• Aucun résultat trouvé

Availability Analysis and Stationary Regime Detection of Markov Processes

N/A
N/A
Protected

Academic year: 2021

Partager "Availability Analysis and Stationary Regime Detection of Markov Processes"

Copied!
21
0
0

Texte intégral

(1)

HAL Id: inria-00073804

https://hal.inria.fr/inria-00073804

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- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Availability Analysis and Stationary Regime Detection of Markov Processes

Bruno Sericola

To cite this version:

Bruno Sericola. Availability Analysis and Stationary Regime Detection of Markov Processes. [Research Report] RR-2886, INRIA. 1996. �inria-00073804�

(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

Availability analysis and stationary regime detection of Markov processes

Bruno Sericola

N ˚ 2886

Mai 1996

TH `EME 1

(3)
(4)

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

123 4 576892:<;95>=<?

@(ACB

DFEGDH$I JLKDMNDPORQTSGD UVMNWXMNU

B

D EGDM

YZ\[]

DFUV^

[9_

DF`

JVORaTa [bZ

U _ D Z Dc

A D Z c A

DedfhgjibijklI ^Om HFnbnjkI HRoapOqbDM

rGs0tvuwxTybuhz Y{[

m|d}U~OPjOm€`O‚Tm€`|m€UƒWORd

_

DFS}apDc„U…D

_

m€d9U…D

Z

bO` OFjORm€`†OR‚Tm|`€m|UNWO Z D _

DFapDFd

_

O‚Tm€`|m€UƒWE‡DOPˆ

MNQ

Z

DM

Z

DMƒapDcvU…m|hDF`€W

_

Dv‰ŠdTD

_

‚9W"U

A

D(a Z\[

‚pO‚Tm€`|m€UƒW"U

A

ORU%O"MNWXMNU\DFE+m†M‹m|d

[

apD

Z

ORU\m

[

dŒOUOVqbm€hD d'm|dpMNUORd9U

ORd

_

‚9WU

A

DE‡DORdapD

Z

cvDFd9UORqjD [RŽ

U…m€E‡D _ Q Z

m€dTqL

A

m†c

A

OLMƒWTMƒU…DFEmM"m€d

[

a‘D

Z

ORU\m [ d [

hD

Z

O‰pdTm|U…D

[

‚ŠMND

Z

bOU…m

[

d’apD Z m

[9_>“L”

D‡c

[

dpMNm

_ D Z O Z

DFapORm

Z

O‚T`€DŒc

[

EGaTQTU\D

Z

MƒWTMƒU…DFE•Od

_

(D‡ObM\MNQTE‡DGOjM'QpMƒQpOR`

U A ORU"U

A

DŒMNWXMNU\DFE–mM$E [9_

DF`€D

_

‚}WO‰ŠdTm€U\DŒ^O Z…—h[

La Z\[

cvDM…M

“'”

