The Performance Accident in wireless multi-hop networks

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Submitted on 19 May 2006

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The Performance Accident in wireless multi-hop networks

Philippe Jacquet, Prateek Mittal

To cite this version:

Philippe Jacquet, Prateek Mittal. The Performance Accident in wireless multi-hop networks. [Re- search Report] RR-5746, INRIA. 2005, pp.15. �inria-00070273�

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ISSN 0249-6399 ISRN INRIA/RR--5746--FR+ENG

a p p o r t

d e r e c h e r c h e

Thème COM

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

The Performance Accident in wireless multi-hop networks

Philippe Jacquet — Prateek Mittal

N° 5746

Novembre 2005

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Unité de recherche INRIA Rocquencourt

Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France)

Téléphone : +33 1 39 63 55 11 — Télécopie : +33 1 39 63 53 30

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Xopd/dhkUV«X f/S0of X"FX"s/b¥lUje~eX¯S0oFdo±fhsqovl0dhV«m f UkCX"s§0{XM~¢mfhS ovlQm{le§0l0m f/X NkUXWkUXjp¡

z0opiq¤FXfqd"¨!<`cm{l0i"X]¢X¢oplNff/j¬ijFVYz0kefhX]fhS0XkU f/mV6ovfhXfhS0shjFkUpSUz0kef#

65 789;:<=>?)@'3

(

R SUXyX"fw¢jFsh¤V6ovz VYje~eXWem{do]dNk0opshX¢m f/SY lUje~eXMd5s/opl0~eV«jp{bovl0~kUlUm¡²jps/VY{b~emndgzLof/iqS0XW~½¨

Ù-ÙªÐI0äåKJ L

(9)

2#354

X¬¤clUj¢ fhS0ovff/SUXdhmlUFXWSUjpz¯f/SUshjFkUpS0zUkef

λS(p, N) ≥ N p(1−p)^N⁻¹©-fhS0X"s/X¡²jps/X¬ovl jFzefhm{V6ov

opkUX jv¡

p ≈ N¹

©¢jFkUn~¥FmFX

λS(p, N) ≥ ¹e

¨\Ajps/X"jpXWs

λS(p, N) s/X"V6opml0d¬LjFkUl0~eXM~ ¢SUX"l

N−>∞

opl0~fhXWl0~Ud f/j WX"s/j«¢SUX"lz m{d §0cXM~opl~UjNXMdlUjpf~UX"z2X"l0~jpl¨

@}{dhj0©f/SUXAVk0 f/m »¼SUjpz f/SUshjFkUpS0zUkef

λM(p, N) ≥ λS(p, N) dhmlLiXf/SUXAdgm{lUFX"»;SUjFz ijplU§0pkUsqof/mjFl mnd£uwk0dgf«o¯dgz2XWi"m{opiWopdhXjp¡}VkUfhm»¼SUjpz ijplU§0pkUsqof/mjFlÛ¨ SUX"l¦ mndY{opshFXp©¢XX"cz2XWif f/jFXfYfhSUX

V6ovcm{Vk0V f/SUshjFkUpS0zUkefjp¡f/SUXjFs/~UX"s¡²jFsz±jp¡f/SUXjFs/~UX"s

1 logN

©5¢S0m{iqS±bcm{X"n~Ud

λM(p, N) ^jp¡fhSUX

jFs/~UX"sjv¡ q _N

logN

¨ 9 . µ µ¼¹ µ /. µ µ ¸ $!! µ U! µ ¹

5

¸ . µ µ /. µ ¹, /$±! U! µ

¹ ,¸ $!!º-±e%$ÒF!!¶ %. $ ¹ 5 ¹ %. µ¯¹ º µ ¹ !¹ : 5 SUX"lAz m{dy§UeXW~ !²z

1 #©ÛjplUX«dhSUjpkUn~AjF0dhX"s/pX odhj¢m{l0is/XWoFdgX jv¡

λM(p, N) ovlL~fhS0X"lodgfhs/jplU~eXWi"shXMopdhXp©C¢SUXWl¯

m{l0i"shXMopdhXWd ovl0~fhS0X"lo«dg{j¢Qm{l0is/XWoFdgX]m{l √ N^¨

5m{pkUs/X 1}~eXWzUm{if/df/SUXyzU{jvfjv¡CfhSUX£opdhbNV«zef/jvf/m{i V kU f/mS0jpz«fhS0shjFkUpSUz0keft¢m f/S6jpkUsdg{jvfhfhXW~«V«je~eXW<¨

