging to a tasks state is not satised.

Running the example. We perform the proposed

algorithm to analyze the s hedulability of the ontrol appli ation

f bn.

hara teristi s of

We propose the following temporal

T1

and

T5 .

• r1 = 2; p1 = 50; j1 = 1. • r5 = 1; p5 = 50; j5 = 1. We suppose the following worst ase exe ution times of the dierent tasks :

By onstru ting the a

essibility graph in the hyper period

[2, 103], the algorithm

veries all the temporal

onstraints and proves that the appli ation is s hedulable. We present a part of su h graph (gure 5). Applying the rst step, we onstru t the rst tasks

C0 = {{T1 , T5 }, T5 , t = 2}. Then, we apply step to onstru t the remainder states.

state

Figure 6. The s hedulability analysis of the FBs network of o

urren es to sele t in su h hyper period. The sele tion me hanism must be ompatible with the generated s hedulability analysis. Let

Ti,m

be two o

urren es to sele t, we note that

Tj,n

if the ECC has to sele t

Ti,m

before

Tj,n Ti,m ≪

and

Tj,n .

Therefore, the s heduler will re eive at a time

t

from an ECC the adequate task that it is dedi ated to pro ess a

ording to the s hedulability analysis. Su h poli y lets to guarantee the onformity between the internal behavior of a FB and the s heduler behavior inside the resour e. Figure 5. The a

essibility graph

We dedu e from the a

essibility graph an o-line s heduling of the appli ation (gure 6). We show in ea h state of this graph the task and the start time of its exe ution. Note that for sake of on iseness, identi al bran hes parts of the tree are merged.

Running Example. We dedu e the following events

priorities for

ECC1 , ECC2

and

ECC3 .

• F B1 : T51 ≪ T11 ≪ T52 ≪ T12 ≪ T53 ≪ T13 • F B2 : T61 ≪ T21 ≪ T62 ≪ T22 ≪ T63 • F B3 : T71 ≪ T31 ≪ T72 ≪ T32 In ea h blo k, the ECC must sele t always the input o

urren es a

ording to su h order to guarantee the

orre t omposition with the s heduler.

6.2 Events priorities poli y In a fun tion blo k

f b,

the sele tion of input o

ur-

ren es must be based on the orresponding tasks deadlines. Indeed, the o

urren e to sele t orresponds to the task that has the earliest deadline. But the

ECC

is unaware of these temporal prop-

erties. We propose therefore to exploit the previous s hedulability analysis to generate events priorities for ea h blo k.

7. CONCLUSION AND FUTURE WORKS This paper presents a ontribution to develop an industrial ontrol appli ation a

ording to the IEC 61499 standard. This ontribution lets to validate the temporal interoperability of su h appli ation. First of all, we propose an abstra tion of the fun tion blo k behavior to take into a

ount all its possible

As the s hedulability analysis is performed in the

exe utions. Moreover, we propose to verify the or-

[rmin + jmin , rmax + jmax + 2.lcm],

re tness of the appli ation with regard to end to end

we propose to generate for ea h ECC the order

delays. To perform su h validation, we propose to

hyper period

transform the appli ation to a parti ular dependant

Ifak (2005). http://www.ifak-md.de/wg7/.

tasks model. We propose then the generation of

Jeay, K., D. Stanat and C. Martel (1991). On non-

tasks deadlines to guarantee the temporal orre t-

preemptive s heduling of periodi and sporadi

ness of the appli ation. Finally, we propose a s hedu-

tasks. In: IEEE Real-Time Systems Symposium.

lability analysis and an o-line s heduling genera-

Khalgui, M., X. Rebeuf and F. Simonot-Lion (2004).

tion. On the other hand, to guarantee the orre t

A behavior model for ie 61499 fun tion blo ks.

omposition between blo ks and the s heduler, we

In: Third Workshop on modelling of Obje ts,

propose to take into a

ount the o-line s heduling

Components and Agents. Denmark.

in the denition of the events sele tion poli y. We are urrently working to nd heuristi s redu ing the number of states in the a

essibility graph in order to redu e the ombinatory explosion. Moreover, we are plan to perform the s hedulability analysis of an appli ation distributed over several resour es of a devi e. We also will extend our work to the distribution over resour es of several devi es. Su h extension imposes to take into a

ount the ommuni ation interfa e inside ea h devi e and the networks delays. On another side, we will extend our resear hes by exploiting the fault tolerant s heduling approa h to redu e temporal onstraints in the ase of non riti-

Klein, M H., T. Ralya, B. Polla k, R. Obenza and MG. Harbour (1993). A pra tioner's hand-

book for Real-Time analysis. Guide to Rate monotoni

Analysis for

Real-Time Systems.

Kluwer A ademi Publisher. Leung, J. and J. Whitehead (1982). On the omplexity of xed-priority s heduling of periodi realtime tasks. In: performan e Evaluation 2(1982).

237250. Lewis, R. (n.d.). Modelling ontrol systems using

IEC 61499. The institution of Ele tri al Engineers. Liu, JWS. (2000). Real-time systems. In: Prenti e

Hall.

al systems. Therefore, we authorize the appli ation

Pe os (2005). http://www.pe os-proje t.org.

to not respe t some of its end to end delays.

Stewart, D B., R A. Volpe and P K. Khosla (1997). Design of dynami ally re ongurable real-time software using port-based obje ts. In: IEEE

Transa tions on Software Engineering.

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