• Aucun résultat trouvé

An Effective Equivalence for Sets of Scenarios Represented by HMSCs

N/A
N/A
Protected

Academic year: 2021

Partager "An Effective Equivalence for Sets of Scenarios Represented by HMSCs"

Copied!
33
0
0

Texte intégral

(1)

HAL Id: inria-00073186

https://hal.inria.fr/inria-00073186

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

An Effective Equivalence for Sets of Scenarios Represented by HMSCs

Loïc Hélouët, Claude Jard, Benoit Caillaud

To cite this version:

Loïc Hélouët, Claude Jard, Benoit Caillaud. An Effective Equivalence for Sets of Scenarios Represented by HMSCs. [Research Report] RR-3499, INRIA. 1998. �inria-00073186�

(2)

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

An effective equivalence for sets of scenarios represented by HMSCs

Lo¨ıc H´elou¨et, Claude Jard, Benoˆıt Caillaud

N ˚ 3499

Septembre 1998

TH `EME 1

(3)
(4)

-/.1032 4+5 #

6798;:=<>@?A7CBEDGFIHKJL?NM9BKO)PQRMTSUOHKVLPGWK79XYFJZM9[Y?\?NM9BEO

] ^`_ba/cdfehgjibklcbm@n`ocqpklr`kspl_ba/cbk

tvusw@xycqpztR{j|=t}{

gm@~~9wGulp €`cusc‚^`cbuƒ^`c…„†ˆ‡G‰G‰e1Š‹cb~pscbaLŒulc/d‚‰@‰GŽe@‰/~Tmˆ‘@c‚k

’“)”b•q–!—˜@•@™ ] ^š›kE~mG~Tc‚uK€`cqpƒmˆš›œ›kEm~m@ulpsšžmˆœ‹wGuƒ€`c‚u)klcbaZmG„Gplš›bkŸ wGuŸ¡m@a/š›œ¢š›cbkEw@Ÿ9klqcb„mGusš›wGk)ulcb~ulcbklcb„‹psc‚€

Œ‹r£jš›‘G^`¤Y¥cq¦@cbœG|§cbkƒklm@‘@cŠ‹c‚¨In`cb„qc ©^Tm@ulplkª\£j|ŠT©k;«¬K­®uƒm@~^‘Guƒm@aZaZm@uƒk}‘@c‚„`cbuƒmˆplš›„`‘jcq¦@c‚„‹p)klpluƒn¤

pƒnulcbkm@ulcŒTcbš›„`‘¯nklcb€°psw¯ulcb~ulcbklcb„‹p®£j|ŠT©kq±Z{²€`cbqš›klš›wG„§~Tusw`c‚€nulcŸ w‹u£j|ŠT©fcb¨In`š›¦!mˆœ›cb„qcZš›k

pƒ^`cb„€`c‚klbusšžŒTc‚€}±L] ^š›kqmG„°Œ9cw‹„ksšž€`c‚usc‚€=m@km³9uƒkspksplcb~°psw!´m@uƒ€µŸ wGuƒaZmˆœKaZm@„`šž~n`œžmˆplš¢w‹„=w@Ÿkƒc¤

„Tm@ulš¢w‹kq±

¶µ·‹¸R¹ƒº» –!¼)”@™ |Š©½c‚¨In`š¢¦!m@œ¢c‚„cG½`cq¦@c‚„‹pklpluƒnqplnulc@½~9wGaZklcqpq½T‘Guƒm@~^‘Guƒm@aZaZm@ub±

¾À¿}ÁlÂAÃbÄÁ Å)ƛÂAÇAÈÉ

ÊÌ˂ÍÏÎÌÐRÑÒ\ÓÐÌÔ;Î%Õ!Ô;Ò¡Ö\Í×Ô;ØÏØÙjÎYÚUՂÕ@ÑÒ Ö\ÛsÜ®ÝqÙjÞ)ØÏßsԃÖ\Ûy؋Ð%ÍÖYËUÍÏàjÖY˂Ûáâ9ã)ÊÌâCäLÔ;ßyÖ\ÍÏÑà

Unit´e de recherche INRIA Rennes

(5)

#") #&") *+" # #&*" ,+ # 032 4+5

” ™ w‹nk€i³9„`šžkƒksw‹„kn„cksi‚aZm@„‹psšž¨In`c€wGuƒ€ulc ~m@ulpsš›cqœ~Tw‹nu€`c‚kŸ¡mGaLš›œ›œ¢c‚k€`ckƒi‚„m!¤

ulš›wGkulcb~ulibklcb„‹psibcbk~mGu€`cbk £jš›‘G^I¤A¥%cb¦@cqœj|=cbkƒklm@‘@c§Š‹c‚¨‹ncb„qc°©^m@ulplkµª\£j|Š© «± ©(cbœ¢œ›c¤Nš~Tc‚ula/cqp

€mGklklw`š›cbu ^Tm@¨In`c£|Š©fn„cLklpluƒnpƒnuscL€ib¦@i‚„`cba/cb„‹pƒkcb„‘@cb„T€ulmGŒ`œ›c~m@un„`cL‘Guƒm@aZaZmˆšžusc€`c

‘‹ulmG~^`c‚k%³C„`š¢cG±®„Z~9cbn`pm@œ¢w‹ulkE€`i‚šž€`cbuEcCc‚plš¢¦Gcba/cb„‹pKœi‚¨‹nš¢¦!mˆœ›cb„Tc €`c€`c‚nIoL£|Š©½@qc¨In`šTwGn`¦`ulc

œžm/¦@wGš¢c/œ›mZaZm@„š›~nœ›m@psš›wG„Ÿ wGuƒaLcbœ¢œ›cŽ€`ckƒib„Tm@ulš¢w‹kq±

…»

•‚”

¹

˜

™ | Š©½(i‚¨In`š¢¦!m@œ¢c‚„cG½jkspƒulnTplnTusc€ib¦@i‚„`cba/cb„‹pƒkq½ w‹ul€ulc§~mGusplš¢cbœ\½j‘Guƒm@aZaZmˆšžusc=€`c

‘‹ulmG~^`c‚kq±

(6)

5 L))#

4657

•b– » ¼)˜ˆ•98» 7 :

; “ =<2> ”Z—

7

¼@? =<2> ” A

±¢d Œ|Š©k®±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± B

± £|Š©k ±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± C

±† gjcq‘Gnœ›mGuco~ulcbkƒksš›wG„k(wG„+|ŠT©kf±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± 

DFE

—`–U•G8¡— » –!¼ · –” ·

7

•G8\˜@”!H » – =<2> ” I

†T±¢d Œ|Š©kmG„€tKmGusplš›m@œ®ul€`c‚ulkj±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± 

†T± £|Š© Šm@„T€+~Tm@ulpsšžmˆœRwGuƒ€`cbuŸ¡mGa/š¢œ›š¢c‚k ±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± ‰

:KJL · 7 • < •q– ˜@•– · ” 4NM

AFO–!—PRQTS9–U— —`–!” 4;

B±¢d £r`~Tc‚us‘‹ulmG~^k±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± dU

B± ­®uƒm@~T^‘‹ulmGa/aZmGulkf±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± dU

U

O–!—PRQTS9–U— —`–VS · 7 · –!—`•G8» 7

HY– »

7 ? =<2>

4ND

W

±¢d ®~9cbuƒmˆplš¢w‹„kwG„µw!¦Gcbul𛄑‘Guƒm@~T^k ±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± d‚†

W ±FX®cbul𛦋šž„`‘Z‘Guƒm@~T^‘‹ulmGa/aZmGulkvŸ¡usw‹a&m/£j|ŠT© ±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± db‡

Y O–!— —–˜ » –U– · ˜@•

7 · ”‚”

4NU

C`±¢d t(usw‹~Tc‚usplš¢c‚kwˆŸEpl^`cuƒn`œ›cbk ±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± d W

C`±FZv¦@cb„‹pklpluƒnpƒnulcbk m@„T€~mGusplš›m@œ}wGuƒ€`cbu(Ÿ¡mGaLš›œ›š¢c‚k±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± d‚

C`±† gn`œ¢cqwGuƒusc‚pƒ„`cbkƒk±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± d‚‰

IF? =<2> ” ·\[ 28L — · 7 ˜ · ;]M

T±¢d_^y„`³9„`š›pscŒuƒm@„^š›„`‘µ±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± a`

T±¢dG±¢d gcb€nT„€m@„Tr cbœ¢šža/š›„m@psš›wG„ ±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± d

T±¢dG± gcba/w!¦I𛄑Lšž„I³9„`š›pscLŒulmG„^`šž„`‘±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± d

T± ©(w‹„„`c‚psš›wG„Tk ~usc‚ksc‚us¦!m@psš›wG„ ±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± G

