Early Experiences in Traffic Engineering Exploiting Path Diversity: A Practical Approach

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Path Diversity: A Practical Approach

Luca Muscariello, Diego Perino

To cite this version:

Luca Muscariello, Diego Perino. Early Experiences in Traﬀic Engineering Exploiting Path Diversity:

A Practical Approach. [Research Report] RR-6474, INRIA. 2008, pp.21. �inria-00263813v2�

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inria-00263813, version 2 - 14 Mar 2008

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Thème COM

Early Experiences in Traffic Engineering Exploiting

Path Diversity: A Practical Approach

Luca Muscariello — Diego Perino

N° 6474

February 2008

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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

Lu a Mus ariello

∗

, DiegoPerino

†

ThèmeCOMSystèmes ommuni ants ProjetsGang

Rapportdere her he n°6474February200821pages

Abstra t: Re ent literaturehas provedthat stable dynami routing algorithmshavesolid the-oreti al foundation that makesthem suitable to be implemented in areal proto ol,and used in pra ti e in many dierent operational network ontexts. Su h algorithms inherit mu h of the properties of ongestion ontrollersimplementingoneofthepossible ombinationof AQM/ECN s hemesatnodesandow ontrolatsour es.

Inthispaperweproposealinearprogramformulationof themulti- ommodity owproblem with ongestion ontrol,undermax-minfairness, omprisingdemandswithorwithoutexogenous peakrates. Ourevaluationsof thegain,using pathdiversity,in s enariosasintra-domaintra engineering and wireless mesh networks en ouragesreal implementations, espe ially in presen e ofhotspotsdemands andnonuniformtra matri es.

Weproposeaowawareperspe tiveofthesubje tbyusinganaturalmulti-pathextensionto urrent ongestion ontrollersandshowitsperforman ewithrespe tto urrentproposals. Sin e owawarear hite turesexploitingpathdiversityarefeasible,s alable,robustandnearlyoptimal inpresen eofowswithexogenouspeakrates,we laimthatoursolutionrethinkedinthe ontext ofrealisti tra assumptionsperformsasbetterasanoptimalapproa h withalltheadditional benetsoftheowawareparadigm.

Key-words: Multi-pathRouting, Congestion ontrol, Tra Engineering, Flow-Aware Ar hi-te tures

∗

lu a.mus arielloorange-ftgroup. om

†

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Résumé : Les algorithmes de routage dynamique possèdent de solides fondements théoriques qui les rendent aptes á une implémentation rèelle dans dièrents rèseaux opèrationnels. Ces algorithmes possèdent de nombreuses propriètès propres aux ontrles de ongestion grâ e á l'utilisationdemé anismesdesignalisationexpli iteet de ontrledesotsálasour e.

Dans etarti le,nousproposonsuneformulationlinèaireduproblèmedemultiotave ontrle de ongestionet ritèred'èquitèdetype"max-min". Lesperforman esobtenuesparl'exploitation de heminsmultiplessonten ourageants,que elasoitenroutageintra-domaineoudanslesrèseaux mesh sans l, et in itent áune implèmentation rèelle, en parti ulierdans le as de matri es de tra non-uniformesetde"points hauds"dedemandes.

Nousproposonsuneappro heparotsquiintègrenaturellementlesmulti- heminsauxmè anismes a tuels de ontrle de ongestion, et nous l'èvaluons par rapport aux solutions a tuelles. Les ar hite turesparotsontrèalisables,robustes, apablesde passerál'è helle, et quasi-optimales lorsque les otsont un dèbit- rête expli ite. Dans un ontexte rèaliste, notre solution possède don lespropriètèsd'unesolutionoptimaleainsiquelesavantagesdel'appro heparots. Mots- lés : Multi- hemins,Contrlede ongestion,Ingènieriedutra , Ar hite tureparots

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1 Introdu tion

Tra engineeringisusuallyper eivedasano-linefun tionalityinordertoimproveperforman e by better mat hing network resour esto tra demands. Optimisationis performed o-line as demandsareaveragesoverthelongtermthatdonot onsidertra u tuationoversmallertime s ales. Intra-domainroutingoptimisation,bymeansofOSPF ostparametrisation[8,9℄,istypi al exampleof theaforementionedproblem. Themaxdegreeof responsivenessis guaranteedat the longterm, in adailyorweekly basisforinstan e. The obje tiveofISPs isto get rid ofagiven tra matrixatthe minimum ost,whi his estimatedasglobalexpendituresforlink upgrades. Thereforeminimisingthemaximumlinkloadisanaturalobje tive. Su hanengineerednetworkis notrobusttoanynergrainedtra u tuation,aslargenumberoffailures,tra ash rowds, BGP re-routes,appli ation re-routing. In urrentba kbones theseee ts are mitigatedby over-provisionedlinks. Inother ontexts,ofin reasingimportan enowadaysaswirelessmeshnetworks, s ar enessofresour espushnetworkengineerstoa eptahigherdegreeofresponsivenessinorder to exploit anysingle pie e of unused apa ity. We only onsider wireless mesh resulting from a radioengineerednetwork,wherelinks guaranteeaminimumavailability.

Literatureonoptimalroutingin networksstartsfrom seminalworksas[3,4℄or[6, 10℄. This omprises entralisedandde entralisedstrategiesproposedintheverybeginningoftheARPAnet proje t. Histori ally the main out ome of optimal routinghas been shortest-path or, at most, minimum- ost routing. Early experien es on dynami routing[37℄ have kept it ba kin spiteof itspotential,as sensitivityto ongestion haslongbeen refusedfor being omplex,unstable, not pronetobeeasilydeployed.

Thereisaquitelargere entliteratureonmulti-pathrouting,raisedfromtheneedto develop dynami yetstablealgorithms,sensitiveto ongestionformanyappli ationsthat ouldee tively exploitunusedresour eswithinthenetwork.

In theInternet, webelievethat veryspe i appli ations antolerate su h dynami environ-ment. Adaptivevideostreamingis, probably, themain appli ationthat would denitelybeable to toleratevariabilityand, at the sametime, take advantageof unused apa ity. It is worth re- alling thatvideoappli ationsare goingtobethemainpartofInternettra verysoon. Video streams usuallylast verylong,and willprobably last longerasbetterappli ations and ontents will beavailable. Furthermoreit islikelythat su h ontentswill betransported by anumberof non-spe iedproto ols,subje ttononbetterspe iedfairness riteria.