Da Z…[

a [

MNDŒm€dU

A

mM$apOapD

Z

OGdTDF

OR`|q [jZ

m€U

A

E˜U [ c [

EGaTQTU\DGU

A

DMNDUN

[

OFbOm€`†OR‚Tm|`€m€UƒW™EGDOjMNQ

Z

DM

“š@(A

mMŒOR`|q [bZ

m€U

A E mM‚pOjMND _›[

d7U A D

cv`†ObM…MƒmcFO`>QTdXm

Žœ[bZ

EGm€PORU…m

[

dŒU…Dc

A

dTm†žŸQXD$m|dG

A

mc

A

OU\DMNU U [Œ_

DFU\DcvU U

A

DMƒUOU…m

[

dpO

Z

WG‚pD

A

OF9m [bZ/[Ž

U A D

MNWXMNU\DFEmM"QpMƒD _ U [

MNU

[

a’U

A

DLc

[

EGaTQTUORU\m

[

dm

Ž U A

DLMNUORU\m

[

dŠO

Z

m|UƒWmM

Z

DOjc A D

_>“L¡

dU

A

ORUlcFObMƒDh¢{U A D

OR`|q [jZ

m€U

A

E£qjm€hDM0d [ U [

dT`€WU

A

D/U

Z

OdpMNm|DFd}U¤OPjOm€`O‚Tm€`|m€UƒWEGDOjMNQ

Z

DM‹‚XQTU OR`†M [ U A

DVMNU…DPO

_

WlMNUOU…D¥OFbOm€`¦ˆ

OR‚Xm€`€m|UƒWh¢R/m|U

A

MNm|qbdTm¦‰§cFORd9U c

[

EGaTQTUORU\m

[

dŠOR`pM\OP9m€dXqhMDMNapDc„mOR`|`€W

A

DFdŒU

A

D/U…m€E‡D/ORU 

A

m†c

A

E‡DObMƒQ

Z

DM

O Z DdTD D

_ D _

mM(`O

Z

qjD

“V¡

dU

A

DlcFObMƒD

A D Z

DU

A

DMNUORU…m

[

dpO

Z

m|UNWLm†M¨d [ U Z

DPObc A D _

¢TU

A

DO`€q [jZ

m|U

A

E–a Z\[

ˆ

9m

_

DMU

A

D"U

Z

ORdpMƒm€DFd9U/OFjORm|`O‚Tm€`|m€UƒWEGDPObMNQ

Z

DM ORd _ ‚ [

QTd _ M

Žœ[jZ

U A DMNU\DO

_

W‡MNUORU\DOFbOm€`†OR‚Tm|`€m€UƒW

“0¡

U(m†M

OR`†M [ M

AT[

/d AT[

+U

A

DdTDF©OR`€q [bZ

m€U

A

E–cFORdL‚pDDFS9U…DFd

_ D _ U [ U A

Dc

[

E‡aTQTUOU…m [ d

[RŽ

apD ZNŽœ[jZ

ELO‚Tm€`|m€UƒW

EGDOjMNQ

Z

DM

“

ª«h¬­…®¯pw°{tjz

J/DFapOm

Z

O‚T`€Dlc

[

E‡aTQTU…D

Z

MNWXMNU…D ELMv¢

_

D a‘D d

_

OR‚Xm€`€m|UƒWh¢pOFbOm€`†OR‚Tm|`€m€UƒWh¢TapD ZƒŽœ[bZ

ELOR‚Tm|`€m|UNW±¢

^O Z\—h[

a Z\[

cvDM\MNDM„¢>MƒUORU\m

[

dpO

Z

m€UƒW

_

DFU\DcvU\m [ d “

²€³´

µN¶¸·F¹

´

µ/º»¦¶ƒ¼¾½„¿

Unit´e de recherche INRIA Rennes

IRISA, Campus universitaire de Beaulieu, 35042 RENNES Cedex (France)

(5)