T±†KZ(¨‹nš¢¦!mˆœ›cb„Tc~ulcbklcbul¦!mˆpsš›wG„ ±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž± ˆ‡

b ’ ¼ · ˜c8¡”98» 7

» ˜ · ¼ – · H» –d? =<2> ·N[ 38

L — · 7 ˜ · ; A

4M0E

– » ˜ · ”‚”¼28

L · –S · 7 ˜ · ¼ · • · ˜ˆ•98 » 7 ;]U

d9`±›dt(usw`c‚klkeX®š›¦@cbul‘@c‚„c ±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±  W

d9`±Ï {jœ¢‘GwGulš¢pƒ^a ±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±±Ž±±Ž±Ž±±Ž±±Ž±®±Ž±±Ž±Ž±±Ž±±Ž±±Ž±Ž±®±Ž±  W

44 >L» 7 ˜ )”G8» 7 ; I

(7)

") ,µv

ŠIrIklpsc‚a$a/w`€`cbœ¢šž„`‘ Œ‹r+a/c‚m@„k w@Ÿklqcb„mGusš}šžkjmqwGaZa/wG„µ~uƒm@plš›qc@±Š‹cq¦GcbuƒmˆœRŸ w‹ulaZmˆœ„`w@pƒmˆpsš›wG„TkklnT^

mGks|=cbkƒkƒmˆ‘@cŠ‹c‚¨In`cb„qc/©^mGuspƒk ª¡| Š© « ^mU¦GcŒTcbcb„=~Tusw‹~Tw‹ksc‚€}±|Š©k®m@ulcaLw‹ksplœ¢rµnklcb€µŸ w‹u€`c‚ky¤

busšžŒ`šž„`‘pl^cLm@qpsš›¦Iš¢plš¢c‚kwˆŸvqwGaZanT„`š›bmˆplš›„`‘c‚„‹psš›psš›cbk𛄝€`šžklplulš›Œnpscb€§ksr`klpscbaZkb±] ^`cqrµqmG„¯ŒTcŸ wGn„T€

šž„Zmœ›wGklcqœ›ruscbœ›m@pscb€Ÿ wGuƒaZmˆœ›š›kƒa+½@qm@œ¢œ›cb€Š‹c‚¨‹ncb„qcX®šžmˆ‘Guƒm@aZkb½!wG„`c w@Ÿ9pƒ^`cj|=¥ ª„`š¢³Tc‚€L|§wI€cqœ›š›„`‘

¥)m@„`‘‹nmˆ‘GcU«Ì¦Iš¢cb´kdY±E{ |Š© ‘Guƒm@~T^`š›bmˆœ›œ¢r€cbkƒqulš›Œ9cbkKqwGaZan„š›bmˆpsš›wG„TkKŒTcbpN´(cbcb„/~usw`qcbkƒksc‚k(ªYqm@œ¤

œ›cb€ ]#' # «±)| Š©k‘@š›¦@cm/¦@cbulršž„Gpƒn`š›psš›¦@cŽm@„€¦Iš›kƒnm@œRulcb~Tusc‚ksc‚„Gpƒmˆplš¢w‹„wˆŸEksr`klpscbaZkŒ9cb^mU¦Iš›wGnuƒkq±

] ^`caZm!xywGu€uƒmU´Œm@jwˆŸpl^š›k‹š›„T€ŽwˆŸT„`wGplm@psš›wG„Žšžk%pƒ^`c(„InaLŒTc‚u%w@ŸTklqcb„mGusšGr@w‹n^mU¦@cKplwqwGaŒš›„`c

plwZ‘@cqpmZw‹a/~œ¢cbpscŽksr`klpsc‚a²kl~9cbqš³9bmˆplš¢w‹„}±K{ ksšžaZ~`œ¢cšž€`cbmLšžkpswŒn`š›œ›€Ÿ¡m@a/š›œ¢š›cbkw@Ÿ)kƒc‚„m@ulš\½`nklšž„`‘/m

‹šž„€¯w@Ÿskƒc‚„m@ulš¢wmGn`psw‹a/m@psw‹„;±] ^`cLa/wGklpcbœ›mGŒTw‹ulm@psc~ulwG~9wGkƒmˆœÌŸ wGu|Š©kšžk®ŒTcbš›„`‘+„`wGuƒaZmˆœ›šbcb€}½

mG„€ šžkbmˆœ›œ¢c‚€ s£jš›‘G^ œ›cq¦Gcqœ®|Š©!§wGu£j|ŠT©"d‚‰ A± £|Š©k+€`c³9„c°|ŠT© wGaZ~9wGklš¢plš¢w‹„k ´ š›pl^

w‹~Tc‚ulm@psw‹ulkkƒn^µm@kklcb¨In`c‚„šž„`‘T½^w@šžc@½Tcb„‹¦Iš›ulwG„a/c‚„GpƒmˆœÌqwGaZ~Tw‹ksš›psš›wG„̽^`š¢c‚ulmGul^š›bmˆœÌw‹aZ~Tw‹ksš›psš›wG„}±

{ £j|Š©&šžkm ‘Guƒm@~T^}½(´^š›^ „`w`€`c‚kqmG„ ŒTc=klplmGusplš›„`‘ „wI€cbkb½c‚„€ „`w`€`c‚kq½ ^`wGš›qcbkb½(|ŠT©kq½wGu

ulcŸ c‚usc‚„c‚kjplwwGpl^`c‚u£|Š©kb± ^y„=w‹ul€`c‚ujplw#@cqcb~§pl^`c/cbkƒklcb„‹psšžmˆœY½R´(c/´ š¢œ›œEwG„`œ›r¯€`cbm@œE𛄧pl^`šžk~m@~9cbu

´ š›pl^µmZkƒnŒklcqp wˆŸ)£j|ŠT©kq½œ›šžaLš›psc‚€+psw ^`wGš›qc®mG„€µksc‚¨‹ncb„qš›„`‘Zw‹~Tc‚ulm@pswGuƒkb±

$cmˆšža&plwZ~Tusw!¦Išž€`c®kƒn^µmZ~Tw!´cbusŸ¡n`œÌ„`wGplm@psš›wG„´ š¢pƒ^+mLŸ w‹ulaZmˆœÌŒTm@‹‘GulwGn„T€}½‹m@œ¢œ›w!´ šž„`‘¬

%

~ulwG~9cbulpNr^`c‚Gšž„`‘µ¬'&TwGucom@aZ~`œ›c@½9š›k pƒ^`cbulcm~9wGkƒksšžŒ`œ›c~ulwIqcbkƒk€`š›¦@c‚us‘Gcb„qc/ªY~Tw‹klklšžŒ`œ¢r+œ›cbm!¤

€`šž„`‘°plw°n„IŒ9wGn„T€`cb€ aLc‚klkƒmˆ‘GcmGqqnTan`œžmˆplš¢w‹„ 𛄠m°qwGaZan„š›bmˆpsš›wG„ a/c‚€`š›nTa«šž„ m°kl~9cbqš¤

³9qm@psš›wG„)( ^AŸ ´(cZ´m@„‹ppsw=aZm*@cZm¯€š›klplulš›ŒTn`psc‚€°šžaZ~`œ›cba/cb„‹plm@psš›wG„}½Em@ulcZpl^`c‚usc mG„‹r§„`wG„œ›w`qmˆœ

^`w@šžc‚kKpl^Tmˆp´ š›œ¢œ9usc‚¨‹nš›ulc€`šžkspƒusšžŒn`plcb€w‹„klcb„kƒnk( { ³Culklpvklpscb~/plw!´mGul€kK~Tusw‹~Tc‚uspNr^cb‹š›„‘

´mGk~usw‹~Tw‹ksc‚€ šž„+¢d W Y±] ^`cŽm@œ¢‘GwGulš¢pƒ^aZk(€`cq³9„`c‚€šž„pl^`šžk m@ulpsšžœ›c®m@œ¢œ›w!´ plwZ€cbšž€`c´^`cbpl^`c‚um

£j|ŠT© €`c‚klbusšžŒ`šž„`‘mZ~usw‹~Tc‚uspNrsaZmˆpƒ^®mG„`w@pƒ^`cbu£|Š© €`cbkƒqulš›Œš›„`‘ZmklrIklpsc‚a²wGu „w@pq±

%

{jn`plwGaZmˆpl𛁧~uswG‘Guƒm@a k,ˆcbœ¢cbpsw‹„ ‘Gcb„`c‚ulm@psš›wG„}½´^`šž^'´ š¢œ›œ®cb„kƒnulc¯pl^m@pm@„‹r cqo`cbqnpsš›wG„ ´ š›œ¢œ

usc‚kl~9cbqp pl^`cŽw‹ul€cbu€`c³C„`cb€+šž„pƒ^`cklqcb„mGusšY±

] ^`šžk~m@~9cbuaZm*ˆc‚kvm³Culklp(qwG„‹plulš›ŒTn`psš›wG„Z´ š›pl^`šž„ pƒ^`šžk(qwG„‹pscqoIpb¬pƒ^`c€`cbqš›klš¢w‹„ZwˆŸÌ£|Š©'c‚¨‹nš¢¦!m!¤