®¼fym{l0i"shXMopdhXWd m{l

A∗q

N logN

¨R S0XlUXfw¢jps/¤opiWimn~eX"lNf}dhSUjpk0{~jei"i"kUsy¢SUXWlf/SUXV kU f/mS0jpzi"opz0opi"m fwb

s/XWoFiqSUXWdf/SUXdgm{lUFXSUjFziWovz0oFimfwb6jv¡ovs/jpkUl0~U¨F0¨

y 1

0,8

0,6

0,4

0,2

0

N

10000 8000

6000 4000

2000

5mFkUs/X1 &t\Aoem{VkUV @}dhbNV«zef/jvf/m{iR SUs/jpk0pSUzUkUf ed}kUV2X"sjp¡}jc~UXWd

Ø²ß5ÙÛØà

(10)

5+1+ 1 +¬5-

R S0X pjNovyjp¡o±dhmV kU{ovfhm{jpls/kUl ¢mfhS _lUje~eXMd"©}iWovl 2X {mV«mfhXM~ fhj fhSUXV«XWopdhkUs/X"V«X"lNfjp¡fhSUX

µ : µ µ µH, /$¹ #

e"$ ¨5R SUXyoKFX"sqovFXtshXMiXWzefhm{jplYV6ofhs/mm{d5f/SUXV6of/shm¢SUjNdgX ijcX 3¬i"mXWlFf

cij

mnd?X Nk0ovLfhjfhSUX]dwfqofhmndgfhmniyjv¡)dhk0iWiXWd/dg¡²kULs/XWi"X"zef/mjFl¬cb l0jc~UX?utjp¡)oz0oFiq¤pXf?fhsqovl0dhV«m fhfhXW~¬Nb«lUje~eX

m;¨

R S0X¢ oKbf/SUXYlUje~eXWd]dgXWXMi&f]fhSUXWms~eXMdwf/mlLofhm{jplovl0~s/jpkUfhX fhSUXWms]z0opiq¤FXfqd£~ejcXMd}lUjpf]m{lNfhXWsg¡²XWshX¢mfhS

f/SUXm{lFf/X"s/l0ovC¡²k0l0i&f/mjFl0ov½jp¡-f/SUXdgm{Vk0{ovfhm{jplÛ¨ tFX"s/b¬lUje~eX]fhsqovl0dhV«m fqdoYz0opiq¤FXf¢m f/So z0shjF0ovUm{{m fwb

z)©U¢S0of/X"FX"s m fqdy~eXMdwf/ml0ovfhm{jplÛ©Udhm{l0iX¢XijplLdgmn~eX"sf/S0off/SUXz0opiq¤FXf ¢opm f/ml0 NkUXWkUXWdopshX]¡²kU{;¨

5. .' ! = ! .= .

R S0XYoKFX"sqovpXlNk0V2X"sjv¡?s/Xf/s/opl0dhVYmnd/dgm{jpl0d !²m{l0i{k0~em{lUfhS0X §Ls/dgf£f/s/opl0dhVYmnd/dgm{jpl #}jv¡oz0oFiq¤pX"f}¡²s/jpV

l0jc~UXYmf/j lUje~eX]u£mnd

1 c_ij

¨ÛX"fkLdi"ov{5fhSUX6V6ovfhs/m

1 c_ij

©½fhS0X«fhsqovl0dhV«m{d/dgm{jplijFdgfV6ofhs/m ©Û¢S0X"s/X

Dij = _c¹_ij ^!²¢XYdhXf Dii = 0 ¡²jpsov{m#¨6R SUX"s/X¡²jFshXfhSUX6oKpXWs/oppXlckUV LXWsjv¡shX"fhsqovl0dhV«m{d/dgm{jpl jv¡o zLopiq¤pX"ff/s/opl0dhVYmfgf/XW~cb¬lUje~eXmCf/j6lUje~eX umnd

Dij

¨

kUs/ml0Rdhjpf/dW©0f/SUX"s/X«ovs/Xml¯oKpXWs/oppXz0£Rz0opiq¤FXfyf/s/opl0dhVYmnd/dgm{jpl ovfgf/X"V«zef/d£m{lAfhS0X lUX"fw¢jFsh¤C¨]®¼¡

