DOE/MICS ProgressReport

Project Title: “TowardsScalableCost-Effective Survivability in Ultra High SpeedNetworks”

Project Website: http://www.cs.wright.edu/� bwang/projects.htm/PI: Bin Wang,Wright StateUniversity

May 3, 2004

ABSTRACT

It is muchdesiredthatthefutureDOEnetwork possessestheability to dynamicallyrearrangetransportnetwork topologiesto enablethesharingof wide areatransportcapabilityamongapplications,andat thesametime dynamicallyvary transportbandwidthto suit different high performanceapplicationneeds. However,the uniquenetwork requirementsto supportDOE’s sciencemissionresult in challengingissuesthat arenotaddressedby existingnetworking techniquesandmethodologies.

Weproposeto studythespace-timedemandschedulingproblemanddesignefficientalgorithmsto auto-mateschedulingof resourcedemands(e.g.,bandwidth)of applications.Theresultantdemandschedule,routesandwavelengthassignmentswill thenbe usedby the signalingprotocolto configurethe network. Sincethespeedof configurationdeterminesrouting andconnectionefficiency (e.g., long configurationtimesareespe-cially not efficient for shortsessions),we considertheefficient establishmentandre-useof logical topologiesin our algorithmsso that the reconfigurationtime is minimizedto speedup provisioning. We will investigatetheprovisioningof multi-resolutionon-demandbandwidthsandefficient terabittraffic groomingin thespace-time schedulingframework. We will alsoconsiderthe needof multicastsupportin the future DOE networkby proposinga dynamicmulticastsessionprovisioning algorithmto facilitate large distributed collaborativeapplications.Theseefforts will bea steptowardsenablingon-demandbandwidthsby decouplingtheservicebandwidthfrom the infrastructurebandwidth. Finally, we will examinewaysin which cost-effective surviv-ability canbeprovided in meshtopologynetworksso that ring like restorationspeedis attainedwhile costofspareresourcesis minimized.Thisprovidesqualityprotectionoptionsfor thefutureDOEnetwork shouldsuchneedsaredeemednecessary.

DESCRIPTION OF ACCOMPLISHMENTS

1. Space-Time DemandScheduling

We arefocusedon dynamicserviceprovisioning in DOE WDM optical networks. We envision, in the nearfuture,thattheschedulingof applicationresourcedemands(e.g.,on-demandbandwidths)maybehandledby acentralserver becauseof therelatively smallscaleof theDOE network. This centralserver basedarchitecturemayevolve. However, thealgorithmsdevelopedcanbeadaptedtowork in adistributedenvironment.Theserverwill runaschedulingalgorithmthatdeterminestheroute,wavelengthassignment(i.e.,spatialinformation),andthetime interval duringwhich ademandis to beaccommodated.Thenetwork will thenbeconfiguredthroughthesignalingprotocolbasedonthescheduledeterminedby theserver. Theproblemis termedasthespace-timedemandschedulingproblem.

Specifically, given thenetwork topology���������

�

, where�

is thesetof nodesand

is thesetoflinks. Eachlink has � wavelengths.A setof light-pathdemands� is given, eachof which is representedby a tuple ( � ������������������ ) where � is thesource,� is thedestination,� is thenumberof light-pathsrequired(traffic groomingwill beconsideredlater),

�and�

arethestartingtime andendingtime of thedemand,�

isthe priority of the demand(for example,

�����indicatesa high priority and

��� �a low priority). A high

1

priority demandis onewhosestartingtimeandendingtimearefixedandthedemandshouldbeaccommodatedduringthegiventime interval while thetime interval of a low priority demandis negotiable,andthereforecanbemovedforwardor backward in time. Theproblemis to routeeachdemandandassigna properwavelengthto eachdemandsuchthat

! In thenon-blocking casein which thenetwork hasenoughresourcesto accommodateall thedemands,thegoalis to minimizethetotal network resourcesusedin termsof

1. thetotalnumberof wavelengthlinks usedby all demands;or

2. themaximumnumberof wavelengthsneededona link to balancethenetworkload.