Conversationalappli ations should be kept away from being routed overmultiple routes but also other data servi es that are made of owsthat last potentially very short. Also, mu h of the present data tra if it in ludes mail, web, instant messaging. However, P2P le sharing appli ationsor ontentdeliverynetworks (CDN)areproneto wellexploit pathdiversityasthey intrinsi ally are robust to rate u tuations. Other data appli ations are downloads of software updateseventhoughthey anbein ludedinthe lassofP2Plesharingsystems.

Inthelastfewyears,intenseresear honmulti-pathroutinghasprogressed. Theoryof optimi-sationhasbeenappliedto developdistributed algorithmssolvingaglobaloptimisationproblem, see [11, 12, 13, 14, 21, 31, 35, 38℄. Optimisation expli its the problem of resour e allo ation under a hosenfairness riteria. Control theory has been used to obtain delay stability of dis-tributedoptimals hemes,see[11,16,21,35℄. Otherresear h onsidersdynami owlevelmodels [22,23,24,30℄in ordertotakeintoa ountarrivalsanddeparturesofuser'ssessions.

Inthispaperwesupportthedeploymentofaowawarear hite tureexploitingpathdiversity for aspe i lass of appli ations, rate adaptivevideo streamingfor instan e orCDN and P2P le sharing. Insu h set up we showthat ow aware paradigmis nearly optimal for any tipi al tra demandrequiring theuseofmultiple paths withouttheneedto assumeany kindof om-montransportproto olamongusers,any ommonfairnesssemanti andanykindof ooperation betweenusers,and networknodesaswell.

InSe tion2weexplainourdenitionofnetworkowswhileinSe tion3themodelling frame-work for optimal routing and ongestion ontrol is introdu ed. The se tion in ludes a set of examplesontoynetworks.

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Finally we introdu e our main out ome in term of performan e evaluation of the optimal solutionof large problems, with an original linearprogram formulation under max-min fairness thatisused toevaluatelargeproblemsinSe tion 4.

Se tion5introdu esourmainoriginalout omeasanewmulti-path ongestion ontroller alled MIRTO.Thealgorithmisborninferringanoptimalstrategyfrompreviousse tions. Moreoverthis algorithmisevaluatedwithintheframeworkofaowawarear hite ture,bringingnewarguments infavourofsu hnetworkparadigm.

2 Tra Chara teristi s

IP tra on a network link an be onsidered asa superposition of independent sessions, ea h session relating to some pie e of user a tivity and being manifested by the transmission of a olle tionofows.

Sessionsand owsaredened lo ally at a onsidered network interfa e. Flows angenerally be identied by ommon values in pa ket header elds (e.g., the 5-tuple of IP addresses, port numbersand transportproto ol)andthefa t thattheintervalbetweensu hpa ketsislessthan some time outvalue (20s, say). It is not usually possible to identify sessions just from data in pa ketsandthisnotion annotthereforebeusedforresour eallo ation. Neverthelesswearemore in linedtothinkaboutusersessionsthanproto oldened ows.

Amoresigni antow hara teristi istheexogenouspeakrateatwhi haow anbeemitted. Thisisthehighestratetheowwouldattainifthelinkwereofunlimited apa ity. Thislimitmay bedue to the usera ess apa ity, themaximumTCPre eivewindow, orthe urrentavailable bandwidthonotherlinksofthepath,orthestreamratein aseofvideoappli ationsforinstan e.

Intherestofthepaperwewilluseinter hangeablythetermsdemandandow.

3 Modelling framework

Thenetworktopologyis modelled by a onne tedgraph

G = (N, L)

givenasaset ofnodesand links. Let

A = [a

ij

]

theadja en ymatrix,

a

ij

= 1

ifthereexists adire tional linkbetween

i

and

j

and

a

ij

= 0

otherwise.

The network arriestra generated by aset of demands

Γ

, ea h demand

d

isgivenwith a triple

(s

d

_{, e}

d

_{, p}

d

₎

, with

s ∈ S

,

e ∈ E

, sour eand destination nodeswith

S, E ⊆ N

, and

p ∈ R

+

exogenous peak rate. Inourmodelanetwork ow

d

getsashare

x

d

ij

x

d

ij

(t)

is a uid approximation of the rate at whi h thesour e

d

is sendingattime

t

throughlink

ij

.

The network ow an be slit among dierent paths that are made available by a network proto olataningressnode. Wemakenomodellingassumptionwhetherpathsaredisjoint,however theabilityto reatemorepathdiversityhelps designhighlyrobustnetworkroutingproto ols.

Inparagraph 3.3 we model route sele tion and bandwidth sharing asan optimisation prob-lem that maximisesusersatisfa tionand minimisenetwork ongestionunder aspe iedfairness riteria.

3.1 Minimum ost routing

The ability to reate the set of optimal paths at the ingress of the network and make them availableto theroutingproto olrequires a ertainknowledgeofthenetworkstatus,aslink load, pathdelayandlength. However,asthis anbedoneinpra ti ebydisseminatinglo almeasures, the proto ol must be also robust to state ina ura y. Assuming perfe t knowledge of network state, optimalrouting anbeformulatedthroughthe followingnon linearoptimisationproblem

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Symbol Meaning

N

nodeset

L

link set

Γ

demandset

d

P

d

pathsetofdemand

d

k

pathnumber

L

d

k

link setofdemand

d

overits

k

k

rateofdemand

d

overits

k

th

path

x

d

rateofdemand

d

(

P

k

x

d

k

)

ρ

ij

loadonlink

(i, j)

(

P

d∈Γ

x

d

_ij

C

ij

) Table1: Summaryofnotationused

withlinear onstrained.

minimise

X

i,j∈N

C

P

d∈Γ

x

d

ij

c

ij

!

subje tto

X

k∈N

a

ik

x

d

ki

−

X

j∈N

a

ji

x

d

ij

=







p

d

i

if

i ∈ S

−p

d

i

if

i ∈ E

0

otherwise

∀d ∈ Γ

(1)

onstraint (4) models zero net ow for relay nodes, positive for sour e nodes and negative for destination nodes. This allowsto obtainoptimalroutesdire tly from theoptimisationproblem.