λs(p, N) m{dfhSUXfhSUs/jpk0pSUzUkUfjv¡ fhS0XdhbcdgfhXWV ©-f/SUXlckUV LXWs jp¡ydgk0iWiXMdhdg¡²kU{b~eX"{m{pX"s/XW~zLopiq¤pX"f/dmnd

λs(p, N)T¨Q`cm{l0iX¢XAopd/dhkUV«Xf/S0of6f/SUXAz0oFiq¤pX"f/d«~eX"{m{pX"s/XW~¥m{l¦fhSUXlUX"fw¢jFsh¤ S0oKpX dgjFkUsqiXovl0~

~UXWdgfhm{l0of/mjFl0dkUlUm¡²jps/VY{b¬~emndwf/shm{Ukef/XW~jplfhSUX]lUje~eXWd opl0~¬f/S0offhS0X"s/X]opshX

(N−1)N z0ovm{s jv¡-dhjpkUsqiX opl0~~eXWdgfhm{l0of/mjFl0d !²m;©u #©efhS0XlNk0V2X"sjv¡5z0opiq¤FXfqd~eXWm{pXWshXM~¬¡²s/jpV%dhjpk0s/i"X£mCf/j«~UXWdgfhm{l0of/mjFlu ~ekUs/mlU

R dg{jvfqd"©emnd λ_s(p,N)T (N−1)N

¨

opiqSf/s/opl0dgV«mndhdhm{jpl¡²s/jpV mNfhj?u-ijNdwfqd)m{l oKFX"sqovpX

Dij

s/XfhsqovlLdgV«mndhdhmjFl0dW©"f/SUX"s/X¡²jFshX

P

i,j

λ_s(p,N)T Dij

(N−1)N

mndX Nk0ov?fhjf/SUX¬f/jvf/op?lckUV LXWsjv¡f/s/opl0dhVYmnd/dgm{jpl ofhfhXWVYzUf/dm{l f/SUXlUX"fw¢jFsh¤¯~ekUs/ml0 R dg{jvfqdovlL~

dhSUjFkU{~2XXNk0ovCf/j

pN T¨R SUXWshX"¡²jps/X

λs= ^pNP²^(N⁻¹⁾

(i,j)D_ij

5.$ .' ! =.! .= .&

opiqS¬lUje~eX£m2i"jpV«zUkef/XWdmf/dLXMdwf shjFkefhXyfhj oplcb«~UXWdgfhm{l0of/mjFlu¨R)jfhSUmndX"l0~6mf zLXWsg¡²jFshV6d?o muw¤edwf/s/o

opFjps/m f/SUV!jpl fhSUX«V6of/shm ¨ÛR S0X 2XWdgfshjFkefhXYm{d£f/SUX«shjFkefhX

(i1, i2, ..., ik) dhk0iqSAf/S0of

i1 =i ^ovl0~

ik=j ^ovl0~dgk0V P Di_li_l+1

m{d V«m{lUm{V«op<¨)Xf

Hij

2XfhSUXV«m{lUm{V«opÛVk0 f/mSUjFz Kopk0Xp¨

XAk0dhX fhS0X !²V«m{lÛ© #¬ov{pjps/mfhSUV,f/j±ijFVYz0kefhX f/SUXAV«ml S0jpz¦V6ofhs/m x¨ XdgX"f

H = D ^ovl0~

¢X m f/X"sqof/X

H ← H ∗D kUlNfhm{}x!mnd6dwfqof/mjFl0ovs/bp©¢m f/S

(H ∗D)ij = minl(Hil+Dlj)¨¦fhSUXWshX i"jpkUn~62X£jFlU{b«oV6oemV kUV jv¡Û{jpYmfhX"sqof/mjFl0dW¨5R5ov¤cm{lU dhmV«novsshXMopdhjplUm{lUoFdtm{lijFV«zUkef/ovfhm{jpl¬jp¡

dhm{lUp{X"SUjFzf/SUs/jpkUFSUzUkefM©e¢XpX"f fhSUXV6oem{VkUV fhSUs/jpk0pSUzUkUf jp¡-f/SUXVkUfhm{SUjFz dhbedwf/X"V

λM(p, N) =^pNP²^(N⁻¹⁾

(i,j)H_ij

Ù-ÙªÐI0äåKJ L

(11)

5.$0 ! '3! 1 .! .