œ›cb„Tc@±

] ^`c(¨‹ncbklpsš›wG„®wˆŸI|Š©°klcbaZm@„‹psšžqk%^m@ǩ9cqc‚„plulcbm@pscb€®šž„ŽaZm@„‹rj~mG~Tc‚ulkKª,†T½@d‚†`½ˆdq‡T½@dG`½@d@d@½ˆd‚I½‚‰ ¡«;½

ŒTn`ppl^cksc‚a/mG„‹psšžqkEŸ w‹uE£j|Š©kvš›kvksplš¢œ›œšž„Zš¢pƒkKš›„`Ÿ¡m@„qr@±K{'³9uƒkspKšž„‹pscbulœ›cbmU¦I𛄑klcbaZmG„Gplš›bk)Ÿ wGuK£|Š©k

´m@kK~Tusw‹~Tw‹ksc‚€šž„-d B.Y±)|=w‹usc ulcbc‚„‹psœ›r@½½ W 9€`c³C„`cb€Z~mGusplš›m@œ¤AwGuƒ€`cbuEklcbaZm@„‹plš›bkq±){j„`wGpl^`c‚uK¦Iš›klš¢w‹„w@Ÿ

£|Š©k ´m@k~ulwG~9wGklcb€šž„+B A½´^`c‚uscŽklwGa/cŽklqcb„mGusš}m@ulc/saZmG„€mˆplwGulr0;½Im@„€µklwGa/cŽm@ulc1swG~psš›wG„m@œ2±

$cqwG„klšž€`cbupl^m@p+m | Š© €`cq³9„`cbk+m ~Tm@ulpsšžmˆœjw‹ul€cbuŒ9cqpN´cqc‚„ cq¦Gcb„‹plkb½jmG„€ pl^Tmˆpµm £j|ŠT©

€cbkƒqulš›Œ9cbkKmZªY~Tw‹klklš›Œœ¢rLš›„I³C„`š¢plcU«Ÿ¡mGa/š¢œ›rw@ŸR~mGusplš›m@œ¢œ›rw‹ul€`c‚usc‚€Lklcqpƒkq±E] ^`šžkEŸ¡m@a/š›œ¢rLš›kvŒn`š›œ¢pKŸ¡ulwGa Œm@klšž

| Š©kª\pl^`cL£j|Š©z„`w`€`c‚k;«½CnTksšž„`‘qwGaZ~Tw‹ksš›psš›wG„+w‹~Tc‚ulm@pswGuƒk¬ ksc‚¨In`cb„q𛄑¯ª¡wGuƒ€`c‚uw‹„qm@pscb„Tmˆpsš›wG„C«

mG„€+^`w@šžcZª\klcqp pƒ^`cqw‹uscbpsšžn„`š›wG„9«±

{ Ÿ¡mGaLš›œ›r§wˆŸ~m@ulpsšžmˆœKw‹ul€cbuƒk®bm@„ŒTc ulcb~Tusc‚ksc‚„Gplcb€Œ‹r§mµ~usšža/ccq¦Gcb„‹pŽkspƒulnqplnulc-dC3A±4$ š¢pƒ^`š›„

mG„ cq¦Gcb„‹pZkspƒulnqplnulc@½Kw‹ul€cbuƒkm@ulculcb~Tusc‚ksc‚„Gplcb€ plw@‘@cbpl^`c‚uq½mG„€ klcb~Tm@uƒmˆpsc‚€ Œ‹r m§w‹„65TšžpZuscbœ›m@psš›wG„}±

] ^š›k~ulwG~9cbulpNr kƒn`‘@‘GcbklplkZnkZpl^Tmˆp~ulš›a/cµcq¦Gcb„‹pkspƒulnqplnulcbkZmGuscµm‘@wIw`€ a/w`€`cqœŸ w‹uZmbm@„`w‹„`šžqmˆœ

ulcb~Tusc‚ksc‚„Gpƒmˆplš¢w‹„ wˆŸ)£j|ŠT©kq±

$c€c³9„`c£j| Š©°cb¨In`š›¦!mˆœ›cb„qc(m@kpl^c(šžksw‹a/wGuƒ~^`šžklazwˆŸpƒ^`cqšžu%cb¦@c‚„Gp)kspƒulnTplnTuscusc‚~usc‚ksc‚„‹plmˆplš¢w‹„kb±

] ^cbulcŸ wGulc@½Rpƒ^`c/~9w@šž„‹pš›k®psw+‘@š›¦@cZm+€`cbqš›klš¢w‹„=~ulw`cb€TnuscLŸ wGupl^š›kšžksw‹a/wGuƒ~^`šžkla+±] ^`cZ~TwGpsc‚„Gplš›m@œ¢œ›r

(8)

šž„I³9„š¢plcLklšbcŽwˆŸ~ulš›a/ccb¦@cb„‹pjklpluƒnqplnulcbk œ›cbmG€knkjpswqwG„klšž€`cbu³C„`š¢plcwGŒ`xycbpƒkjulcb~ulcbklcb„‹plš›„`‘Zpƒ^`cba+±

$c^`wIwGklc‘Guƒm@~^‘Guƒm@aZaZm@uƒkq½ˆmGkcb¦@c‚„GpKklpluƒnpƒnulcbkKqmG„LŒ9culcb~ulcbklcb„‹psc‚€Œ‹rpƒ^`cqšžuKw!¦Gcbul𛄑j‘Guƒm@~T^kq±

] ^`c/€`cbqš›klš›wG„¯~ulw`cb€Tnusculcqœ›š›cbkw‹„µco`šžksplš›„`‘usc‚kln`œ›plkb½9m@œ¢œ›w!´ šž„`‘psw+€`cbqš›€`cš›„=~9w@œ›r`„`wGa/šžmˆœÌplš›a/c

´^cqpl^cbu pN´w ‘Guƒm@~T^k m@ulc¯šžksw‹aLw‹ul~T^`𛁵w‹u „`wGp 𛄠pl^`c§bm@klc=wˆŸ€`cbpsc‚ula/šž„`š›klpsšž¯‘‹ulmG~^'‘Guƒm@aZaZm@uƒk

‘Gcb„`c‚ulm@psšž„`‘/³9„`š›pscŒTulmG„^`šž„`‘wG„T„`cbqpscb€+‘‹ulmG~^k .Y±] ^`c^mGul€+plcb^„`šžqm@œ%~9w@šž„Gp šžkplwcb„kƒnulcŽpl^`c

³C„`š¢plcLŒuƒm@„T^`𛄑pNrI~9cw@ŸKwGnuj‘Guƒm@~^kb± ] ^`šžkjšžkjaZm@€cpl^Tusw‹n`‘G^µm‘‹ulmGa/aZmGu pluƒm@„ksŸ wGuƒaZmˆplš¢w‹„pƒ^mˆp

cbœ¢šža/š›„Tmˆpsc‚kšž„I³9„`š›pscµŒuƒm@„^š›„`‘¯šž„ ‘‹ulmG~^ ‘Guƒm@aZaZm@uƒkwGŒ`pƒmˆšž„`cb€ Ÿ¡usw‹a £|Š©kb½K´^`š¢œ›c~Tusc‚ksc‚us¦Išž„`‘

c‚¨In`š¢¦!m@œ¢c‚„cŽ~ulwG~9cbulpsš›cbkb±

®nu ~Tm@ulpsšžmˆœRwGuƒ€`cbuulcb~ulcbklcb„‹pƒmˆpsš›wG„wˆŸ)£j|Š©k m@œ¢œ›w!´k(Ÿ wGu mG„c‚¨‹nš¢¦!mˆœ›cb„TcŽ€`cbqš›klš›wG„}±K] ^`šžkš›k m

klplmGuspl𛄑/~9w@šž„‹p wˆŸ)Ÿ wGuƒa/m@œ}usc‚m@klwG„`šž„`‘Zm@Œ9wGn`p |ŠT©kq±

] ^`cŽ~mG~Tc‚uš›kwGul‘GmG„`šqcb€m@k(Ÿ w@œ›œ¢w!´kb¬Š‹cbqpsš›wG„šž„Gpƒusw`€nTcbkpƒ^`c|Š© mG„€ £|Š© Ÿ wGuƒa/m@œ¢šžkƒa±

ŠIcbplš¢w‹„ † €`c³C„`cbkm ~m@ulpsšžmˆœw‹ul€cbuklcbaZm@„‹psšžqkŸ wGu|ŠT© mG„€ £j| Š©±Š‹c‚plš¢w‹„ ‡ usc‚qmˆœ›œžk Œm@klšž