‹ 0-’ „ ˜$ $%'&  ¥!R#

%' ' - .& '–# ,ŒF

«9t «ez O _

m†MNa

[

dXm€‚Tm|`€m€UXKDa

[

dpcvU\QTDF`|`€DD U.`†O

_

m†MNa

[

dTm|‚Tm€`|m€UXKDE

[

WhDFdTdTDMNQ

Z

QXd m€d9U…D

Z

bO`€`|D

M [ d}U

_

DPM'EGDMƒQ

Z

DPM

_

D‡MQ Z D UTKD _ D

Žœ[

dŠcvU…m

[

dTdTD EGDFd9U

Z

DMNapDcvU\m€hDFE‡Dvd9U

_ KDv‰pdXm€DM"apO

Z

`†OGa Z…[

‚pOR‚Tm|`€m|UTKD

žhQQTd‡MNWXMNU

B

DFEGDVM

[

m€U [ a KD Z

ORU\m

[

dTdTDF`

B

O'QXdGm€dpMƒUOd}U _}[

dTd/KD"DFU apO

Z

`|D$a [ Q Z

cvDFd9UOqbD

_

D"U…DFE‡apM{E

[

WhDFd

_ Q Z

ORd9U `€DžhQTDF`h`|DVMNWXMNU

B

D EGD DMNU

[

a/KD Z ORU…m

[

dTdXDF`§MNQ

Z

QXdTD/a/KD Z m [9_

D _ [

‚pMƒD

Z

jOU…m

[

d‰ŠdTm€D

“

dŒc

[

dpMƒm _§B

D Z D

QTd MNWXMNU

B

DFEGDŒm€d

Žœ[jZ

ELOU…m†žŸQTD Z KDFapO

Z

OR‚X`€DLDFU`

[

d7MƒQTaTa

[

MƒDh¢ c

[

EGE‡DŒM

[

QXhDFd}U ¢ žŸQXDG`€DLMƒWTMƒU

B

DFE‡DDMƒU

E

[9_

K

D `€mM9KD{aŠO

Z

QTda Z…[

cvDPM…MNQŠM>ELO Z\—h[

9m€D d¨‰pdXm

“

d'a Z…[

a [ MND

_

ORdpM0cvDFUCO

Z

U\mcv`|DQTdd

[

QThDF`hO`€q [bZ

m|U

A

E‡D

a [ Q Z

cFO`cvQT`|D

Z

cvDM

_

DFQTSGEGDPMNQ

Z

DM _ D _

m†MNa

[

dXm€‚Tm|`€m€UXKD

“

DFU¥OR`|q [bZ

m€U

A

EGD"DMƒU/‚pObM9KDMƒQ

Z

`†OU…Dc

A

dTm†žŸQXD

cv`†ObM…MƒmžhQTD

_

D$`QTdXm

Žœ[bZ

EGmM\ORU\m [ d _

ORdpM `ObžhQTDF`|`€D/QTd‡U…DMƒU

_ KDFU\DcvUORd9U`|DVc

[

E‡a [jZ

U\DFEGDFd9UMƒUOU…m

[

dTdpOm Z D

_ Q MNWXMNU

B

DFEGDŒDMNUQXU…m€`|mM9KDGa [ Q Z O

Z\Z

DFU\D

Z

`|DLcFOR`†cvQT` MNm/`€D

Z KDFqjm€EGD‡MNUORU…m

[

dTdŠORm

Z

DLDMNUŒOU…U…D m€d9U

“

ORdpM

cvD‡cFObM„¢`OR`€q [bZ

m€U

A

EGD

Žœ[

Q Z dTm€Ud

[ d MNDFQT`|DFEGDFd9UV`€DMEGDMNQ

Z

DM _ D _

mMƒa

[

dTm|‚Tm€`|m€UXKDŒU

Z

ORdpMƒm€U [ mZ

DM'E ORmM

ORQŠM…MNmp`†O

_

mMƒa

[

dTm|‚Tm€`|m€UXKDVMƒUOU…m

[

dTdpOm

Z

D±¢}OFhDc QTdTD DcK [ d [

EGm€D

_

DVcFOR`†cvQT`†MMNm|qbdTm¦‰§cFORU\m€hDh¢DFdapO

Z

U\mcvQT`|m€D

Z

`

[jZ

M\žŸQTD `m€dŠMNUOd}U0OQpžhQTDF`h`€DPM>EGDMNQ

Z

DM§M

[

d9U

_

DFELOd

_ KDFDMpDMNU0m€E‡a [jZ

UORd9U

“

ORdŠM‹`|D(c ObM [§B

Q`|D

Z KDFqjm€EGD

MNUORU\m

[

dXdpORm

Z

DŒdDMƒU"apOjM