R S0X¬oKpX"sqovFXs/XWi"X"zef/mjFlV6of/shm ZmndijFVYz0kefhXM~cmno dgm{VkUnof/mjFl0dW¨yj¢©)fhSUXWshX6i"oplLX«fw¢jAovze»

z0shjNopiqSUXMd5¡²jpsiWovnikUnof/mjFl«jv¡ÛV6of/shm¬Z£¨NR SUX§0sqdgfovz0zUshjNopiqSYk0dhXWdf/SUX£dhm{VkUnof/mjFlYjp¡Ûz0opiq¤FXff/s/opl0dw»

V«mndhdhm{jpl±¢SUm{{Xf/SUXdgXMijplL~±ovzUz0shjNopiqS m{lNFjp{pXMdijFV«zUkefhm{lUfhSUXzUs/jp0opUm{mfwb ~em{dgfhs/m{Ukefhm{jpl¥jv¡}s/X»

i"X"m{pXM~XWlUX"s/pb¬ovf XMopiqSlUje~eXp¨ SUm{{X¢XS0oKFX£m{V«zUXWV«X"lNfhXM~2jvf/SfhSUXopzUzUs/jFopiqS0XWdW©pf/SUXzUs/jpU{X"V

¢mfhS¬fhSUX}dhm{VkUnof/mjFl6jv¡½z0opiq¤FXff/s/opl0dgV«mndhdhm{jpl«m{dtfhS0ovf¢X}ovs/XlUjpfov0X f/j d/i"ov{Xjpk0sijFV«zUkef/ovfhm{jpl0d

f/j¬ovlAoFi"iXWzef/opU{XXWpX";¨ R SUXs/XWdhkU fqdzUs/XWdhX"lNfhXM~SUX"s/X"m{lk0dhXfhSUXdhXWi"jpl0~opzUzUs/jFoFiqSjv¡ti"jpV«zUkef/mlU

f/SUXzUs/jp0opUm{mfwb¬~emndwf/shm{Ukef/mjFljp¡-s/XWi"X"m{pXW~X"l0X"s/pb¬ofyXMopiqSlUje~eXp¨

R SUX ~emndwf/shm{Ukef/mjFljv¡ef/SUXX"lUXWshFb£s/XWi"X"m{pXW~ovf-lUje~eXm<©

Wi

©S0opd

2^N⁻¹ofhjFV6d"©K¢SUmniqSmnd-o}zUs/jpU{X"V

¡²jFs-novs/pXov{kUXWd-jv¡L¨

XdhzUmf5fhSUXmlNf/X"s/KopFjp¡0{jpFopshmfhS0V jp¡0lUjFm{dhX?m{lNfhj]X"pXWldhX"pV«XWlFfqd-opl0~V«XWshFX

op2lUjFm{dhX}{X"FX"ndtjplXWopiqSdgXWpV«X"lNfW¨R SUmndX"l0opUXMdtk0df/j d/i"ov{XykUzjpkUs ijFV«zUkef/ovfhm{jpl0dtfhj fhSUjFk0d/ovl0~Ud

jp¡tlUje~eXWdW¨R SUXV«X"s/pm{lU¬jFlAlUje~eXMdy¡²jFs£novs/pXopkUXMdyjp¡XWl0ovU{XWd£k0d}fhjshXM~ek0iXfhSUX«ijFV«zUX"em fwb

jp¡)f/SUXzUs/jpU{X"V¡²s/jpV XezLjFlUX"lNf/m{opCfhm{VYXfhj«zLjFbclUjFV«m{opCfhm{VYXF¨

R SUXXWlUX"s/pb¬~Um{dgfhs/m0kefhm{jploflUje~eXm !

Wi

#mndijFVYz0kefhXM~oFd¡²jp{j¢yd&

(

UjFsXMopiqS¬l0jc~UX?u !Ò~emndwf/mlLi&f ¡²shjFVm#©cfhSUXXWlUX"s/pb«s/XWiXWmFXW~6mnd

1 r_ij^α

¢mfhSzUs/jp0opUm{mfwbYz)©copl0~

¢m f/S zUshjF0ov0m{m fwb 1»¼zÛ¨

(

R SUX}z0shjF0ovUm{{m fwb jv¡ÛijFshs/XWiftshXMiX"zUfhm{jpl«jv¡)ozLopiq¤pX"f?dgXWlNf?cb lUje~eXtu?of?lUje~eX}mLmnd P(Wi<

r−α ij K ) (1−p)