! In the blocking casein which the network doesnot have enoughresourcesto accommodateall thedemandsasspecified,thegoalis

1. to minimizethenumberof demandsto berearranged(i.e., to minimizethesubsetof demandsthatmayhave to bemovedforwardor backward in time) in orderto have all thedemandsin theset �accommodatedby thenetwork; or

2. to minimize the total time from the time whenthe first demandarrivesto the time whenthe lastdemandends(termedastheschedulelength) it takesto satisfyall thedemandsin � .

Resource Demand Model A goodmodelfor on-demandbandwidthsis very important. We initially usethedemandmodel( � ������������������ ) to characterizetheapplicationresourcerequirements.This modelis differentfrom thesimpledynamictraffic modelcommonlyassumedin theliterature.Themodelthatis closestto oursisperhapsthatof [6]. In our model,thetime dimensionof demandsis explicitly consideredsincetransactionsinultra high-speednetworkswill beshort-lived in contrastto "$#&%(' operations.We believe that this modelmaybemoresuitableto characterizecertainDOEnetwork applicationresourcerequirements(e.g.,non-IPdedicatedconnections).Notethatthemodelmayallow theapplicationsto negotiatetheir startingtimesandendingtimeswith thescheduler. Thevalidity of this modelis subjectto whetheror not theparameters(i.e., startingtime,endingtime, bandwidthrequirementetc) canbe provided by the applications.The availability andaccuracyof the network stateinformationandaccessibilityby the centralserver arealso issuesto considerwhentheschedulingalgorithmis to be deployed. The modelwill be refinedandmodifiedasthe PI interactswith theDOEapplicationcommunityandDOEUtraNetstaff. For example,anew modelmayallow arangefor startingtimesandendingtimes,or allow multiplesplit timeintervalsduringwhichanapplicationmayrequireresourcesandsoon.

Theoptimizationof space-timedemandschedulingproblemswith differentobjectivesareformulatedand given in Appendix B. The solutionsto the optimizationproblemsserve as the baselinefor comparingproposedspace-timedemandschedulingalgorithms. We have designedschedulingalgorithmsto solve thespace-timedemandschedulingproblemandits variants.

1.1Time Window BasedSchedulingAlgorithm

Thehardnessof theproblemlies in thespatialandtemporalconstraintsimposedon thesetof demands.In thespatialdomain,demandsareroutedthroughthemeshnetwork topologyandmaysharethesamewavelengthon thesamelink. In thetemporaldomain,demandsmayoverlapin time. We proposeheuristicalgorithmsthattake advantageof resourcereusein bothdomains.

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Table1: An exampleof ascheduleddemandset

demand � � � � � �)+* , - 1 05:00 09:20 0 (low))/. , 0 1 07:00 12:40 0 (low))/1 2 3 2 08:00 14:00 1 (high))54 2 0 2 11:00 16:00 0 (low))/6 0 3 12:00 14:50 0 (low))/7 3 1 17:00 21:00 1 (high))98 - 2 3 18:00 21:00 0 (low)Ouralgorithmis basedon thefollowing observations.Demandsthatoverlapin timemustbedisjoint in

thespatialdomain(e.g.,they cannotsharethesamewavelengthon thesamelink). Network resourcesusedbyonedemandcanbereusedby anotherdemandaslongasthey donotoverlapin time. Thismotivatesusto dividethesetof demandsinto subsetsbasedon thedemands’startingandendingtimessuchthatdemandsin differentsubsetsaredisjoint in time. We representthesetof demands� usinganinterval graph(e.g.,Fig. 2)(b) whereaninterval representsthestartingandendingtimesof ademand.Basedontheinterval graphrepresentation,wecanthendivide thedemandsinto subsetscalledtimewindows(Fig. 2)(b). An algorithmto dividedemandsintotimewindows is givenlater. A virtual network topologyis associatedwith eachtimewindow. Notethatit is notalwayspossibleto assigna demandinto asingletime window. This demandis termedasa straddlingdemand,e.g., ) . and )/1 of Fig. 2(b). Theresources(e.g.,wavelength-links)usedby demandsin onetimewindow canbereusedby thedemandsin otherwindows exceptthosedemandsthatstraddlethesetime windows. Therefore,for straddlingdemandsthe sameresourceshave to be reserved acrosstime windows. In the following, wefirst describethe detailsof dividing the demandset into time windows andthe algorithmfor schedulingallthe demandsbasedon thesewindows. We thengive the algorithmfor solving the entirespace-timedemandschedulingproblem.