_ KDFU…Dc„UTKDh¢p`OR`€q [bZ

m€U

A

EGD

Žœ[

Q Z

dTm€U"`|DM$EGDPMNQ

Z

DM¨U

Z

OdpMNm|U [ mZ

DMVDFU

_

DM"‚

[bZ

dTDM

a [ Q Z

`O

_

m†MNa

[

dTm|‚Tm€`|m€UXKDMNUORU\m

[

dXdpORm Z D

“

d™E

[

d}U

Z

DOQpM…Mƒm/c

[

EGEGDFdhUVc„Dd

[

QThDF` O`€q [bZ

m|U

A

E‡DapDFQTU

DFU

Z

D™KDFU…D d

_

QLOQcFO`cvQT`

_

DEGDMƒQ

Z

DM

_

DapD ZNŽœ[jZ

ELO‚Tm€`|m€UXKD “

e¯Tutv­y«7z

WTMƒU

B

DFEGDm|d

Žœ[bZ

ELORU\mžhQTD Z KDFapO

Z

OR‚X`€Dh¢0MQ Z D UTKD _ D

Žœ[

dŠcvU…m

[

dTdTD EGDFd9UF¢

_

mMƒa

[

dTm€‚Xm€`€m|UXKDh¢

apD ZNŽœ[jZ

ELO‚Tm€`|m€UXKDh¢ha Z…[

cvDPM…MNQŠM¨ELO Z…—h[

9m€DFd¢

_ KDFU…DPcvU…m

[ d _ Q Z KDFqjm€EGD¥MNUORU\m

[

dXdpORm Z D “

(6)

< =

% .& 

¡

dU A D _

DFapDFd

_

O‚Tm€`|m€UƒWORdpO`€WXMNmM [RŽZ

DFapOm

Z

O‚T`€DVc

[

EGaTQXU…m€dXq"MƒWTMƒU…DFELM„¢RU A D Z

D/mMOdm€dpc

Z

DObMƒm€dTq¥m€d9U…D Z ˆ

DMƒUm€d"DFjO`€QpOU…m€dXq$U

Z

ORdŠMNm€D d}U§EGDObMƒQ

Z

DPMv¢Fm€d¥apO

Z

U…mc„QT`O

Z

¢FU

A

Da

[

m€d9U0OPjOm€`O‚Tm€`|m€UƒWVORd _ U A

D(OFjORm|`O‚Tm€`|m€UƒW

[

hD

Z

O~qjm€hDFdapD Z m

[9_>“%@(A

mMapOapD Z _

DOR`†M{/m€U A U A

DVc

[

EGaTQXUORU\m [ d

[RŽ

U A DVa

[

m|d}U OFjORm|`O‚Tm€`|m€UƒWORd _[Ž

U A

DDFS}apDc„U…D

_

m€d9U…D

Z

bO`OFjORm|`O‚Tm€`|m€UƒW

Z

DPMNapDcvU\m€hDF`|W

_

D„‰pdTD

_

‚9WLU

A

Da Z\[

‚pO‚Tm€`|m€UƒWLU

A

OU"U

A

DŒMNWXMNU…D E

mMVm€d

[

apD

Z

OU…m

[

dšORUOGqbm€hD dm€dŠMNUOd}UOd

_

‚9WU

A

DEGDOdapD

Z

cvD d}UORqbD

U\m€EGD _ Q Z

m€dTqL

A

m†c A U A D

MNWXMNU\DFE m†M$m€d

[

apD

Z

ORU…m [ d [

hD

Z

O‰pdXm€U…D

[

‚pMND

Z

jORU\m

[

d™apD Z m

[9_>“>Š[jZ

ELO`€`|Wh¢‘U

A

DMƒWTMƒU…DFEmM$E [9_

DF`€D

_

‚9WLO^O Z…—h[

Ga Z\[

cvDM\M

“/¡

UM/MƒUOU…DMƒapObc„DmM

_

m€9m _ D _

m|d}U

[

UN

[Œ_

mM ]…[

m|d}U¥MNDFUM(

A

mc ALZ

DFa

Z

DMƒDFd}U/U A D

? 6

MNUOU…DM/m€dL

A

m†c A U A

DMƒWTMƒU…DFE

_

DF`€m|hD

Z

M U

A

DMNapDc„m‰pD

_

MND

Z

}m†cvDOd _ U A D

@A

MƒUORU\DM/m€dL

A

mc

A

U A D Z DGm†M'd

[ E [bZ

D‡MND

Z

9mcvD

_

DF`|m€hD Z D

_>“@‹Z

ORdpMƒm€U…m

[

dpM

ŽœZ\[

E•U

A

D2?