C

anbe thought modelling the link delay oftenused in tra engineering formulations of the multi- ommodityowproblem,

C(x

ij

) =

x

ij

c

ij

− x

ij

(2) withthis formulathe ost fun tion be omes theaverage delay in a M/M/1 queueas a on-sequen e of the Kleinro k independen e approximation and Ja kson's Theorem. This problem formulationdatesba kto [6,10℄inthe ontext ofminimumdelayrouting. Usingstandard te h-niquesin onvex onstrainedoptimisation( onvexoptimisationoverasimplex)in[3,4℄,itisshown that theoptimalsolutionalwayssele tpathswith minimum(andequal) rs ost derivativesfor anystri tly onvex ostfun tion. Thereforetheproblem anbere-formulatedasashortestpath problemwherepathlengthsaretherstderivativesofthe ostfun tionalongthepath,that an bewritten withabuseofnotation,

C

′

(x

d

p

) = C

′

P

d∈Γ

x

d

ij

c

ij

!

(3) where

x

d

p

is the portion of ow of demand

d

owing through path

p

. This is what, in [4℄, Bertsekasand Gallager allrst derivative pathlengths. Therefore, at optimum allpaths have equallengths. Thisfa twill beuseinthefollowingse tionrepeatedly.

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Anotherplausibleobje tiveistominimisethemostloadedlink,frequentintra engineering networkoperator'sba kboneoptimizationin onjun tionwithlink apa ityover-provisioning. In the ontextofmulti-pathroutingthis hasbeenusedtodesignTEXCP[16℄.

3.2 Bandwidth sharing and fairness

Bandwidth is shared between ows a ording to a ertain obje tive realised by one transport proto ol as TCP fordata transfersmakinguse of oneof its ongestion ontrol proto ols (Reno, Vegas, Cubi , high speed et .) or TCP friendly rate ontrol (TFRC) for adaptive streaming appli ations. Ingeneraltheseproto olsrealisedierentfairness riteria,whilstin this ontextwe assumethat allowsaresubje ttoa ommonfairnessobje tive. Theproblemformulationdates ba k to Kelly [18℄ where this problem is formulated as anon linear optimization problem with linear onstrainedwithobje tivegivenbyautilityfun tion

U (x)

oftheowrate

x

.

maximise

X

i∈S,d∈Γ

U

d

(φ

d

i

)

subje tto

X

k∈N

a

ik

x

d

ki

−

X

j∈N

a

ji

x

d

ij

=







φ

d

i

if

i ∈ S

−φ

d

i

if

i ∈ E

0

otherwise

∀d ∈ Γ

(4)

X

d∈Γ

x

d

ij

≤ c

ij

∀i, j ∈ L

(5)

demandsareassumedelasti ,meaningthatthey ouldgetasmu hbandwidthasnetworkstatus allows,andhavenoexogenouspeakrates. Ageneral lassofutilityfun tionshasbeenintrodu es in[27℄,

U

d

(x) =

w

d

log x

α = 1

w

d

(1 − α)

−1

x

1−α

α 6= 1

(6)

if

α → ∞

fairness riteriaismax-min.

Thisformulationiswidelyandsu esfullyusedinnetworkmodeling. [11,12,19,20,21,33℄have onsidered the problem of single and multiple path routing and ongestion ontrol under this frameworkas onstraint(4)may ounteitherasingleoramultipleset ofroutes.

3.3 User utility and network ost

Userutilityandnetwork ostaretwo oni tingobje tiveinamathemati alformulation. [12,13, 16℄haveusedthe ostfun tionasTEobje tivelikelymodeledbytheISPsinorderedtokeeplow linkloads,i.e. minimise ostsforupgrades. [11,14,21,31,35,38℄havejustusedthenetwork ost aspenaltyfun tionin pla eofhard onstraintsin theoptimisationframework.

Congestionsensitivemultiple routes sele tion an be formulatedasamathemati al program withnonlinearobje tiveandlinear onstraints.

maximise

X

i∈S,d∈Γ

U

d

(φ

d

i

) −

X

i,j∈N

C

P

d∈Γ

x

d

ij

c

ij

!

subje tto

X

k∈N

a

ik

x

d

ki

−

X

j∈N

a

ji

x

d

ij

=







φ

d

i

if

i ∈ S

−φ

d

i

if

i ∈ E

0

otherwise

∀d ∈ Γ

(7)

(10)

X

d∈Γ

x

d

ij

≤ c

ij

∀i, j ∈ L

(8)

φ

d

i

≤ p

d

∀d ∈ Γ ∀i ∈ S

(9)

Asanewadditional onstraintsweaddexgenousratesasthishassigni antimpa tinthepro ess ofsele tionofoptimalroutes.

In thisformulationthe userutilityis afun tionof thetotal owratetraversingthe network through the available paths. In a path-demand formulation the ow rate

φ

of a given user an be re-written asthe sum of the rates overthe set of available paths

P

, i.e.

φ =

P

p∈P

φ

p

. A

userisfreeto oordinatesendingratesoverthepathsjointly,aimingat maximiseitsownutility. Considernowthefolllowingrelaxationoftheobje tive

U (

X

p∈P

φ

p

) ≥

X

p∈P

U (φ

p

)

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ea huser'spathwouldbeseenasindependent,inotherwordsasifitwereaseparateuserandthe fairnessobje tivewouldbeatapath,andnotuserbase. Aproto oldesignedobservingsu hrule would break path oordination,while anetwork imposing perlink fair bandwith sharing,would realisethisobje tiveforanymulti-path ontrollerregardlessitsoriginaldesign.

3.4 Toy Examples

α = 2

and ostfun tion(2). Weassumedemandsfullyelasti .

1

2

3

1

2

3

4

(a) (b)

Figure1: Fullmeshtriangleandsquaretopologies. Hot-spotdestinationinnode2andsour esin node1and3.

3.4.1 Triangle

Fig.2showsthesplitratiosoverthetworoutes(one-hopandtwo-hops)andtheratioofthetotal users' rate (global goodput) over the total onsumed network bandwidth (network utilisation). Let us all this ratio GCR (goodputto ostratio). Top plotrelates to oordinated multi-path (CM), whilstbottom plottoun oordinated(UM). When

C

12 = C

31 = C

thetwoproblemshave ompletely dierent solutions as CM splits all tra to the shortest-path and UM splits rates equally. Atthis stage GCR forCM is 30%largerthan UM's. As

C

12 = C

31 > C

in reasesCM looksformoreresour esforthese onddemandalongthetwo-hoppath,resultinginmorenetwork ostandGCRde reases. HoweverusingUM,GCRisinsensitivetothesplitratios. Aftera ertain pointCMand UMhavethesameperforman e.