Time Window Division Thealgorithmdividesthesetof demandsinto disjoint timewindows. Demandswithina timewindow overlapin timepairwise. Therefore,all demandswithin thesamewindow have to bedisjoint inthespatialdomain,i.e., they cannotsharethesamewavelengthon thesamelink. Specifically, let

: �= ?@=ACB *ED � AGF (1)beanorderedsetof H : H demandendingtime values: *JI : .KIMLNLNLOI : = PQ= ( H : H�RSH �TH sincesome� A ’s maybethesame).We take thevaluesin

:aspossibledivision points.We definethata demandlies in a time interval

if its startingtime or endingtime lies in the interval. We thenadaptthemaximumindependentsetalgorithmover aninterval graph[5] to find a maximumtime interval (startingfrom theendingtime of theprevioustimewindow) during which all demandsoverlapin time pairwise. The algorithmpseudocodeis given in Fig. 1.Figure2(b)shows thetimewindow division resultof anexampledemandsetshown in Table1 whichhassevendemandsin anexamplenetwork shown in Fig. 2(a). In particular, )/. and ) 1 arestraddlingdemands.

After the time window division, a demandmay residewithin a certaintime window or straddletwoor morewindows. In the latter case,the demandis accommodatedonly when the samepathcanbe foundandresourceson the pathcanbe reserved in all the virtual networks associatedwith all the time windows itstraddles.Otherwisethedemandhasto be rearrangedsothatsufficient network resourcescanbeprovided inthenew windows it straddles.

Routing and WavelengthAssignment(RWA) Basedon Time Windows After dividing theoriginal demandsetusingthetimewindow divisionalgorithm,wehaveanumberof demandsubsets:0@UWV , 0XUWY , : � VA , : � YA

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Time Window Division Algorithm (M)Begin

T = the set of possible division points;

t0=T1; t1 = T1; W= Z ;for i = 1 to |T|

t2 = Ti;find all demands in [t0,t2] and put them in W;

find the cardinality of the maximum independent set of W, W*;

if (W* > 1) then

a new time window TW[t0, t1] and demands in it are determined;

t0 = t1; W= Z ;endif

t1 = t2;

endfor

End

Figure1: Pseudocodefor timewindow divisionalgorithm.

where 0 U[V and 0 UWY arethe setsof high-priority straddlingdemandsandlow-priority straddlingdemands,respectively;

: � VA and : � YA arethe setsof high-priority andlow-priority demandswithin time window \ ,respectively. Table2 shows thesubsetsafterthetime window divisionof theexampleshown in Fig. 2(b).

In additionto theabove subsets,we keepa virtual network� A for eachtime window : � A to recordits

residualnetwork resources.For eachnon-straddlingdemand] : � A , weapplyamodifiedDijkstra’s algorithmto the wavelengthgraphof the network to find the bestpath for the demandin the virtual network of timewindow

: � A . By bestpath,we meanthat thenumberof wavelengthsavailableon all thelinks alongthepathsatisfiesthe capacityrequirementof the demandandthe pathhasthe minimum total cost (in termsof e.g.,path length). Oncesucha path is found for the demand,we updatethe network status,i.e., remove all thenetwork resourcesusedby thepathfrom thevirtual network of time window

: � A . If thedemandcannotbesatisfiedin its time window, the next proceduredependson the priority of thedemand.If its priority is high(i.e., thedemandbelongsto some

: � VA ), theRWA algorithmstopsbecausea high-priority demandcouldnotbesatisfiedor thisdemandcanbedemotedto

: � YA andgivenapreferentialtreatmentwithin : � YA ; otherwise(i.e., thedemandbelongsto

: � YA ), we put thedemandinto demandsubset0X^ in whichall thedemandsneedto berearranged(Fig. 3).