6CB

Z

DPMNa

“

@DFE

MƒUORU\DMU [ U A D

@AGB Z

DMƒa

“ ? 6HE

MNUORU\DMO

Z D cFOR`|`€D

_ .

?

#",IB Z

DMƒa

“ )"645E “@(A

Dm|d}U\D

Z

jOR`¤OPjOm€`O‚Tm€`|m€UƒW

[

hD

Z

BJLK9M)E

m†MU

A

DFdGU A D

ŽœZ

OjcvU…m [ d

U A D"m|d}U\D

Z

jO`

BJ(K9M)E _ Q Z

m|dTq

A

m†c A U A

D¥a Z…[

cvDPM…M(mM m€dŒU

A

DN?

6

MNUOU…DM

“

@(A

m†M

Z

ORd _9[

EjO

Z

mOR‚X`€D

A

ObM"‚pDFDFdšMNU\Q

_

m€D

_

m|da

Z

DF9m

[

QpM"apORapD

Z

MOjM

Žœ[jZ

m€dpMƒUORdŠcvDm|dPOHQ<¢ROg:Q ORd

_

O; Q{

A D Z

Dm€UM

_

mMNU

Z

m|‚TQTU…m

[

dmM(DFjOR`|QpORU\D

_

QŠMNm€dXqGU

A

DQTdTm

Žœ[bZ

E‡m€OU…m

[

dGU…DPc

A

dXmžhQTD

“ @(A

mMVORaTa Z…[

Ojc

A

mMVm€d9U…D

Z

DMNU\m€dTq‚pDcFOQpMNDm|U

A

ObM"q [h[9_

d}QXEGD

Z

m†cFOR`§a Z…[

apD

Z

U\m€DM"Od

_

m€U~OR`€`

[

VM¨U

A

DQpMND Z U [

apD ZƒŽœ[bZ

E

U A Dc

[

EGaTQXUORU\m

[

d./m|U

A

ORdLD Z\Z…[jZ

OjM/MNELO`€`OjM

_

DMNm Z D

_>“

S

d™ORaTa Z\[

Ojc A U

[_

DFU…DPcvU"U

A

DGMƒUORU\m

[

dpO

Z

m€UƒW [RŽ

^O Z…—h[

a Z…[

cvDPM…MNDPM

A

ObM'‚pDFD da Z\[

a [ MƒD

_

m|dTOVUWQ ¢

OYX:Q

“%@(A

mMOaTa Z\[

Obc

A

mM0‚pObMƒD _[

dU

A

D/QTdTm

Žœ[bZ

E‡m€OU…m

[

dEGDFU

AX[9_>“0@(A

DVMNUORU…D/a Z…[

‚ŠOR‚Tm|`€m€UƒWhDcvU [bZ

M

U A D"QTdTm

Žœ[bZ

E‡m€FD

_

^O Z\—h[

Gc

A

ORm|dLO

Z

DMNQŠcFcvDM\MNm€hD `€WŒc

[

EGaTQTU\D

_

Od _ U A

Dm|U…D

Z

ORU…DPMU

A

ORUVO

Z

DMNaŠObcvD

_

Z m|U…D

Z

ORU\m

[

dŠM$OapO

Z

U"O

Z

Dc

[

E‡apO Z D

_>“” A

DFdU A D _

m [§D

Z

DFdŠcvD‚‘D UN DFDFdGUƒ

[

MƒQpc

A

m|U…D

Z

ORU…DPM(mM/MNE OR`€`

DFd

[

QTq

A

¢‘U

A

Dc

[

EGaTQTUORU\m

[

dLm†M$MƒU

[

aXa‘D _>“V@(A

DELORm|d.a Z…[

‚X`€DFE /m|U A U A

m†M¨EGD U AT[9_

mM(U

A

ORU ¢‘QXdT`€m

— D

U A D"MƒUORd

_ O Z_

QTdTm

Žœ[bZ

E‡m€OU…m

[

d¢bU A D Z

DVmMd

[

O‚Tm€`|m€UƒWU

[

MNapDc„m

Ž

WD Z…Z…[jZ

‚ [ QTd

_

M(DPObMNm|`€Wlc

[

EGaXQTUO‚T`€D

“

¡ d U A

mMaŠORapD

Z

¢V(D

_

D hDF`

[ a OdTD  EGDFU

AT[9_

U [ c [

EGaXQTU…DLU

A

Da

[

m€d9UOPjOm€`O‚Tm€`|m€UƒW›Od _ U A D

DFS9apDcvU…D

_

m€d9U…D

Z

jOR`¥OFbOm€`†OR‚Tm|`€m€UƒW’