¨

R S0X«¡Òopi&f/jpsjp¡

1 1−p

mndfhjs/X"V«jpXYf/SUXijFlNfhs/mUkUfhm{jpljv¡ lUje~eXuml

Wi

¨R SUX6opkUX6jp¡ %¡²jFsjpkUs

V«je~eXW½m{d 1MU¨

(-+'&-(

X ovs/bfhSUXfhsqovlLdgV«mndhdhmjFlzUs/jpLovUm{mfwbovl0~fhS0XlckUV LXWsjv¡0l0jc~UXWdm{lf/SUX lUXfw¢jps/¤C©ml«ovlYofgf/X"V«zef

f/j«kUl0~eXWs/dgf/opl0~¬f/SUXl0ovfhkUs/Xjv¡5fhSUXf/SUshjFkUpS0zUkef¢sgff/jYfhSUXMdgXz0ops/opV«XfhXWs/dW¨

1% .('3 ! '3! : . +.

XWX"zUm{lU«f/SUXf/s/opl0dgV«mndhdhm{jpl zUs/jp0opUm{mfwbi"jpl0dgf/oplFfM©0¢Xd/i"ov{XkUzf/SUXlckUV LXWs}jp¡l0jc~UXWdW¨ 5mFkUshX

dhSUj¢ydSUj¢ fhS0Xdgm{lUFXWSUjpz¯fhS0shjFkUpSUz0kefovs/mXMd]¡²jpsfw¢jAi"oFdgXMd"©-z /]U¨pNopl0~z /]U¨1F¨ 5mFkUs/X

~UX"zUmni&fqd fhSUX\k0 f/mSUjFzfhSUs/jpkUFSUzUkef¡²jFsz /]U¨pNopl0~z /]U¨1F¨

0

( $# : !µ . ¹, = ¹

#

: -e/$¹ #

X jp0dhX"s/pXfhS0ovf6fhSUX V6oem{VkUV dgm{lUp{X"S0jpz±f/SUs/jpkUFSUzUkefY¡²jps«§UeXM~ z m{d6ovf

N ≈ ¹p

¨ @yndgjL©opd

N−>∞

©

λS(p, N)fhXWl0~Ud f/j«Y¢SUXWl zmnd§UeXW~ opl0~~UjNXMd lUjvf}~UX"z2X"l0~kUz2jpl¨

Ø²ß5ÙÛØà

(12)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0 200 400 600 800 1000 1200 1400

Throughput

Number of Nodes

’0.005’

’0.01’

5m{pkUs/X&R SUs/jpkUFSUzUkefedy ¡²jpsz/]U¨pFU©N0¨1

0 ' !Ò/$. ¹ , = ¹ # : )e%$¹ #

XiWovl±jF0dhX"s/pX«fhSLofYfhSUXWshXm{dYovl±m{lUmfhmnovmlLis/XWopdhX¬m{l fhS0shjFkUpSUz0kefW©¡²jF{j¢XM~cbo dgS0opshz¥~eshjFz

opl0~f/SUX"l odg{j¢m{l0is/XWoFdgX mljFs/~eXWs£jp¡ √

N¨YR SUX«jei"opV6oemV6oof

N ≈ ¹_p

jei"i"kUsqd]~UkUXYfhjfhSUX

dhm{lUp{X"SUjFz6l0of/kUs/Xyjv¡½f/s/opl0dgV«mndhdhm{jpl0d !;`cm{lUp{X"SUjFz¬ijFle§0pk0s/ovfhm{jpl«m{d)uwk0dgfo dgz2XWi"m{opLi"oFdgX}jv¡)\kUfhm{SUjFz

i"jple§LpkUsqof/mjFl #&©W¢SUm{iqSoFi"ijFkUlNf/dC¡²jFs½fhS0Xtml0m f/m{oppm{l0is/XWoFdgXovlL~}f/SUX?dhkU0dhXNkUXWlFf)~UshjFz]m{lfhS0shjFkUpSUz0kefW¨

@£d¢X¤FX"X"z jFl mlLis/XWopdhm{lU fhSUXlckUV6~eX"s jv¡ylUje~eXMdm{l fhSUXlUXfw¢jps/¤C©)f/SUX6f/SUshjFkUpS0zUkef 2X"FmlLdfhj

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0 200 400 600 800 1000 1200 1400

Throughput

Number of Nodes

’0.005’