„w@psš›wG„Tkjm@Œ9wGnpjcq¦Gcb„‹pjklpluƒnpƒnulcbkb±®Š‹cbqpsš›wG„ B 𛄋pƒusw`€nqcbkj‘Guƒm@~^µ‘‹ulmGa/aZmGulkb½Tm@„T€°Š‹cbqpsš›wG„ W ‘@š›¦@cbk

m+klcqp®wˆŸuƒn`œ›cbkjŸ wGu®pl^c/‘Gcb„`c‚ulm@psš›wG„¯w@Ÿv‘Guƒm@aZaZm@uƒkjŸ¡usw‹am£|Š©kb±/Š‹cbqpsš›wG„ Cšžk®pl^`cqwGuƒusc‚pl„cbkƒk

~TuswIwˆŸ`Ÿ w‹u)pl^`culnœ¢c‚kq±KŠ‹cbqpsš›wG„®€`cq³9„`cbk)pƒ^`c(c‚¨In`š¢¦!m@œ¢c‚„cŒTcbpN´(cbcb„pN´(w£j|Š©kb±Š‹cbqpsš›wG„‰j‘@š›¦@c‚kmG„

c‚¨In`š¢¦!m@œ¢c‚„c€`c‚šžksš›wG„m@œ¢‘GwGulš¢pƒ^afŸ¡ulwGa ‘Guƒm@~^/‘‹ulmGa/aZmGulkb½ˆŒm@klcb€Zw‹„Zm„`wGuƒaZmˆœ`Ÿ w‹ula w‹a/~Tn`plm@psš›wG„}±

ŠIcbplš¢w‹„§d9`Zkl^`w!´kmklš›aZ~`œ›cŽ~ulwG~9cbulpNr€`cqplcbqpsš›wG„Ÿ¡usw‹a²wGnu ulcb~Tusc‚ksc‚„Gpƒmˆplš¢w‹„}±

-2 4+5 #², 02 45 #

|§cbkƒklm@‘@cŠ‹c‚¨‹ncb„qc®©^m@ulplkjª¡|ŠT©kŸ w‹uvkƒ^`wGulp;«)‘‹ulmG~^`šžqm@œ¢œ›rL€`cq³9„`c®€`š›klplulšžŒn`psc‚€ klrIklpsc‚aZkvm@„T€ w‹a¤

aLn„`šžqm@psš›wG„ǩ9cqpN´cqc‚„Žpl^cvw‹a/~9wG„cb„‹plk%wˆŸ`pl^`šžk)ksr`klpscba+±)] ^`cv~nuƒ~9wGklcwˆŸ`pl^š›k)ksc‚plš¢w‹„š›k%pswj~ulw!¦Iš›€c

pƒ^`culcbmG€`cbu´ š¢pƒ^pl^`cjŸ cbm@plnulcbk(m@„€Z¦GwIbm@Œnœ›mGusrL´(c´ š›œ›œCnklcšž„pl^culcbklpwˆŸÌpƒ^`cmGusplš›qœ¢cuƒmˆpƒ^`cbuvpl^mG„

~Tusw!¦Išž€`𛄑Lm/wGaZ~`œ›cqplc®€cbkƒqulš›~`plš¢w‹„ w@Ÿ%|Š©kª\´^`š›^qmG„Œ9cŸ w‹n„€š›„pl^c ^y]1f„`w‹ula)±›d‚a` C3¡«;±

{ Œ`|ŠT© ª)klplmG„€`šž„`‘Ÿ w‹u(ŒTm@klš›|Š© «(€`cq³9„`cbkm/ksšžaZ~`œ¢c®klqcb„mGusš›wT½‹š›c®mG„ m@Œklpluƒm@qpsš›wG„Zw@Ÿmklr`ksplcba

Œ9cb^TmU¦‹š›wGnTuq± $ š¢pƒ^`šž„+Œ|Š©kb½I~Tusw`c‚klklcbkm@ulcqmˆœ›œ›cb€

]#' #

½mG„€mGuscusc‚~ulcbklcb„‹psc‚€ Œ‹r m¦Gcbulpsšžqmˆœ

mˆo`š›kb½Gm@œ¢w‹„`‘Ž´^`šž^Zcq¦@c‚„‹plkmGusc~npvšž„mŽpsw‹~€`w!´„/wGuƒ€`cbub±|§cbkƒklm@‘@cco^mG„`‘@c‚kKm@ulcusc‚~usc‚ksc‚„‹pscb€ZŒ‹r

mGululw!´kRœžm@Œ9cqœ›cb€Œ‹rŽa/cbkƒklm@‘@cv„mGa/cbk}Ÿ¡ulwGa pƒ^`cvc‚aLš›pspl𛄑plwpl^`culcbcbš¢¦Išž„`‘šž„klplm@„Tc@± w®m@kƒklnaZ~`plš¢w‹„

´^TmˆplklwIcq¦Gcbušžk®a/mG€`cLmGŒTw‹n`p®pl^`cZw‹a/aLn„`šžqm@psš›wG„¯a/cb€`šžna+± &E𢑋nulc d/kƒnaZaZm@ulšbcbkjpl^`cZ€`šCc‚usc‚„Gp

‹šž„€+wˆŸ)cq¦@c‚„‹plkpl^TmˆpqmG„Œ9cŸ wGnT„€+´ š¢pƒ^`𛄵mZŒ`|ŠT©±

{ Œ`| Š© €c³9„`c‚kmZ~ulcbc‚€`cb„TcŽuscbœ›m@psš›wG„ŒTcbpN´(cbcb„+cq¦Gcb„‹plk¬

%

pl^`cŽc‚a/š›kƒksš›wG„wˆŸKmZa/cbkƒklm@‘@c~usc‚c‚€`cbkš›plk ulcbqcb~`plš¢w‹„}±

%

Ÿ wGumG„‹r¯cq¦@c‚„‹pG½)mˆœ›œKcq¦Gcb„‹plkŽklš¢pƒnmˆplcb€ n~~9cbupl^mG„wG„°pl^`c kƒm@a/cšž„kspƒm@„qcm!o`š›kŽmGusc~ulc¤

€`cbqcbkƒksw‹ulkwˆŸ‹±§] ^`cwGuƒ€`cbuwG„ pl^c+mˆoIšžkbm@„ Œ9culcqœžm!o`cb€ šž„ klwGa/c~mGuspƒkw@Ÿpl^`cš›„klplmG„c

qm@œ¢œ›cb€ $ g ± ] ^`cbklcqwˆ¤Nuscb‘@š›wG„kmGuscusc‚~usc‚ksc‚„‹pscb€ Œ‹r €mGkl^`c‚€ ~mGuspƒkwˆŸpl^`cš›„klplmG„c

m!o`šžkq±RZ¦Gcb„‹plk klš¢pƒnmˆplcb€š›„µmZw@¤Aulcq‘Gš¢w‹„ m@ulc„`w@p „`c‚cbkƒkƒm@ulš¢œ›rwG„Tqnuƒusc‚„‹p¬Kpƒ^`cqšžuwGuƒ€`cbušžk „`w@p

kl~9cbqš³9cb€+r@cbpq½`wGušžk„`wGpš›aZ~9wGulplm@„‹pŸ wGupƒ^`ckƒ~Tc‚š¢³9qm@psš›wG„}±

] ^`cklcqpw@Ÿ³9„š¢plcŒ`|Š©k šžk €`c‚„`w@plcb€µŒ‹r ±

(9)

W

a

m

m

Timer 1

Message events

Timer Events

Instance events

Timer 1

Timer 1

Set

Timeout Reset

Creation

Internal action Stop Receiving

Sending

&E𢑋nuscZdG¬ &9cbm@plnulcbkw@ŸEŒ`| Š©k

A B

timer1

timer1 m1

m2

a1 a2

a3 a4

a5 a6

&Eš›‘Gnulc`¬{„cqom@aZ~`œ›cŒ|Š©±

(10)

{ Œ|Š© €`c³9„cbkwG„œ¢rwG„`cŽkƒcb„Tm@ulš¢w9±3ZKo`plcb„€`šž„`‘Œ|Š©k ulcb¨In`šžusc‚k m/^𢑋^`cbus¤Yœ›cq¦Gcqœ}„`wGplmˆplš¢w‹„}½m@„T€

m@œ¢œ›w!´ šž„`‘ZŸ wGujpl^`cZkl~9cbqš³Cqmˆplš¢w‹„µwˆŸvm klcqpƒkjw@Ÿvklqcb„mGusšY½9aZmG€`cwˆŸvqwGaLŒ`š›„Tmˆpsš›wG„TkwˆŸvŒ|Š©kb±£j|ŠT©

klplmG„€kŸ wGu£jš›‘G^I¤Aœ¢cb¦@cbœ%|Š©±}{ £j|Š© qm@„¯Œ9cZkscbcb„¯m@k®m ‘‹ulmG~^}½9pl^`cZ„`w`€`cbkjwˆŸ´^`šž^=mGusc/kspƒm@ulp