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à

æ

_æ

æ

ò

0

2

4

6

8

10

12

14

0.0

0.2

0.4

0.6

0.8

1.0 C

12 C = C

31 C

x

i

d

x

d

ò

_H

_x

1 +x

2 L

Cost

æ

_x

2 à

_x

1 à

à

_à

à

æ

_æ

æ

ò

0

2

4

6

8

10

12

14

0.0

0.2

0.4

0.6

0.8

1.0 C

12 C = C

31 C

x

i

d

x

d

ò

_H

_x

1 +x

2 L

Cost

æ

_x

2 à

_x

1

Figure 2: Ratedistributionamongtheavailablepathsanduserratetonetwork ostratio.

3.4.2 Square

Ing.3wehavesimilarperforman etothetriangle,despiteCMneedstousemorepathstoattain theoptimum,eventogatherasmallamountofbandwidth. FurthermoreGCRforCMisnotthat mu hlargerthanin aseUMisused. Inarealproto ol,se ondarypathswouldnotbeusedifthe attained gaindoesnotmeet the ost forthe overhead that is not onsidered herein the model, howeversigni ativeinpra ti e.

3.4.3 Dis ussion

MChasalargerstabilityregion,asit onsumeslessbandwithtoprovidethesameglobalgoodput asUM.Thismightturnoutnotbetrueinpra ti easweaklyusedse ondarypaths ould ostto mu hin termsofover-headduetosignallingtosetupthe onne tion,orprobestomonitorpaths thatarebeing oordinated.

à

æ

ò

_ò

ò

0

2

4

6

8

10

12

14

0.0

0.2

0.4

0.6

0.8

1.0 C

12 C = C

31 C

x

i

d

x

d

ò

_H

_x

1 +x

2 L

Cost

æ

_x

2 à

_x

1 à

à

_à

à

_à

à

æ

_æ

æ

_æ

æ

ò

0

2

4

6

8

10

12

14

0.0

0.2

0.4

0.6

0.8

1.0 C

12 C = C

31 C

x

i

d

x

d

ò

_H

_x

1 +x

2 L

Cost

æ

_x

2 à

_x

1

Figure 3: Ratedistributionamongtheavailablepathsanduserratetonetwork ostratio.

3.5 A Linear Program formulation

Inthisse tionwe onsiderproblem(7)inse .3.3andsele tone parti ularfairness riteria: max-min. We write an original formulationof problem (4) asan iterative linearprogram assuming linear osts

C(x)

. Atea h iterationalinearsub-problemissolvedwhom, at optimum, givesthe samenetwork owshare to everydemand. This share is the maximum bandwidththat anbe allo ated to the most onstraineddemand. The network graph

G

is redu ed to

G

˜

through the followingtransformation:

˜

c

ij

= c

ij

−

P

d∈Γ

x

d

ij

, i.e. apa ities arerepla edbyresidual apa ities aftertheallo ationofthisshareofbandwidth. if

c

˜

ij

= 0

thelink isremovedfromthegraph. The sub-problemsareformalisedasfollows.

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maximise

z −

X

i,j∈N

C

P

d∈Γ

x

d

ij

c

ij

!

subje tto

X

k∈N

a

ik

x

d

ki

−

X

j∈N

a

ji

x

d

ij

=







z

if

i ∈ S

−z

if

i ∈ E

0

otherwise

∀d ∈ Γ

(11)

X

d∈Γ

x

d

ij

≤ ˜

c

ij

∀i, j ∈ L

(12)

z ≤ p

d

∀d ∈ Γ ∀i ∈ S

(13)

Inthefollowingse tionweusethisiterativeLPinordertoobtainthegainthat anbeobtained exploitingpathdiversityforlargenetworkswithalargenumberofdemands.

4 Analysis of large problems 4.1 Simulation set-up

Westudytwotopologiesasshowning.4. TherstistheAbileneba kbonenetwork[1℄,whilethe se ond isapossiblewirelessmesh network ba khaul. Thelink apa itydistribution isaNormal distributionwithaverage

C

¯

andstandarddeviation

C/10

¯

. TheAbilene topology ounts

N = 11

nodes and weperform simulationswith mean link apa ity set to twos enarios:

C = 100M b/s

¯

and

C = 50M b/s

¯

. Thewirelessmeshtopology ounts

N = 16

nodesand,similarly,twos enarios

are onsidered:

C = 50M b/s ¯

¯

C = 25M b/s

. Inthislatter ase apa itiesareredu edtorepresent radio hannelswithloweravailablebitrate.

1

3

2

4

5

6

7

8

9 1 0

1 1

1

3

2

4

5

7

6

8

9 1 1

1 0

1 2

1 3

1 5

1 4

1 6

(a) (b)

Figure4: (a)Abilene ba kbonetopology;(b)aplannedwirelessmeshnetwork.

Thedistributionof peak rate is takenLog-Normal with parameters

µ = 16.6

and

σ = 1.04

. ThesevaluesaretakenfromasetoftsperformedonmeasurementsgatheredfromSprintba kbone [29℄. Twotra matri esare onsidered:

Uniform. Everynodesendstra to allothernodes. There arethus

N (N − 1)

demands where

N

isthenumberof nodes. Tomat h owratesto sour e-destinationpairs weusea te hniquedes ribein [29℄, assumingminimum ost-paththe routingused. This te hnique

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a hievesthe best mat h betweena set of demands and a set of SD pairs onne ted by a given routing. This tra pattern might be representative of an Intra-domainoptimised ba kbone. Sin ethe Abilene network has11 nodes, in oursimulationswegenerate atotal numberof110demands. Wedonot onsiderthistra matrixoverawirelessmeshtopology asunlikelyallnodessend tra toallnodesinsu hnetworks.

Hot-Spot

|S|

nodeshave

r

owsdire tedtoa ommonsinknode. Wexthesinknodeand randomlysele t

|S|

sour enodes.

|S|r

demandsarerandomlyassignedto these

|S|

Sour e-Sinkpairs. Inourexperien esweset

|S| = 4

,

r = 25

,foratotalnumberof100demands. Node6issele tedassinkinbothtopologies. Thistra pattern anberapresentativeofa data enterlo atedinaba kbonetopologyoragatewaynodein awirelessmesh network. A ordingtotheaforementionedset-upwesimulateatra matrixwhi hisusedasinputtothe LPdes ribedinse .3.5andsolvedusingtheMATLABoptimisationtoolbox. Foreverys enariowe evaluatethesatisfa tionofea hdemandastheratiobetweenitsattainedrateand itsexogenous peakrate. A demandis fullyelasti ifitsexogenousrate islargerthat themaximumattainable bandwidth in an empty network. Hen e, satisfa tion is always dened as we need not assume innitepeakratetoelasti ows. Weusethisperforman eparameterasitisabletoexpli ithow bandwidthis allo ated withrespe t tothe distribution oftheexogenous rates. Outputdata are averagedovermultipleruns.