A

mc

A

mM‡OR`M

[

‚pObMƒD _7[

d U A DQTdTm

Žœ[bZ

E‡m€OU…m

[

d7U\Dc

A

dTmžhQTDORd

_

[

dšU

A

D‡MNUORU…m

[

dpO Z W Z

DFqbm|EGD

_

DFU…Dc„U…m [ d

“L¡

da

Z

Obc„U…mc„D

[

dTDGQŠMNQpO`€`€W _9[

DMd

[ U — d [   A

DFU

A D Z U A D

U…m|EGD AT[bZ

m€

[ d A

D5\M

A

DmM"c

[

dpMNm _ D Z

m€dTqŒmM$`†O

Z

qbDD d

[

QTq A Žœ[jZ

OGMƒU…DO

_

WMƒUORU\DOdpOR`|WTMƒmM

“@(A

DELORm|d

O _

bOd}UORqjD [Ž[

Q Z O`€q

[jZ

m|U

A E mMŒU

A

OUGU A D c [

E‡aTQTUOU…m

[

d7m†MGMNU

[

aTapD

_  A

DFd U A D™MƒU…DO

_ W MNUORU…D

OFjORm€`†OR‚Tm|`€m|UNW [RŽ

U A

D~MNWXMNU…D E m†M

Z

DPObc A D _

qbm€9m€dXq‚

[ U A U Z

ORdpMƒm€DFd9U/Od

_

MNU\DO

_

W‡MNUORU\D"EGDOjMNQ

Z

DM/m|U

A

ORdD Z…Z\[bZ

U [

`€D

Z

ORdŠcvD MNapDcvm¦‰pD

_

m€dO

_

bOdpcvD

“0” A

DFdU

A

D MNUORU\m

[

dŠO

Z

m|UƒW"mM>d [ U Z

DObc A D _

¢FU A D OR`€q

[bZ

m€U A E

qbm|hDMU

A

DU

Z

ORdpMƒm€DFd9U/EGDOjMNQ

Z

DM/ORd _ ‚ [

QXd _ M

Žœ[jZ

U A DMNU…DPO

_

WLMƒUOU…DOFbOm€`†OR‚Tm|`€m€UƒW

“

@(A

D Z DFELOm€d

_ D Z([Ž

U A

DapOa‘D

Z

m†M [jZ

q±ORdTm|FD

_

ObM

Žœ[

`€`

[

VM

“"¡

dU A D

Žœ[

`€`

[

/m|dTq‡MNDcvU\m

[

d¢‘ D

Z

Dc OR`€`

U A

Dcv`†ObM…MƒmcFO`/OFWLU [ c [

EGaTQXU…DU

A

Da

[

m€d9U¥OPjOm€`O‚Tm€`|m€UƒW‡ORd

_

 D _ D Z

m€hD"dXDF

Z

DPMNQT`|UM/U

[

MƒU

[

aU A D

c [

EGaTQTUORU…m

[

A

DFdU

A D MNUORU…m

[

dpO Z W Z

DFqjm€EGDm†M

Z

DObc A D

_§“‹”

D OR`†M

[

qjm€hD m€dU

A

m†M{MƒDcvU…m

[

dU

A

D(apMƒDFQ _}[

c

[9_

D

‚ [ U A O`€q

[jZ

m|U

A

ELM

“V¡

d

DcvU\m [ d ;