„wI€cbkb½`cb„€µ„`w`€`c‚kq½Œ`| Š©kq½9wG„T„`cbqpsš›wG„+ksr`aŒ9w@œžkb½wG„T€`š¢plš¢w‹„kb½`wGu ulcŸ cbulcb„Tcbkplw/wGpl^`c‚u£j|ŠT©kq±

£|Š©kmˆœ›œ¢w!´kŸ wGu(pl^`cnklcjw@Ÿmˆœ›psc‚ul„m@psš›¦@c‚kq½‹m@„€pƒ^`cbulcŸ w‹usc®€`c³C„`c®klcqpƒkvw@Ÿ%klqcb„mGusšY±)£j|Š©

šž„ &E𢑋nuscކZ€`cq³9„`cbkpN´w~Tw‹klklšžŒ`œ¢cŽkƒc‚„m@ulš\½ulcb~Tusc‚ksc‚„Gplcb€š›„ &E𢑋nulc®‡9±

A B

m1 M1

A B

m2

M2 M3

m3

A B

&)š›‘GnTuscކ¬K£|Š©ª\´ š¢pƒ^µ„`wG„I¤Aœ›wIbmˆœÌ^`wGš›qcU«

A B

m1

m2

A B

m1 m3

&E𢑋nulc®‡9¬vŠIc‚„m@ulšÌ€`c³C„`cb€µŒ‹r pl^cŽ£j|Š© šž„#&Eš›‘Gnulcކ

{f£|Š© qm@„+mˆœžklwZ€cbkƒqulš›Œ9cŽm@„š›„I³C„`š¢plcŒ9cb^mU¦Iš›wGnub½`m@kšž„#&Eš›‘Gnulc!B`±

] ^`culcb~ulcbklcb„‹pƒmˆpsš›wG„µw@Ÿ(klrIklpsc‚aŒTc‚^mU¦Iš¢w‹nuƒk´ š›pl^°|Š©kmˆœ›œ¢w!´kjŸ wGu®pƒ^`cLšž„‹plulw`€nplš¢w‹„=w@Ÿ(n„I¤

€cbklš›uƒm@Œ`œ›c¯Ÿ c‚mˆplnTusc‚kq± &9wGucom@aZ~`œ›c@½ £|Š© ~ulcbklcb„‹plcb€ šž„ &E𢑋nusc°† šž„œžn€`c‚km@„ coœžnklš¢¦Gc

(11)

B C

b2 c2

A B C

a b1

c1

D

d

M1 M2

M3

&Eš›‘Gnulc!B`¬K£|Š©

€š›klplulš›ŒTn`psc‚€+^w@šžcŽŒTcbpN´(cbcb„+pN´wZkƒc‚„m@ulšŽm@„T€ˆ±(©(wG„Tksc‚¨‹ncb„‹psœ›r@½`pƒ^`cpN´wZ~9wGkƒklš›Œ`œ›cŽklqcb„mGusš

€cbkƒqulš›Œ9cb€ZŒ‹r mGusc jm@„€±)]%wŒ9cjqwG„klš›klplmG„‹pK´ š¢pƒ^pl^`ckl~9cbqš³9bmˆplš¢w‹„}½GmG„Zš›aZ~`œ›c¤

a/c‚„Gpƒmˆplš¢w‹„L´ š›œ›œC^mU¦Gc pswŽc‚„klnTuscpƒ^mˆpvwG„`œ›rLpƒ^`cbklcpN´wklqcb„mGusš9qm@„ZŒ9c~9cbusŸ wGuƒa/cb€}±E{jkvpl^`c®€`cbqš›klš¢w‹„

plw~Tc‚uyŸ w‹ulawGušžk€`šžkspƒusšžŒn`plcb€}½Gpl^`šžkvbm@„pKŒTc€`wG„`c´ š›pl^`w‹n`pmŽklrI„T^usw‹„`šbmˆplš¢w‹„Œ9cqpN´cqc‚„/{

mG„€±!] ^`šžkEksš›plnm@psš›wG„´ š¢œ›œ`ŒTc qm@œ¢œ›cb€Lm

G ]]

±vŠ‹c‚plš¢w‹„ dG`®€`c‚klbusšžŒTc‚kmG„`w@pƒ^`cbu)~ulwGŒ`œ›cba+½

bmˆœ›œ¢c‚€ %$G *( \ ±ŠIn^ ŒmG€°~Tusw‹~Tc‚usplš¢c‚kw@Ÿm+ksr`klpsc‚a €`cbkƒqulšž~`psš›wG„uscbš›„`Ÿ wGuƒcbkpl^c „`cqc‚€

Ÿ w‹uŸ wGuƒaZmˆœÌaZm@„`šž~n`œžmˆplš¢w‹„w@Ÿ|ŠT©kq±

!#"$%'&)( $* ,+.-0/- /

$cj„`w!´ €`cq³9„`cmށw‹„‹¦@cb„š¢c‚„Gp„w@plm@psš›wG„LŸ wGuva/mG„`šž~n`œžmˆpsšž„`‘Ž£|Š©kb±)£|Š©k€c³9„`ckscbpwˆŸ}klqcb„mGusš

pƒ^mˆpbm@„ŒTc€`c³9„cb€ Œ‹r§uscb‘Gn`œžm@u®cqo`~Tusc‚klklš¢w‹„kw!¦@c‚uŒ`|Š©kb± ]%w¯c‚m@^°£j|ŠT©½Ì´(c mGklklw`šžmˆplc/mG„

cqo~usc‚klklš›wG„=¬ ¬›¬2143657 598

:;

=<><? : :

5A@ CBEDGFIHJK57D ½`´^`c‚uscLNM š›kmŒ|Š©½POTš›km

klcb¨In`c‚„cwG~9cbuƒmˆpsw‹uq½Q3®€cb„`wGpscbkjpl^`cLcb„€µw@Ÿvm£j| Š©½QR š›k®m Œ9wGn„T€¯¦!m@ulš›mGŒ`œ¢cG½ 8

:;

E<><? : :

šžkjm

=g

wG„=m³9„`š›pscZ„InaŒ9cbuwˆŸvcqo~usc‚klklš›wG„kjwˆŸpl^c‹šž„€S Z½RmG„€G@ CB€cb„`wGpscbk®ulcbqnTulklš¢w‹„}± &TwGu

m‘@š›¦@c‚„-9½

: :

´ š¢œ›œKŒTc/qmˆœ›œ›cb€=m

)$ =

w@Ÿvpl^`c/^`w@šžcG±{„¯š›„Tkspƒm@„qcšžkkƒmˆšž€¯psw+ŒTc a

šž„

mŒuƒm@„^µš¢Ÿvš›p®~9cbusŸ wGuƒaZkjmˆpœ¢c‚m@klpmG„=m@qpsš›wG„¯šž„=pƒ^`š›k®Œuƒm@„^̱] ^`c/co~ulcbkƒksš›wG„µmGklklw`šžmˆpsc‚€µpsw+pl^`c

£|Š© 𛄠&Eš›‘Gnulc!Bšžk ¬¢¬21T@ CBEDGFIH.DVUWTX*Y.DSJ±

Z [

"% ",+ " # q(# ! " 2 45 #

"\/ ]_^"$a`*+#"\!cb$Q]K$

¥cqpnTkw‹„klš›€`c‚um Œ|Š©d €`cbkƒqulš›Œš›„`‘ pƒ^`c°Œ9cb^TmU¦‹š›wGnTuwˆŸm ³9„š¢plc°klcqp w@Ÿš›„klplmG„c‚kq½ bmˆœ›œ¢c‚€

e ^cbulcbm!Ÿ plcbub±']´w cq¦Gcb„‹plkZ~9cbusŸ wGuƒaLc‚€ Œ‹r pƒ^`c=kƒm@a/cšž„klplmG„c¯m@ulc+wGuƒ€`cbulcb€ m@qqwGuƒ€`šž„`‘°plw pl^`cbš›u

(12)

qwIwGuƒ€`š›„Tmˆpsc‚kw‹„ pl^cšž„klplm@„Tcmˆo`š›kb½`~usw!¦Išž€`cb€Zpƒ^`cqr mGusc®„`w@pšž„mqwGulcq‘Gš¢w‹„}±3^AŸpl^`cbr m@ulc~9cbusŸ wGuƒaLc‚€