4.2 Numeri al results

Resultsarereportedin g.5and6and,asexpe ted, showmulti-pathroutingoutperforms mini-mum ostroutingoverbothnetworktopologiesandforbothtra patterns. However,thepoint is to measure theentity of the improvement. In parti ular, the gainis largerfor wireless mesh topologyand fors enariosadoptinglargerlink apa ities.

Thegainof multi-path is, in great part, limited to ows with largerpeak rate, whilst ows with lower peak rate are ompletely satised by both routings hemes. This be ause MinCost routing,under max-minfairness, penaliseslarger owsby fairlysharingthe apa ityof thelink thata tsas bottlene kamongallowstherein progress.

Multi-pathrouting,undermax-minfairness,a tssimilarlyex eptthatows anretrieve band-width, notonlyontheirminimum ostpath,butalsoontheirse ondaryroutes. Indeed, simula-tionsshowthat lowrateowsdonottakeanyadvantageof pathdiversity, whilehighrateows retrieveadditionalbandwidthalongotherpaths.

Max-min multi-path routingavoids to usemorethan onepathto route lowrate ows. This hasbene ial ee t inpra ti easitavoidswastageofresour esdue totheoverhead,that might bejustiedonlyabovea ertainminimumrate.

20

40

60

80

100

0

0.2

0.4

0.6

0.8

1 Demand ID

Satisfation

Abilene Uniform Scenario

min-cost ¯

C=100

multi-path ¯

C=100

min-cost ¯

C=50

multi-path ¯

C=50

20

40

60

80

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 Abilene Hot−Spot Scenario

Demand ID

Satisfation

min-cost ¯

C=100

multi-path ¯

C=100

min-cost ¯

C=50

multi-patht ¯

C=50

Figure 5: Abilene topology. Satisfa tion distribution for uniform (top) and hot-spot (bottom) tra matrix.

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Fig.5reportsresultsfortheAbilenenetwork. Thegainofmax-minmulti-pathroutingisvery largeforhot-spottra matri es, andeven moresigni antwhen network apa ities arelarger. Theroutings hemeisabletotransfer65%additionaltra when

C = 100

¯

and41%when

Of ourse, as the apa ity isfairly large,resulting in alightly loaded network,boths hemes havesimilar performan easallowsaresatisedalongthemin ostroute.

The varian e of the satisfa tion is quite small, and between 0.05 and 2.3 for all s enarios. However it is not uniformly distributed among all ows. In fa t, large ows are ae ted by larger varian e than small ows. This is due to the max-min fairness riteria that allo ates a minimumamountof bandwidthto allows. Thisalwaysassures omplete satisfa tionforsmall owswhilesatisfa tionoflargeowsdependsonthenetwork apa itiesthatvariesfromsimulation tosimulation.

0

20

40

60

80

100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 Demand ID

Satisfation

Hot Spot Wireless Mesh Scenario

min-cost ¯

C=50

multi-path ¯

C=50

min-cost ¯

C=25

multi-path C=25

Figure6: Wirelessmesh topology. Satisfa tiondistribution hot-spottra matrix.

5 Ar hite tures and proto ols 5.1 Ar hite tures

Anyoftheproposalsfor ongestion ontrol,and ongestion ontrolexploiting pathdiversity, an be restated in the ontext of an optimisation problem of the kind of (7) or the un oordinated ounterpart (10). Su h problems lead to dierent ar hite tures based on dierent theoreti al foundations.

We divide su h ar hite tures in three groups: fully de entralised, quasi de entralised, ow aware. This lassi ationisfortheeaseofexpositionandforsakeof larity,howeveritlaysitself opento riti s.

Fully de entralised (FD). Insu h ar hite turenetworknodesstore, swit hand forward pa ketsfromaninputtoanoutputinterfa e. Neithers hedulingnora tivequeue managa-ment is implemented into the nodes. A form of ooperation is assumed between sour es, that implement a ommon rate ontrol algorithm and, ifneeded, a ommonmultiple path splitter. Ingeneralsour esneedtobe onformanttoa ommonfairness riteria. Thisisthe aseforthe urrentInternetandmulti-pathTCP[11℄isoneexampleofsu h ontroller.

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Quasi de entralised (QED). Nodes implement any form of a tive queue management (AQM),to prevent ongestion,and expli it ongestionnoti ation(ECN)that istriggered a ording to some temporisation. ECN might also be result of a lo al node al ulation. Sour esexploit su h noti ationto ontrolsendingrateandsplit de isions. [12,13,16℄ are twoexamplesinthe ontextofintra-domaintra engineering.

Flow aware (FA).Nodesimplementpa kets hedulersthatrealisefairbandwidthsharing betweenows. Sour esbalan etra among theavailableroutessubje ttotherestri tion imposedbypa kets hedulersandautonomouslyde idehowtoexploitasbetterasthey an networkresour es. Congestion ontroland bandwidthallo ationaresolvedseparately. [30℄ proposearoutings hemeinspiredbythethete hniqueof"trunkreservation"usedinPSTN to allo ate ir uitstose ondarypathsin asethedire t pathswereexperien ing overload. [30℄

Ea h of above-mentionedar hite tureshaveits ounterpartthat makeno use ofpath diver-sity. It appears di ultto unequivo ally sele t oneapproa h. Forinstan e, thequestionof the deploymentofa ertain ongestion ontrolalgorithmisstillhotlydebated(seethenewsletter[40℄). Theuseofexperimental proto ols (e.g. ubi in Linux)s ares,asFD ar hite turesassumea ommonformof ooperationbetweenusersand anar hymightbe ostly,whetherdegeneratesin ongestion ollapse,orbeinglessnegative,in unfairnessinsharingresour es.

Manifest truth is that FD are very simple and do not require any sort of parametrisation, espe ially at nodes, andextensions that makeuse ofpath diversityare easyto deploy assour e routingis made available. However, the main on ern that obstru tsthe deployment of sour e routingisse urity.