¢§(Dc

[

dpMƒm _ D Z U A

DDFS}apDc„U…D

_

m€d9U…D

Z

jOR`0OFjORm|`OR‚Xm€`€m|UƒWLORd

_

(DM AT[



AX[

©m€UVcFOd‚‘Dlc

[

E‡aTQTU…D

_

QpMNm|dTqŒU

A

DlMNUOU…m

[

dpO

Z

m€UƒW

_

DFU\DcvU\m [ d

“(¡

d

DcvU\m

[

dIUT¢p(DM AT[



‚9W’EGDOdpM

O d9QTEGD

Z

mc OR`DFSXORE‡aT`€DGU

A

ORU [ Q Z

dTDF–O`€q [jZ

m|U

A E c ORd c [

dŠMNm _ D Z

O‚T`€W Z D _

Qpc„D.U A D

c [

EGaTQTUORU…m

[

d™U…m|EGD [RŽ

U A

DLOFjORm€`†OR‚Tm|`€m|UNWEGDOjMNQ

Z

DMc

[

dpMƒm _ D Z D

_A

D Z Dh¢{

A

D d’U

A

DŒU…m|EGDŒORU

A

mc

A

EGDOjMNQ

Z

DMŒO

Z

DdTDFD _ D _

m†MGMNQ(] cvm|DFd}U\`€W™`O

Z

qbD

“+¡

UGmMŒOR`†M [ M

AT[

/d U A OULc

[

EGaTQTUORU…m

[

dpO`"M\OF}m|dTqhM

(7)

U ?

cFOd7‚pD

[

‚TUORm€dXD

_

DFhD d’

A

DFd U A

DLU…m|EGD AT[bZ

m€

[

d7mMMƒELOR`|`

“š¡

d

DPcvU…m

[

dPX}¢( DM AT[



AT[

 U A D

Z

DPMNQT`|UM

[

‚TUOm€dTD _‡Žœ[jZ

U A

D~OPjOm€`O‚Tm€`|m€UƒWEGDOjMNQ

Z

DM cFORdL‚pD"DOjMNm|`€WŒDFS}U\DFd

_ D _ U [ U A

Dc [jZ…Z

DPMNa [ d _

m€dTq

apD ZNŽœ[jZ

ELO‚Tm€`|m€UƒWEGDOjMNQ

Z

DM

“%@(A

D`OjMNU¥MNDcvU\m

[

dGmM

_

D 

[

U…D

_ U [ M [

EGD~c

[

dpc„`€QpMƒm

[

dŠM

“

ΠF

[

dŠMNm _ D Z

ORdm Z\Z

D _

Qpcvm€‚X`€Dc

[

d9U…m€d9Q

[

QpM¸ˆ U…m|EGD AT[

E [ qbDFdXD

[

QpM^O Z…—h[

La Z…[

cvDPM…M

K9M J

¢

[

hD

Z

O¨‰pdXm€U…D MNUORU…D MNapOjcvD

_

DFd

[

U\D

_

‚9W

“@(A

D MNUOU…DM [RŽ

O Z D _ m|}m

_ D _

m€d9U

[

Uƒ

[¥_

mM ]…[

m€d9U0MNQX‚pMNDFUM

¢TU

A

D~MNDFU [RŽ

U A D [ apD

Z

OU…m

[

dpOR`%MNUORU\DM

B

[jZ

U A

D"QXaMƒUOU…DM

E

ORd _

¢TU

A

DMƒDFU

U A DQTd

[

a‘D

Z

ORU\m

[

dpOR`

MNUORU\DM B [jZ

U A D _}[

/dŒMNUOU…DM E “c>T[bZ

O"MNWXMNU\DFE¢FE [9_

D `€D

_

‚}WMNQŠc

A

O$a Z…[

c„DM…M„¢ŸU

A

D/a

[

m|d}U OFjORm|`O‚Tm€`|m€UƒW

ORUVU…m|EGD

M

mM

_

DFd

[

U\D

_

‚}W B M)E

ORd __

Dv‰pdXD

_

‚}W

B M)E

YZ "!