Œ‹r €`šCc‚usc‚„‹pLšž„klplm@„Tcbkb½Kpl^cqr m@ulcw‹ul€`c‚usc‚€ šŸ®m@„€ w‹„`œ›rš¢Ÿjpƒ^`cqr mGusc+ksc‚~m@uƒmˆplcb€ Œ‹r mˆpœ›cbmGkspLwG„`c

a/c‚klkƒmˆ‘Gcco^mG„`‘@cG±®Š‹wT½}m| Š©f€`cq³9„`cbk®m~Tm@ulpsšžmˆœ%w‹ul€cbujŒ9cqpN´cqc‚„¯cq¦Gcb„‹plkb±^y„ &E𢑋nusc/`½ m@„T€

m@ulc/wGuƒ€`cbulcb€}½Œn`p*/m@„€,/mGusc„`wGpq±Z] ^`c klcbaZm@„‹psšžqk®w@ŸmµŒ`|Š© qmG„§Œ9cZŸ wGuƒaZmˆœ›šbcb€§Œ‹r§m

~9wGklcqp e ´^`cbulc$šžk®m+klcqpwˆŸvcb¦@c‚„Gpƒkq½ š›km+~m@ulpsšžmˆœEw‹ul€`c‚uulcqœžmˆplš¢w‹„ ªYusc 5Tco`š›¦@c@½

pƒulmG„klš¢plš¢¦GcmG„€µm@„‹psšžklrIaZa/cqpƒusšžŽŒ`šž„m@ulrulcqœžmˆplš¢w‹„9«(wG„ qm@œ¢œ›cb€ NR(a"%(c -$ ½…š›k

mZklcqp w@Ÿ)mˆplwGa/šž®mGplš¢w‹„k „m@a/c‚kq½mG„€ š›km/œžm@Œ9cqœ›š›„‘LŸ¡nT„plš¢w‹„Ÿ¡ulwGa plweT±

­š›¦@c‚„°mG„=cq¦Gcb„‹p M½Ì´cL´ulš¢plc HAJ "!´^`c‚„§cb¦@c‚„Gp šžk~Tc‚uyŸ w‹ula/cb€Œ‹r¯š›„Tkspƒm@„qc! MWe

H$#%M&45' HAJ(4H)*+!#Jƒ«;±

¥cqpc ,- . / e ²m@„€W ,- . e &ŒTc+pN´(w§|Š©kb±] ^`c

w@Ÿ mG„€ ½´ulš¢plpsc‚„ (0 š›k€c³9„`c‚€Œ‹r°¬

(0 ,1 32 46587+9/5;:<= 2 32 e 2 e ޽´^cbulc@¬

6587+9/5;: 1 >2 ?2@ H J M& 5

#'HBA BA J M (C HBA J3D HBA J C BA C BA 'E

|=w‹uscv𛄋plnš¢plš¢¦Gcqœ›r@½!mw‹„qm@psc‚„mˆplš¢w‹„1s‘@œžn`c‚kKpswG‘@cqpƒ^`cbuÌpN´(w| Š©k%m@œ¢w‹„`‘ pl^`cbš›u)w‹aZaLw‹„®š›„klplmG„c

mˆo`š›kb±

"\/ ] ( "$a`*+."! -$Y] $1F"GV+!.+.

©(œ›cbmGusœ›r@½£j|ŠT©kL€`cq³9„`cklcqpƒkŽwˆŸkƒc‚„m@ulš\½)pl^Tmˆp´ š›œ¢œŒTc+qm@œ¢œ›cb€ %g# $(c<H-# ª¡t &zŸ wGu

kƒ^`w‹usp«^`cbulcbmˆŸ pscbub±1$°cLqm@„¯€c³9„`c𛄀Tnplš¢¦Gcqœ›r+mZt & w@ŸEšž„€`cqo&I}½9„`wGpscb€J

:

½9m@kƒklwIqš›m@psc‚€plwm@„‹r

£|Š© M HK .ML;.@ CB' 3EJ®¬

%ON

>J HJ3 @BP%E

% J : H3EJ3

@BP%E

% J :

HJ3 @ 0>Q 5 Q MJ

:SR AHJ E

% J : HTL

U;

E<><? U U

J3 V

U;

E<><? H @ U 0>Q

U 5 Q U MWJ

:SR H UJ E J

% J : H@ CBEDWHJ.J(XJ

:SR

7H(YZ?[\^]/_a`bZ <dcfe4gihJ

¥cqpkj €`cb„w@pscpƒ^`cklcqpw@Ÿ´cqœ›œKŸ w‹n„€`c‚€ ~m@ulpsšžmˆœw‹ul€cbu®Ÿ¡m@a/š›œ¢š›cbkb±+¥%cqpkJ9M1j Œ9cm¯~m@ulpsšžmˆœ

w‹ul€cbuvŸ¡m@a/š¢œ›r m@„T€ Q Œ9cŽm@„wGuƒ€`cbu(wˆŸ^J+±] ^`c

$%l

wˆŸEm@„ cb¦@c‚„Gp wˆŸ Q š›kpƒ^`cŽn~~9cbuŒ9wGn„€wˆŸ)pl^`c

œ›cb„‘@pl^wˆŸEcq¦Gcbulr kspƒusšžplœ¢r€`cbbusc‚m@klš›„`‘Zklcb¨In`cb„TcŽkspƒm@ulpsšž„`‘/Ÿ¡usw‹a ‹±

$c„`[email protected]

Q

J½IŸ wGuporqts/pl^`ckƒnŒklcqpwˆŸ

Q

aZmG€`cwˆŸEcq¦@c‚„‹plkwˆŸEulmG„ œ›cbkƒkwGuc‚¨‹nTmˆœ}pl^Tm@„Woy±

¥cqp Q mG„€uŒTcŽplwZ´(cbœ¢œ¢¤\Ÿ w‹n„€`c‚€µ~Tw‹kscbplkb± $c€`cq³9„`cŽpl^c€`š›klplmG„cŽŒ9cqpN´cqc‚„ Q m@„€vum@k ¬

w HQ au*J( X R*x Ufy{z

n)|}4~cfSg)€  }4~cƒ‚Mg…„

¥cqppJVMj mG„€W†dMj Œ9cŽpN´w/t &±9] ^`cŽ€`š›klplmG„cŽŒ9cqpN´cqc‚„J$m@„€†$š›k€cbŒ`šž„`cb€µŒ‹r=¬

w H)J‡† J( ˆ!b‰

Š‹Œ6=Ž

H)ˆW Hw HQ au*JK5aHQ au*J M,J J

(13)

{k

w HJW/† J U w

H…† J?q

w

H)J

w

H)J‡† J

w

H…† +JcJ½Cm@„€

w HJW/† J Ds J-D†=½

w

šžk mZ€`šžkspƒm@„qcm@„€°ª…j w

«(šžkmZwGaZ~`œ›cqplcŽaLcbplulš›Žkƒ~mGc@±

N

4MHK .‡L; @ B< 3EJMH J : HJ J

:

šžkm ©m@n^‹r klcb¨In`cb„TcZ¬

HN

3pts=‡# qts5

N

‰+ˆ qw HJ y HJM+J

x HJ J %3EJ±

] ^`c‚uscqŸ wGulc@½ HJ : HJ.J

:

wG„‹¦Gcbul‘@cbkb½@mG„€Zš¢pƒkvœ›šžaLš›pvšžkv„w@psc‚€J HJ±] ^cj~m@ulpsšžmˆœ9wGuƒ€`cbuKŸ¡m@a/š¢œ›r

mGklklw`šžmˆplcb€ plwmZ£j|Š© t š›k>J H

4 ")v)") #

{²~Tusšža/c/cb¦@c‚„GpŽklpluƒnpƒnulc+ªZŠ=Ÿ wGuŽkƒ^`wGulp;«šžkŽm

W

¤Apln~œ¢c" eO ´^`c‚usc Z½{ ½

mG„€^mU¦@cjpl^`cklmGa/cja/cbm@„š›„`‘Lpl^mG„šž„ ksc‚plš¢w‹„ †±›d@½Im@„€Kšžk(mLksr`aZa/cqplulšžjm@„‹plš¤Nusc 5Tco`š›¦@cŒ`šž„mGusr

ulcqœžmˆplš¢w‹„bmˆœ›œ¢c‚€ $ ½9kƒn^pƒ^mˆpެ

N M

N A M A

N AA M H A AA AAJLªpl^`cZw‹„65TšžpƒkmGuscLš›„^cbulš¢plcb€

pl^ulwGn‘G^+qm@nTklm@œ¢š›pNr uscbœ›m@psš›wG„9«±

{„Zcq¦@c‚„‹pkspƒulnqplnulc €`c³C„`cbkmŽ€wGaZmˆšž„/wˆŸ

$ g

½@pƒ^mˆp(qm@„/Œ9cjkscbcb„Zm@kv~Tw‹klklš›Œœ¢c klplmˆplcbk

w@ŸTpl^cklr`ksplcba+±){'w‹„I³T‘‹nulm@psš›wG„šžkEmkƒnŒklcqp©wˆŸ&Z°pƒ^mˆp)š›kEqwG„65Tšžps¤\Ÿ¡ulcqcª