QD enhan esFDandmakeitmoree ientandstable. XCP[17℄isanexampleofproto ols of this kindwhile, in the ontext of intra-domainTE, TEXCP[16℄and TRUMP [12℄ belong to this lass.

5.2 Flow aware ar hite ture 5.2.1 Per-ow fair queueing

Thebenetofper-owfairqueueinghaslongbeenre ognised[7,28℄. Besides,itisrobustagaints unfair use of resour es be ause of non standard onformantuse of network transport proto ols resulting from bad implementations (rare), absen e of ommon agreement (the ase of ubi in Linux [40℄) as well as mali ious use that exploits others' weakness (more aggressive ongestion ontrollersfor instan e). Per-owfair queueingrelievesthe network to assumestandard onfor-man eofendtoend proto ols. Assuredfairnessallowsnewtransport proto olstobeintrodu ed withoutrelyingondetailedfairnesspropertiesofpreexistingalgorithms.

5.2.2 Overload ontrol

Per-owfairqueueingisfeasibleands alableinpresen eofoverload ontrol[25,26℄. Whendemand ex eeds apa itythes hedulerassuresequalperforman edegradationtoallows. However,arising ongestionatowlevelisatransientphenomena,asuserswouldquittheservi ein rowdsbringing ba kutilisationto normalloads. Thisisper eivedbytheuserasservi ebreak-down.

Atpresent,nooverload ontrolisimplemented,inanyform,withinthenetwork. Ata ertain extent,thisisassuredwithintheISPsba kbone,andinpartwithinthea ess,byover-provisioning link apa ities a ording to an estimated tra matrix (using netow or similar tools). Su h methodology does not solve lo al ongestion in small periods of time and for e users to quit protingfromaservi e.

Inwirelessmeshba khauloverprovisioningwouldnotbeanymoreafeasiblesolutionand multi-pathroutingmightbene essary.

Overload ontrol has to be dynami and fast rea ting to ongestion. This an be realised lookingforresour esfromotheravailableways,forinstan etheavailabilitymultipleroutestojoin aservi e.

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5.2.3 Per-ow path sele tionand admission ontrol

Asuboptimalapproa histosele tonesinglepathamongmanyothers. Inpresen eofanumber ofpathstorea hadestination,aow anbedee tedtoabetterroute,e.g. withlargerfairrate orwith minimum ost. Su h a greedy s heme is not stable and would led to os illations if the drivingmetri isnotstable enough. Thisisthe aseoffairrate.

5.2.4 Per-ow multiple path routing

Thepresen eofper-owfairqueueingineverylinkimposeper-pathfairbandwidthsharing. This means that the utility of asingle user is not a fun tion of the total attained rate as he is not allowedtogetmorebandwithofthefairsharealongitsminimum ostpath. Thereforetheutility is given by the sum of the utility of ea h singular path as (10). We know that in generalthis problemis suboptimalwithrespe t toa oordinated splitter. Inthis asethe optimumattained rate is given by

x

d

i

= ∂

x

d

i

U (q

d

i

)

−1

being

q

d

i

the ost of path

i

for user

d

. Thesplit ratio is the inversely proportional to the ost. In a re ent paper Key et al. [22℄ prove that in absen e of oordination, the stability region of the number of ow in progress in the network,is redu ed. This is shown for atriangle topologyand uniform tra matrix. Theowmodel assumesthat owsarrivea ordingto asto hasti pro essandleavethesystemafter beingservedanamount ofdata whi h is distributed. A redu edrateregionat owlevelis a onsequen eof (10) as,the same rate is obtained at a larger ost. As we show in the example 3.4.1. Noti e also that in presen eof uniformtra matri es, theover-headrequestedbymulti-path isnotreallyjustied withrespe t tominimum ostpathsele tionasthereis almostnogain,aswehaveshownin the previousse tion.

5.3 Multi-path Iterative Routing Tra Optimizer

Inthis se tionwepropose oneof the main out omeof the paper: Multi-path IterativeRouting Tra Optimiser(MIRTO), afullydistributed algorithmaimed at obtaining,in ade entralised way,amulti-pathoptimalstrategyproposedin se .3.5.

ItisdesignedaroundTCP(AIMD)anditallows oordinatedtra splitovermultiple paths. MIRTOmightlikelyrunonend-hostsand anworkinanyofthear hite turesdes ribedinse .5.1. InordertorunMIRTO,hostsshould dis overavailableroutesandlink apa itiesalongthem torea hadestination. Thewaysu hinformationis olle tedisoutofthes opeofouralgorithm butthey anforexamplebedis overedthroughlink-stateroutingproto ols. Thealgorithmworks even whetherinformation isin ompletebut in alessee tiveway, asin asepathsarepartially dis overedandpathdiversitylimited.

Flowsplittingovermultiplepaths anbeperformedinseveralwaysa ordingtotheappli ation ontext. Bymeans of path omputation apabilities ofMPLS for intra-domainTE, orthrough middlewaresrunningonproxynodesa tiveasmiddle-layer.

Symbol Meaning

∆

+

positivestep

∈ R

+

∆

−

negativestep

∈ R

−

Q

d

k

oringeneralwhennew informationareavailableonthestateofpath

k

. Path ostsare omputeda ordingto(14). They onlydependon apa ityof thelink alongtheroute. Indeed,in aseoflinear ost(3)is equalto

P

ij∈L

d

k

1 C

ij

(17)

(14)justindi ates ongestion noti ationàlaTCPandtherouteismarked ongested.