@(A

D/a Z\[

cvDM\M#–m†Mv¢hOjM¤QŠMNQpO`<¢hqbm|hDFd‚9Wm|UM{m|d}‰pdTm|U…DMƒm€ELO`bqbD dTD

Z

OU [jZ

¢ _ DFd

[

U…D

_

‚9W¢bm€d

A

m†c A U A D

$U A_

mORq

[

dpO`}D d}U

Z

W%

B $ K $ E

hD

Z

m¦‰pDM&

B $ K $ E

('*),+.-

/10

B $ K32 E “¡

UM>m|dTm€U\mOR`ja Z…[

‚pOR‚Xm€`€m|UƒW

_

m†MNU

Z

m€‚XQTU…m [ d

mM

_

DFd

[

U\D

_

‚}W‡U A D

Z…[

+hDPcvU [jZ54 “

@(A

DQTdTm

Žœ[bZ

EGm€FD

_

^O Z…—h[

Lc

A

ORm|dOjM…M

[

cvmOU…D

_ U [ U A

Da Z\[

cvDM\M6 m†M/c A O Z

OjcvU…D

Z

m€ D

_

‚}WGm|UM/QTdTm¦ˆ

Žœ[bZ

EGm€PORU…m [ d Z

OU…D7GOd

_

‚}WŒm€UMU

Z

OdpMNm|U…m

[

dLa Z…[

‚pOR‚Xm€`€m|UƒWELORU

Z

m€S8 OkWQ

“%@(A

D"QTdXm

Žœ[bZ

EGm€PORU…m [ d Z

OU…D

7hD

Z

m¦‰pDM 7

ELORS

B

' B $ K $

E:9

$

;

E

Od

_ mM

Z

DF`†ORU…D

_ U [ ‚9W<==> ?@A7>¢h

A D Z

D>

_

DFd

[

U…DM

U A D'm

_

DFd9U…m|UNWE ORU

Z

m€S

“ B

Mƒm€dTqU

A

mM(d

[

UOU…m

[

d¢p(D"qjDFU

B M)E

4 CED

HFHGJI

K

L

/1M CN"O

B 7 M)E

L

PRQ 4 L

HSF

K B H E

 A D Z

DHF›mMOc

[

`€QTEGdhDPcvU [jZ



AX[

MND

$U A

DFd9U

Z

Wm†MHŒm

ŽT$

¢ ORd

_ J m

ŽU$

G“L”

D _ DFd

[

U…D

‚9WV

L U A Dlc

[

`|QTEGdGhDPcvU [jZV_

Dv‰pdTD

_

‚9WV

L

W

L

HXF

“V¡

U

Žœ[

`€`

[

VM¨U

A

ORU

Žœ[jZ

D hD

Z

WYP

J

¢>(D

A

OFhD

L

=

L NJZ Od

_ M

eHF

“ ¡

dU A D

Žœ[

`€`

[

/m|dTqT¢h D

_

D„‰pdTD

Žœ[bZ

D hD

Z

W[P

J

¢J\

L 4 L

HF 4 L “

]T^`_ acbTd(egfihkjJjJlieghkf,mnUlpoEqsrut livgh wJliq5nxt dgwbTq6y

@(A

Dc„`ObM\MNm†cFOR`p/OFWU [ c [

EGaTQTU\D/U

A

DVa

[

m€d9U/OFjORm|`O‚Tm€`|m€UƒWOU(U…m|EGD

M

m†M¤‚ŠObMND _[

dLJ/DF`†ORU…m

[ d B H E “

DFU

z ‚pDOqbm€hD dLMNapDcvm¦‰pD _ D

Z\Z…[bZ

U [

`|D

Z

OdpcvDORd _|{

‚pD

_

Dv‰ŠdTD

_

ObM

{ EGm€d~}

€

P

¡ ‚‚‚‚‚‚ L

K

+

/1M CN"O

B 7 M)E

+

2 Q

H5' z„ƒ…

† ! B g E

@(A

DFdL D

[

‚TUOm€d

B M)E

‡

K

L /1M C N"O

B 7 M)E

L

PRQ

\ L ? C B { E4K

Références

Documents relatifs

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

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

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

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

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

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

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