N M # A M 5 A«;½

mG„€§€w!´„G´m@uƒ€I¤Nœ›wGklcb€ª

N

M A A M!«;±&TwGuŸ¡nulpl^cbuusc‚m@€`šž„`‘wG„=cb¦@c‚„Gpklpluƒnpƒnusc‚kq½

qwG„kƒn`œ›p dC3Y±

] ^`c

%g$

Œ9cqpN´cqc‚„pN´w ZŠIk šžk „`wGpscb€" "

mG„€š›k pƒ^`c ZЧ¬

" "

,

2

*

>2

#

2

޽Ikƒn^pl^Tmˆp$(TH…

J 2

H)

J 2

42

±

$cŽ‘@c‚„`cbuƒmˆœ›šbcpƒ^`c„`wGplmˆplš¢w‹„plw m@„+m@uƒŒ`š›pluƒm@ulrZ„InaLŒTc‚u wˆŸ2ZŠ´ š¢pƒ^

U; E<><

y

H%"

U

{„cb¦@cb„‹p)kspƒulnqplnulcqm@„LŒTculcb~ulcbklcb„‹psc‚€Œ‹rm‘‹ulmG~^Ž´^`šž^mGklklw`šžmˆpsc‚kmj¦@c‚usplcoŽpsw®cbmG^Žcq¦Gcb„‹pq½

mG„€mpNr`~9cb€cb€‘@cZpsw¯c‚m@^§qwG„659š›qpm@„€°cbmG^°~m@š›ušž„°pl^`cw‹ul€`c‚uŽuscbœ›m@psš›wG„}±^y„I³9„š¢plcŒTc‚^mU¦Iš¢w‹nuƒk

œ›cbmG€/pswŽšž„I³9„`š›psc‘‹ulmG~^kb± ®„IŸ wGulpln„Tmˆpscbœ¢rG½@pƒ^`cjulcbkƒn`œ¢pl𛄑®‘‹ulmG~^/š›kv„`w@p„`c‚c‚klkƒm@ulš¢œ›rmŽulcq‘‹n`œ›mGu)‘Guƒm@~^}½

´^š›^+a/cbm@„Tkpl^m@p š¢pbm@„+„`w@pm@œ¢´mUr`kŒ9c‘@c‚„`cbuƒmˆplcb€+ŒGrmL‘‹ulmG~^‘Guƒm@aZaZm@ub±

{ ³9uƒksp®š›„‹pƒn`š¢plš¢¦GcLklw@œžn`psš›wG„§š›kpswµulcb~ulcbklcb„‹pw‹„`œ¢r¯a/šž„`š›aZm@œEqwG„659š›qplkb½RmG„€=pƒ^`cZw!¦@c‚usšž„`‘w@Ÿvpl^`c

bm@nkƒmˆœ›š›pNrw‹ul€cbub± ] ^`cµw@pƒ^`cbuZw‹„65TšžpZm@„€'qmGnkƒmˆœ›š¢pNr cb€‘@cbkZbm@„ Œ9c=€`c‚€nplcb€ Ÿ¡usw‹a pl^`cµ‘‹ulmG~^

ulcb~Tusc‚ksc‚„Gpƒmˆplš¢w‹„}½9nklšž„`‘pƒ^`c/qwG„659š›qpjšž„^`cbulš›plm@„TcL~Tusw‹~Tc‚uspNrµm@„€=pl^`c/pluƒm@„klš›ps𛦋š›pNrµwˆŸpƒ^`cLw‹ul€cbujulc¤

œžmˆplš¢w‹„}±!®„IŸ wGulpln„Tmˆpscbœ¢rG½9mG„cb¦@c‚„Gp bm@„µusc‚aZmˆšž„+qwG„„cbplcb€+psw mG„+š›„I³C„`š¢plc„InaŒ9cbuwˆŸEcq¦@c‚„‹plk ¦Išžm/m

qwG„659š›qpq½m@„T€w‹nu‘Guƒm@~^+aZmUr ksplš¢œ›œ%„`wGpŒTcŽulcq‘‹n`œ›mGu®¬KšŸE´(cpƒusr ‘Gcb„`c‚ulm@psšž„`‘ZmL‘‹ulmG~^Ÿ wGupl^c®cb¦@c‚„Gp

klpluƒnqplnulculcb~ulcbklcb„‹plm@psš›wG„wˆŸpƒ^`c£|Š© šž„ &Eš›‘Gnulc

W

½E´cw‹Œ`plm@𛄠pƒ^`c‘‹ulmG~^𛄠&E𢑋nusc CI±Gr

ulcbklplulšžpsšž„`‘Lpl^`šžk‘Guƒm@~^psw/cq¦Gcb„‹plkœžm@Œ9cqœ›cb€+ŒGrm@„€+w‹„65Tšžpcb€`‘Gcbkb½`´(cqmG„ co`pƒulmGppl^`c‘Guƒm@~T^ šž„

&Eš›‘GnulcŽ½`´^`šž^š›km/´cqœ›œ:I„`w!´„šžuƒuscb‘Gn`œžm@u(‘Guƒm@~^̱

^y„/wGuƒ€`c‚u%plwklw@œ›¦@cpl^c~usw‹Œ`œ›cba w@ŸCulcq‘Gnœ›mGusš›pNrށqm@nTksc‚€Œ‹rw‹„65TšžpEcb€‘@cbkEšž„Lpl^`c ‘‹ulmG~^ulcb~ulcbklcb„`¤

pƒmˆplš¢w‹„w@Ÿm@„µcq¦Gcb„‹pklpluƒnpƒnuscG½T´c€`c³C„`cLm„`cb´fpNrI~9cw@ŸEc‚€`‘@cG½9bmˆœ›œ¢c‚€+qwG„659š›qpš›„T^`cbulš¢pƒm@„qcŽcb€`‘Gc@±

] ^š›kulcqœžmˆplš¢w‹„=´ š›œ¢œ(mˆœ›œ¢w!´ m@„cq¦Gcb„‹p A pswµš›„T^`cbulš¢pm@œ¢œ(wG„ 5Tš›qplk®Ÿ¡ulwGa3m@„°cq¦@c‚„‹pG½´ š¢pƒ^`wGnpŒTcbš›„`‘

bm@nkƒmˆœ›œ›r €`cb~9cb„€Tm@„‹p wG„ ‹±

{„dZŠ+qm@„+Œ9cusc‚~usc‚ksc‚„‹pscb€Œ‹rm

# a$ %*

¬pt'&)( *

`

/(/e޽kƒn^pƒ^mˆpެ

%

&+(1

@ H AJ ML5-, AC ,# AA M&.&

@

AE AA AE

šžk pƒ^`cw!¦Gcbulš›„`‘LwˆŸ ޽

(14)

A M1

a

M2 B

b

&E𢑋nusc W ¬)£|Š© ´ š›pl^µm@„š›uƒulcq‘Gnœ›mGuŠ\Z ulcb~ulcbklcb„‹pƒmˆpsš›wG„

#

# #

# # #

#

# #

#

#

#

#

a #

a

a b

b

b

b a

a b

b a

b a

&E𢑋nulc!C`¬ ^yululcq‘‹n`œžm@u Š\Z ‘Guƒm@~^ Ÿ wGu£j| Š© wˆŸ&Eš›‘Gnulc

W

a a a a

# # #

#

#

# #

&Eš›‘GnulcŽ¬K{j„+šžululcq‘‹n`œ›mGuklnŒ‘Guƒm@~^co`pluƒm@qpscb€Ÿ¡ulwGa²pƒ^`cŽ‘Guƒm@~^𛄠&Eš›‘GnulcVC

(15)

% * šžk m@„µw‹„65Tšžpš›„T^`cbulš¢pƒm@„qcŽuscbœ›m@psš›wG„°ª * N A M& 5 A A

«½

% ` š›k pƒ^`cklcqpwˆŸKa/š›„`šžaZmˆœÌqwG„65Tšžpƒkq½Tš\±c@± @ H A

J)5,# C H

A

* AJ C E ±

] ^`cށqwG„65Tšžpšž„^`cbulš›plm@„Tcuscbœ›m@psš›wG„m@œ¢œ›w!´knkpswZ‘@c‚„`cbuƒmˆplcw!¦Gcbul𛄑‘Guƒm@~^Tk(kƒn^pl^m@pm³9„`š›psc

klcqpw@ŸEqwG„65Tšžpc‚€`‘@c‚k kspƒm@ulplkŸ¡ulwGa&mG„Grcq¦@c‚„‹p LMW ª @ L5<# A ` AE š›k³C„`š¢plcU«±