Q

d

k

(t) =

(

P

ij∈L

d

k

∆

+

C

ij

if

∀(i, j) ∈ L

d

k

ρ

ij

(t) < C

ij

∞

if

∃(i, j) ∈ L

d

k

ρ

ij

(t) ≥ C

ij

(14)

Algorithm1MIRTO algorithmforagivendemand

d

for

k ∈ P

d

do ompute

Q

d

k

(t + RT T

k

d

)

endfor if

Q

d

k

(t + RT T

k

d

) = ∞ ∀k ∈ P

d

then for

k ∈ P

d

do

x

d

k

(t + RT T

k

d

) ← x

d

k

(t) − x

d

(t)∆

−

endfor elseif

p

d

_{(t) ≥ x}

d

_(t)

and

Q

d

k

(t + RT T

d

k

) = min

k

Q

d

k

(t + RT T

d

k

)

then

x

d

k

(t + RT T

d

k

) ← x

d

k

(t) + ∆

+

elseif

p

d

_{(t) < x}

d

_(t)

and

Q

d

k

(t + RT T

d

k

) = max

k

Q

d

k

(t + RT T

d

k

)

then

x

d

k

(t + RT T

d

k

) ← x

d

k

(t) − ∆

−

endif Anin reaseof

∆

+

isdoneovertheminimum ostpathwhenthereisatleastonenon ongested path,andthetotalowrate anstillgetin reasediflowerthanitsownpeakrate. Theratein rease is hosen onstantandindependenttoowratenottofavourhigherrateows. Thisin rease an be onsideredasaprobeinordertodis overtheglobaloptimumsplit. Inprin ipleallpathmight beprobedas,whenthosebetterrankedare ongested,worserankedroutes anbeexploited. The importan e ofprobingin su hkindof ontrollerto avoidtobetrappedin non optimaequilibria hasbeenhighlightedin[21℄.

Flowrateisde reasedin twowaysa ordingto network onditions. Firstly MIRTOredu es sendingrateoverallpathswhen theyareall ongested. Theratede reaseisproportionalto the totalowrate. Thisguaranteesfairness. Otherwise,smallowsornew omingowsstartingwith lowerrateswouldbedisadvantagedwithrespe ttohigherows. Moreoverde rementisperformed overallpathsat thesametimeinorderto allowowsplitre-arranging.

Infa t,after thisde rease,there isnewly available bandwidthandowswill growa ording to theaforementionedrules. So,ifthe urrentsplit isonlylo ally optimumthe ontrollerwould move towards a global optimum a ording to this sear h strategy. On the other hand, a rate de rease isperformedanytimethe totalowrate islargerthanowpeakrateand at leastone non- ongestedpathisavailable. Thismeans that, asabetterrankedrouteis willingto in rease itsrate, thismustbedoneto thedetrimentofaworserankedroute,withoutalteringtheglobal ratewhi his bounded bytheexogenous rate. Infa t evenifthetotalowrateisequalto peak rate,thepathsplitting ouldbeonlylo allyoptimumi.e. moreexpensive. Itworthre allingthat amoreexpensivepathmightalsobe hara terizedbylargerend toenddelays. Ifmorethanone maximum/minimum ostpathsexist,thede rease/in reaseissharedamong them.

This me hanism allows MIRTO to rea h a global optimum in presen e of demands with or withoutexogenous rateasitfollowsthe lassi alwaterlling pro edurethat laysat thebaseof themax-minfairness riteria.

Thesele tion ofthe minimum-maximum ost path when performing in rease/de rease oper-ations guarantees oordinationbetween dierent paths of thesame ow aslong asthe network doesnotimposeanyadditionalfairnesssemanti .

5.4 Stabilityand optimality

MIRTO an be des ribed througha uid equation that approximates itsbehaviour and anbe usedtoprove onvergen eandstability. Wesupposerstnonetworkdelayandthenwegenerealise totherealisti ase.

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5.4.1 Absen eof network delays

First onsider the asetheowhasnoexogenousrate.

dx

i

(t)

dt

= ∆

+

_{[1 − q(t)]κ}

i

(t) − ∆

−

q(t)

N

X

k=1

x

k

(t)

κ

i

(t)

istheprobabilitythat

i

istheminimum ostpathattime

t

.

q(t)

istheprobabilitythat all pathare ongested. Thereforeat steadystate

X

k

x

k

(∞) = κ

max

(∞)

1 − q(∞)

q(∞)

∆

+

∆

−

where

κ

max

(∞) = max

k

κ

j

(∞)

. This meanstra is split amongminimum ost paths,possibly a single path. All the others are subje t to ontinuous probing su h that

x

i

(t) ∼ κ

i

(t)

. This featureallowsthe ontrollernottobetrappedinequilibriapointsthat arenotoptima. Apathis probedasfrequentasitisrankedthebestamongtheothers. This anbeseenfromsimulationsin Se tion5.5 ing. 8. In asetheowispeakratelimitedthepreviousequation anberewritten asfollows.

dx

d

i

(t)

dt

= {∆

+

κ

i

(t)s

d

(t) − ∆

−

r

i

(t)[1 − s

d

(t)]}[1 − q

d

(t)] + −∆

−

q

d

(t)

X

k

x

k

(t)

where

s

d

_{(t) = P r[x}

d

_{(t) > p}

d

_]

and

r

i

(t)

is the probability that

i

is the more expensive path. Convergen e anbedis ussedasintheprevious asewhentherewerenopeakrate.

5.4.2 Presen e ofnetworkdelays

Inpresen e of network delays

κ(t)

,

q(t)

,

r(t)

and

s(t)

aredelayed informationat thesour e. A problem of stability in the sense of theory of ontrol arises. We do not provide here rules on how to set

∆

+

and

∆

−

in order to keep the system asintoti ally stable in presen e of delays. Using standardte hniquesasdes ribedin [33℄ this anbe easilyobtainedfor simpletopologies. Cumbersome al ulations, andthe useofthe generalisedNyquist riterion anbeusedto prove stabilityforageneraltopology.

5.5 A ase study

In this se tion weevaluate the performan e of the above mentioned ar hite tures by means of uid simulationsin order to diplaythe onvergen e behaviourof three sele ted s enarios. Ea h s enariorepresentsoneofthethreear hite tures onsideredinSe tion 5.1

1

3

2

4

5 1 0 0 M b / s

2 . 5 m s

1 0 0 M b / s

2 . 5 m s

1 0 0 M b / s

2 . 5 m s

1 0 0 M b / s

2 . 5 m s

1 M b / s

2 5 0 m s

1 0 M b / s

2 5 m s

1 0 0 M b / s

2 . 5 m s

1

3

2

4

5 X 1

X 2

X 3

X 4

1

3

2

4

5 X 1

X 2

X 3

X 4

1

3

2

4

5 X 1

X 2

X 3

X 4

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5.5.1 Simulation setup

The FD and the FA ar hite tures are analyzedby supposing nodes runthe MIRTOalgorithm. Re all MIRTO has beenspe i ally designed for FD solutionsand requires to set rate in rease andde reasevalues. Theyshouldallowthealgorithmtoover omelo aloptimalsplittoattainthe globaloptimumand,at thesametime,limittra u tuation. Theproblem ofsetting in rease-de reasevaluesis awellknown trade-oof TCPandTCP-likeproto olsand MIRTOinherits it aswell. Inoursimulationsweset themto

∆

+

_{= 0.5M b/s}

and

∆

−

_{= 0.013}

.