For straddlingdemands(in 0XU[V or 0@U_Y ), we handlethem in the sameway except that the virtualnetwork in which eachdemandis routedis the intersectionof all the virtual networks of the time windowsstraddledby thedemand,andall thesevirtual networksmustbeupdatedif a pathis found. For eachdemand

Table2: Subsetsaftertime window division�`\ �a�Wb(cd� �

B C

A D

E F Time Window 3Time Window 2Time Window 1

r1

r2

r3

r4

r5

r6

r7

(a) (b)

Figure2: (a)A 6-nodenetwork; (b) A timewindow divisionexample.

subset( 0 U[V and 0 U_Y ), in addition,weselectademandfor routingandwavelengthassignmentin thedescend-ing orderof requestcapacityin theset.Ourobjective is to accommodateasmany demandswith highercapacityrequirementsaspossiblefirst. Therefore,thisalgorithm,in thissense,is agreedyRWA algorithm.Thepseudocodeof thealgorithmthathandles

: � VA , : � YA , 0@UWV , and 0@U_Y is givenin Fig. 3.Greedy Time Window RWA Algorithm (G, R)Begin // R: the set of demands to be scheduled

while (R fhg ) dochoose demand r which has the highest capacity requirement in R;G’ = G;for each time window TWi straddled by demand r

G’ = G’ i Gi;endforfind the shortest path pr for demand r in G’ ;if pr is found

R = R – r;for each time window TWi straddled by demand r

Gi = Gi - pr ;endfor

elseif the priority of demand r is high

demote r; else

put r in DR ;endif

endwhileEnd

Figure3: Greedytime window basedRWA algorithm.

If thenetwork resourcesarenotsufficienttosatisfyall thedemandsasspecifiedin theiroriginalrequests,someof the low-priority demandshave to be rearranged.That is, someof the low-priority demandscanbeaccommodatedin termsof their capacityrequirementsat thecostof changedschedules.0@^ is thedemandsetin whichall thedemandsmustberearranged.For eachdemandin 0 ^ , wetry to find oneor moretimewindowsin which thedemandcanbeaccommodatedandthewindow(s) starts/startasearlyaspossible.Therationaleisthatwe preferto schedulethedemandby reusingresourcesandwe would like to preventtherearrangementof

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Rearrange RWA Algorithm (G, R)Begin //TWi has an associated virtual network Gi

while (R jlk ) dochoose demand r which has the highest capacity requirement in R;pr = k ; i = 1; // pr route and wavelength assignment for rwhile (pr = k ) do

find the most right time window TWj such that windows i to j can accommodate demand r;if no such time window is found

create a new time window TWj with Gj for demand r;else

G’ = Gi m … m Gj;endiffind the shortest path pr for demand r in G’ ;if pr is found

R = R – r;for each time window TWi straddled by demand r

Gi = Gi – pr;endfor

elsei = i + 1 ;

endifendwhile

endwhileEnd

Figure4: RWA algorithmfor rearrangeddemands.

thedemandfrom prolongingthetotal time it takesto scheduleall demandsin � (alsotermedastheschedulelength).Thepseudocodeof theRWA algorithmfor rearrangeddemandsis givenin Fig. 4.

Space-Time Demand Scheduling Algorithm In the space-timedemandschedulingproblem,our objectiveis to accommodateall high-priority demandsandasmany low-priority demandsaspossiblewith both theircapacityrequirementsandschedulerequirements.If notall thedemandscanbesatisfiedin bothspaceandtimedomainsat thesametime,somelow-priority demandsmustbeselectedasvictims to berearranged.Therefore,to schedulethedemandset � , we try to routeandassignmentwavelengthsto high-priority demandsfirst, andthensolve the RWA problemfor low-priority demands.In addition,straddlingdemandsare routedprior tothedemandsresidingin a singletime window sinceit is morelikely to routea straddlingdemandearlier. Thepseudocodeof theoverall time window basedRWA algorithmis givenin Fig. 5.

Time Space Demand Scheduling Algorithm(G, M)

Begin

run Time Window Division Algorithm (M);

run Greedy Time Window RWA Algorithm (G, DSH);

run Greedy Time Window RWA Algorithm (G, TWiH) for all time window TWi;

run Greedy Time Window RWA Algorithm (G, DSL);

run Greedy Time Window RWA Algorithm (G, TWiL) for all time window TWi;

if (DR n�o ), run Rearrange RWA Algorithm (DR);End

Figure5: Space-timedemandschedulingalgorithm.