{²qw!¦@cbulšž„`‘‘‹ulmG~^=w@Ÿpƒ^`ccq¦Gcb„‹pŽkspƒulnTplnTuscZwˆŸ1&E𢑋nulc*Cšžkulcb~ulcbklcb„‹psc‚€=šž„ &)š›‘GnTusc‰±&)( š›k

ulcb~Tusc‚ksc‚„Gplcb€°ŒGr=klšža/~œ¢c mGululw!´kq½*šžkŽusc‚~ulcbklcb„‹psc‚€§Œ‹r§€`wGpspsc‚€°mGululw!´kb½RmG„€ jšžkŽulcb~ulcbklcb„‹psc‚€§Œ‹r

mG„c‚€`‘@cœžm@Œ9cqœ›œ¢c‚€µŒGr ±

a b

a b a b

a b a b a ba b

#

# #

# # # #

&Eš›‘Gnulcމ¬Egcb‘Gn`œžm@u qw!¦@cbulšž„`‘‘‹ulmG~^Ÿ w‹u£j|Š© &E𢑋nulc W

")* ") ")#

®„œ¢r m kƒ^`wGulp/𛄋plulw`€nqpsš›wG„'psw ‘Guƒm@~T^ ‘Guƒm@aZaZm@uƒkLš›kZ‘Gš¢¦Gcb„}± &Tw‹u/Ÿ¡nulpl^`c‚uusc‚m@€`šž„`‘T½ ‡ aZmUr ŒTc

qwG„kƒn`œ›psc‚€}±

)( $*$Y" (

+ %a$ %* ­ š›kmL~mˆšžu HLHJ HJ.J½`´^`cbulc HJKšžkm³C„`š¢plc‘‹ulmG~^}½Im@„€HJvšžkmLkscbp(w@Ÿ

^‹r`~9cbuƒm@uƒqkb±{j„ N+ %g$ šžk(m´(w‹ul€oCAFF

y

½I´^`š›^ œ›mGŒTcbœ o%ŒTcbœ¢w‹„`‘Gk(psw/m@„ m@œ›~^Tm@Œ9cqpv¥(½‹mG„€ ´^cbulc

@ UE m@ulc¦@c‚usplš›qcbkEwˆŸLHJ± ®„/pl^`cj^‹r`~9cbul‘Guƒm@~^/usc‚~ulcbklcb„‹psc‚€šž„&)š›‘GnTuscŽd9`½@pƒ^`c ¦@c‚usplš›qcbk{<!

mGusc®œ›š›„ @cb€µŒ‹rm@„+^‹r`~Tc‚ulmGulœ›mGŒTcbœ¢c‚€µŒGr±(ŠIn^µmG„^‹r`~Tc‚ulmGul´ š›œ¢œÌpƒ^`cb„µŒ9c„`w@plcb€ ±

" $*"( 0$*"G-G "$

{ $#%a 'HH qwG„klšžkspƒk 𛄝mG„µ^Gr`~9cbul‘Guƒm@~^#

bmˆœ›œ¢c‚€pƒ^`c !$a<H w@Ÿ)pƒ^`c‘Guƒm@aZaZm@ub½m@„T€w@ŸEm

klcqp>mw@ŸKulcq´ulš›psšž„`‘uln`œ›cbkb±({ uscb´usš›psšž„`‘ulnœ¢cŽšžkjm~m@š›uLHD J½´^cbulc DšžkmG„¯^Gr`~9cbuƒm@uƒˆ½mG„€

šžk pƒ^`c^‹r`~Tc‚us‘‹ulmG~^ulcq´ulš¢plpsc‚„Ÿ¡ulwGa D k ¦@c‚usplš›qcbkb±!$°c´ š¢œ›œÌwˆŸ plcb„µ´ulš¢plcŽpl^`šžkjuƒn`œ›c D&%' ±&9wGu mG„

^‹r`~9cbul‘Guƒm@~^| ½`´(c„w@psc &)(

(*)

Z

ŸE|qmG„Œ9cuscb´usš›psplcb„𛄋plw Œ‹r+usc‚~`œ›mGšž„`‘ R…ŒGr£ š›„+| ±

(16)

s3 s1

s4 s5

s2

s6 A

&Eš›‘GnulcZdG`T¬)£r`~Tc‚us‘‹ulmG~^

{ ( $ (a#

w@ŸEmG„^‹r`~9cbul‘Guƒm@~^# ŒGrmuln`œ›ccHD J MWm šžkm@„µ^‹r`~Tc‚us‘‹ulmG~^ A klnT^

pƒ^mˆp A YZ?[\ } h± $c/´ulš›psc &+(

(*)

cZ )} g A±Z{²ksc‚¨In`cb„qcLw@Ÿ€`šžulcbpŽ€`c‚usš›¦!mˆplš¢w‹„k &+(

(*) cZ 7 )

}^7 g

&+(

(*) cZ : )} :g

FFF &)(

(*) cZ

)} g y

šžk qm@œ¢œ›cb€+m

(a# a ±

$ (a# ‘Gcb„`c‚ulm@œ¢šqc‚k€š›ulcbqp€cbulš¢¦!mˆplš¢w‹„}½Œ‹rc‚„m@Œ`œ›šž„`‘ksšžan`œ›plmG„`cqw‹nk ^‹r`~Tc‚ulmGulbkulc¤

~œ›mGcba/c‚„Gpƒkq±-$c´ulš›psc

(

š›kLm§~mGulm@œ¢œ›cqœ(€`cbulš¢¦!m@psš›wG„ wˆŸ | Œ‹rK«Žš'pƒ^`cbulc cqoIšžklplkm

klcqpwˆŸjuƒn`œ¢c‚k HD JEFFFHD y

y

JŽwˆŸ(½K| w‹aZ~usšžklcbkcqom@plœ¢r‰ ^‹rI~9cbuƒm@uƒqkb½mG„€ Ÿ w‹um@„‹r

~9cbuƒanplmˆplš¢w‹„ wG„ @ FF‰ E ½* &+(

( )cZ 7

)} 7

g FFF &)(

(*)

cZ )} g ±

$c„`w@plcÌpƒ^`cŽ~usw@xycbqpsš›wG„ w@Ÿ)mG„^‹r`~Tc‚us‘‹ulmG~^| wG„š¢pƒk psc‚ula/šž„mˆœRc‚€`‘@c‚kq±$c„`w@plc

HTJ

pƒ^`c ~Tw‹klklš›Œœ¢r šž„I³9„`š›psc‘Guƒm@~^ ‘Gcb„`c‚ulm@psc‚€ Ÿ wGuƒa | ½€c³9„`c‚€ Œ‹r

HTJ V y y HTJA½´^cbulc

HTJ( m@„T€

y HTJ(

(

y

HTJ±

")* ") " ")q !")

02 45

b( $Y" `*+.-0/- / -"!0P$Y+./ $*"(

¥cqpe Œ9c§m klcqpwˆŸšž„kspƒm@„qcbkb½ M m |Š©½vmG„€# @*HTJ, "'&+( * e $š›plk

qw!¦@c‚usšž„`‘‘‹ulmG~^}±$c€`c³9„cŽpl^`c®Ÿ w@œ›œ›w!´ š›„`‘Zw‹~Tc‚ulm@psš›wG„k®¬

% " U @ 6M"5< HCJ( ! E H)!0Me

% e ‰ Q H$ @*HTJ.J @ M"5 N A

M" H

A

CJ ,M & ( E ¬a/š›„`šžaZmˆœ}cb¦@cb„‹pƒkwˆŸ%P@*H TJ´Ž±ub±p & ( ±

%

"&(' H @*H TJ.J3 @ 6M "%5

N A M"r H{ AJ ,M &+( E ¬aZm!o`šžaZmˆœ}cq¦Gcb„‹plkw@Ÿ @YHTJv´Ž±ub±p &+( ±

% e ‰ Q U

H @YHTJ.J> @ M " U 5 N A M " U

H ACJ ,M & ( E H)!)M e,JެaLšž„`šžaZmˆœ)cq¦@c‚„‹pwG„µšž„klplm@„Tcš

ª¡š¢ŸKpl^`šžk cq¦Gcb„‹pco`šžkspƒk;«±

%

"&('

U

H$ @*HTJ.J @ LM"

U 5 N A M " U H{ AJ ,M & ( E

H)! MGe,J¬vaZm!o`šžaZmˆœÌcb¦@cb„‹p w‹„šž„klplmG„cŽš

ª¡š¢ŸKpl^`šžk cq¦Gcb„‹pco`šžkspƒk;«±

Références

Documents relatifs

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST

Unit´e de recherche INRIA Rennes, Irisa, Campus universitaire de Beaulieu, 35042 RENNES Cedex Unit´e de recherche INRIA Rhˆone-Alpes, 655, avenue de l’Europe, 38330 MONTBONNOT ST