As on ernQDar hite tures,weimplementamodiedversionoftheTRUMP[13℄algorithm. Itdiersfrom theoriginalonesimplybe auseit anworkeven inpresen eofowswithagiven peak rate. This is a hieved by de reasing the rate of a ow over all paths when its total rate over omesitspeakrate. TRUMPrequirestoset threeparameters. Arstparameter, alled

w

is aweighttoadjustbalan ebetweenutilityand ostfun tion. Itisstronglyrelatedtotopologyand link apa itiesandittunesthemaximumnetworkload. Ase ondone, alled

β

,weighstheimpa t ofa ongestedlink,whileathird one, alled

γ

,isthein rease/de reasestep. Forour omparison purposes weset them to

w = 10

−2

toallow owsto fully utilizelinks,

β = 10

−3

to respe t link apa itiesand

γ = 10

−3

∞

55

Table3: Peruserpeakrateevolutionovertime. Ratesvaluesareexpressed inMb/s.

5.5.2 Results

Figure7reportsthetopologyusedinthesimulationsweshowinthisse tiontoshowthebehaviour of MIRTO. Link apa ities and laten ieshavebeensele ted in orderto have pathdiversityand dierentresponse time. There arethreeowsinthenetworkand wesele tassour e-destination pairs1-2,3-2and4-5. Flowpeakrates hangeovertimeasspe iedintable 3. Notethat,

∞

is usedtoindi ate elasti ows. Thisjustmeansowpeakrateislargerthantheavailablenetwork resour es. Everyow anbesplitoverfourdierentpathsasshowninFigure.

Figure 8showsthetotalowratesand theows splittingobtainedbyrunning MIRTOover aFD ar hite tures. MIRTOrates are ompared to thoseobtainedbyrunning theLP optimizer des ribedinse tion4. Asexpe ted,totalowratesandratesplitsoverpathsa hievedbyMIRTO followthoseobtainedbytheLP.Flu tuationso urandaremorepronoun edwhentwoormore owsareelasti . Thisisduetotheprobingnatureofthealgorithmthatallowstheglobaloptimum attainment.

Figure9showsowratesobtainedbyrunningMIRTOoveraFQar hite tureanda omparison withtheLP.Overthisar hite tureonlytotalowratesfollowthetrendoftheLPwhiletheow spitting is quite dierent from optimum. This onrms what stated in se tion 5 as FA breaks oordinationamongows. Inthatway,ows annota hieverateslargerthantheirfairrateover paths. Thisleadstoasub-optimalsolutioneveniftotalowratesarethesameasbefore. Infa t, they have been a hieved with alarger network ost. As expe ted, with aFA ar hite ture rate u tuationsareredu edandthealgorithm onvergesinashortertime.

Finally, Figure 10reports performan e of theTRUMP algorithm. TRUMPa hievesoptimal ratesandsplittingbutittakeslongtimeto onvergeandsomelongtermu tuationso ur. This is a onsequen e of theset of parameterswe used. With dierentvalues we would have seena dierentbehaviourswithmu hfaster onvergen eandnou tuations. Howevertheoptimisation

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3 X

1 X

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80

90 Time [sec]

Rate [Mb/s]

Rate split User 3

X

1 X

3 X

4

Figure8: Timeevolutionoftherateallo ationforMIRTOinaFDar hite ture. Pointsindi ate theoptimalallo ation.

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Rate split User 3

X

1 X

3 X

4 X

2

Figure9: Timeevolutionof therate allo ationforMIRTOinaFA ar hite ture. Pointsindi ate theoptimalallo ation.

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solutionwouldhavebeensigni antlydierentfromthatwewanttoa hieve. A tuallythisisnot adrawba kofTRUMPasithasbeendesignedinthe ontextofintra-domainTEtolimitthelink loads within the network,even thoughauthors assume possible to implement su h ontrollerat endhosts. UnfortunatelyTRUMPdoesnotallowto predi tat whi h levelofutilisationlink an beset. Hen e the hoi e of parametersmightbevery omplex in networks with heterogeneous apa ities.

Wehavetested TRUMP fordierentsetup and dierent parametersand measuredits good propertiesin termoffast onvergen eastheauthorsin[13℄.

This show the hoi e of parameters in su h algorithms is a key point and ould be quite ompli ated. Moreoveritisstronglyrelatedtotopologyand oulddrivetoverydierentsolutions.

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Figure10: Timeevolutionoftherateallo ationforTRUMPinaQDar hite ture. Pointsindi ate theoptimalallo ation.

6 Dis ussion and Con lusions Theout omesofthis papersaremultiple:

we have studied ongestion ontrol and multi-path routing in presen e of demands with exogenous peak rates and we have found that multiple routes an be likely exploited by higherrateows.

innetworks enariothatare ommoninpra ti e, oordinatedandun oordinatedmulti-path routingperformthesame.

intypi als enarioswhere oordinationoutperformsun- oordination,multiplepathdoesnot gainmu h withrespe ttosinglepathrouting.

furthermoreweproposeanewmulti-pathoptimal ontroller alledMIRTO.This ontroller is ableto allo atemax-minbandwidthamongdemandsexploiting pathdiversity. The

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on-trollerhasbeen omparedwithothersolutionsandhasprovedtobeeasytobedeployedin dierentar hite tures.

Theabovementionedout omesallowtopositivelyrethinkaowawarear hite ture,intrinsi ally un oordinated,inpresen eofmulti-pathrouting. Indeedmulti-path ontrollersasMIRTO anbe ee tivelyusedinordertoexploitpathdiversityevenwhenaowawarenetworkimposesfairness atalinkbase. Task ofthe ontrollerremainstodynami allydenesplit ratiosoverthepathsas network onditions hange.

We suggest the use of multiple paths for a ertain lass of appli ations that are naturally robust to variability as adaptivevideo streaming, P2P le sharingand CDN as they an ee -tively exploitunused apa ity within thenetworkin bothInternet ba kbonesand wirelessmesh ba khaulingsystems. Ontheother hand,takinginto a ountthe overheadrequiredbymultiple routestransmissions,thisshouldnotbeusedformore onversationaltra asvoi e,web,orshort transa tionsasmail orinstantmessaging.

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