’0.01’

Ù-ÙªÐI0äåKJ L

(13)

$ 1% .('3 ! '3! : ' !# "! ' ! #!;

®°l fhS0m{dtd/iXWl0ovs/m{j0©K¢X ¤FX"X"z fhS0XlNk0V2X"sjv¡2lUje~eXWdm{lYfhSUX lUX"fw¢jFsh¤§0cXM~ opl0~ KopshbfhSUXfhsqovlLdgV«mndhdhmjFl

z0shjF0ovUm{{m fwbF¨ 5m{pkUs/XWd «dgS0j¢yd?f/SUXdhmlUFXWSUjpzfhSUs/jpk0pSUzUkUf opshmnof/mjFl¢shf z¡²jps 1Mp0©epp ovl0~ pF

0 ' ( $# : !

µF·

. ¹ ,

%.)

¹ :<.

,

-

p≈N¹

¨ @yndgj

λS(p, N)s/X"V6opml0d 2jpk0l0~eXW~¢SUXWl

N−>∞

¨

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0 0.01 0.02 0.03 0.04 0.05 0.06

Throughput

Probability

’100’

’200’

’300’

Ø²ß5ÙÛØà

(14)

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Throughput

Probability

’500’

’750’

’1000’

Ù-ÙªÐI0äåKJ L

(15)

0 ' ' !Ò/$· . ¹,

9

.- ¹ ;: . , )

p≈ N¹

m{d~ek0X£f/jf/SUXdgm{lUFXWSUjpzl0of/kUshX]jv¡)fhSUXlUX"fw¢jFsh¤C¨5®¼f mndpXWshb

m{lNfhXWshXMdwf/mlU f/j dhX"X6f/SUX~eXWpXWjFzUV«X"lNfjv¡yoAdhXWi"jpl0~{jei"ov?V«ovemV6oAoFd¢XdhiWov{X¬kUzfhS0XlUje~eXMdm{l

§LpkUs/Xc¨®°V«zLjFsgfqovlNfh{bp©UfhSUXd/i"opm{lU«kUz jv¡lUje~eXWd}ovndgj«m{l0is/XWoFdgXMd?f/SUXov{kUXjv¡5fhS0m{dV6ovcm{V6oU©UoFdm f

iWovlA2X«dgXWX"lAm{l§0FkUshXCU¨ XYlUjpfhXf/S0of]fhS0XYdhXWi"jpl0~{jei"op)V6oem{V«ojei"ik0s/d]of

p≈ logN^c

©½¢S0X"s/X

c≈0.07®¼f]m{d}~em3¬i"kU f£fhj¬XMdwf/mV6ovfhXf/SUXzUs/XWi"m{dhXov{kUXjv¡ti~ek0Xfhj«f/SUX i"kUs/KovfhkUs/Xoff/SUX dhXWi"jpl0~

V6ovcm{V6oYLXWmlU«jp¡oYpXWshb ofyl0ovfhkUs/Xp¨

0.15 0.2 0.25 0.3 0.35 0.4 0.45

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Throughput

Probability

’100’

’200’

’300’

0.2 0.25 0.3 0.35 0.4 0.45

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

Throughput

Probability

’500’

’750’

’1000’

Ø²ß5ÙÛØà

(16)

0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Throughput

Probability

’1150’

’1400’

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Unité de recherche INRIA Rocquencourt

Domaine de Voluceau - Rocquencourt - BP 105 - 78153 Le Chesnay Cedex (France)

Unité de recherche INRIA Futurs : Parc Club Orsay Université - ZAC des Vignes 4, rue Jacques Monod - 91893 ORSAY Cedex (France)

Unité de recherche INRIA Lorraine : LORIA, Technopôle de Nancy-Brabois - Campus scientifique 615, rue du Jardin Botanique - BP 101 - 54602 Villers-lès-Nancy Cedex (France)

Unité de recherche INRIA Rennes : IRISA, Campus universitaire de Beaulieu - 35042 Rennes Cedex (France) Unité de recherche INRIA Rhône-Alpes : 655, avenue de l’Europe - 38334 Montbonnot Saint-Ismier (France) Unité de recherche INRIA Sophia Antipolis : 2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex (France)

Éditeur

INRIA - Domaine de Voluceau - Rocquencourt, BP 105 - 78153 Le Chesnay Cedex (France)

ISSN 0249-6399