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1.2Traffic Matrix BasedSchedulingAlgorithm

In this algorithm,we divide thedemandset � into a numberof subsetsusinga similar approachusedby thetimewindow basedschedulingalgorithm.Thedifferenceis thatdemandsin asubsetsdonothave to bedisjointin time pairwise.We thenconstructa traffic matrix for eachdemandsubset.A traffic matrix characterizesthetraffic betweensource-destinationnodepairs.Thedemandset � canthenbeconsideredastimevaryingtrafficthatis modeledby asetof traffic matrices.A framework wasproposedin [18] to solve theRWA problemwhentheofferedtraffic is characterizedby a setof traffic matrices- a variantof dynamicallychangingtraffic. Weobserve that thedemandmatriceswe obtaincanberegardedasthetraffic matricesof [18]. We thenadaptthealgorithmproposedin [18] to solveourspace-timedemandschedulingproblem.Morespecifically, theadaptedalgorithmneedsto handlepriorities of demands,straddlingdemands(demandsthat residein multiple trafficmatrices),andrearrangementof demands.

1.3PerformanceEvaluation

We arecurrentlyperformingsimulationstudiesto evaluatetheperformanceof theproposedalgorithmsandtoenhancethealgorithms.Wearelookingat timecomplexity of theproposedalgorithms,algorithmperformancewith respectto demandtime correlation(i.e., to whatextentdemandsarecorrelatedin time), the tradeoff be-tweendemandtimecorrelationandtimewindow selectionin thetraffic matrixbasedschedulingalgorithm,andsoon. As theon-demandbandwidthsmayvary for differentapplications,we plan to includetraffic grooming(i.e., to efficiently dealwith multi-resolutionon-demandbandwidths)in thespace-timeschedulingframework.Finally, we alsoplan to adapttheproposedalgorithmsto handledynamicallyarrived demands(i.e., demandsarenot given by a known set � ; rather, a demanddynamicallyarriveswith a requestedlastingtime) usingamoving time window basedschedulingapproach.

Theperformanceresultsandfine-tunedalgorithmswill bereportedin thenext progressreport.

2. Dynamic Multicast SessionProvisioning in WDM Optical Networks

Large,distributedcollaborative projectsareincreasinglycommonin DOE.CurrentIP-multicastis still a fragiletechnology. While effortsonmakingIP-multicastmorerobustareon-going,webelievethatastheDOEnetworkmigratesto WDM basedopticalnetworks,supportof multicastwithin theopticalnetwork becomesnecessaryfor many reasons,for example,highbandwidthrequirements,guaranteedperformance,andeffectivesharingofresourceswith othertypesof services(e.g.,dedicatednon-IPservice).

In orderto effectively supportmulticast,nodesin a WDM network needto have additionalcapabilitiesthantypical WDM nodeshave. Nodesmay have the capabilityof tappinga small amountof optical powerfrom a wavelengthsignalandforwardingthe restto appropriatenodes.This capabilityis termedastap-and-continue(TaC). In this case,multicastcanbe achieved throughoneor more light-pathsthat includeall thenodesin themulticastgroup.Eachlight-pathrequiresa separatetransmissionfrom thesource.This approachis characterizedby thelight-pathmodel[13]. Ontheotherhand,if anodeis equippedwith light splitters(calleda splitting anddelivery node(SaDnode)),it cansplit the optical power of a wavelengthsignal into multiplepartsandroutethemto multiple outgoinglinks. Eachtransmissionfrom thesourceresultsin a light-tree.Thisapproachis characterizedby thelight-treemodel[14]. With all thenodeshaving bothsplitting andwavelengthconversioncapability, a singlelight-treemay beconstructedfor a multicastsession.In networks with sparsesplitting capability(i.e., to reducecost),it maynot bepossibleto includeall thenodesof a multicastgroupinasinglemulticasttree,therebycalling for theconstructionof asetof light-trees.Thesetof light-treesrequired

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for a singlemulticastsessionis calleda light-forest. Eachlight-treerequiresoneseparatetransmissionusinga differentwavelengthon the samelink, or may usethe samewavelengthon a different link, or a differentwavelengthonadifferentlink.

In this work [19], we considerdynamicmulticastsessionprovisioning in a futuristic scenarioin theDOE network. We assumethe wavelength-routedWDM network with an arbitrarymeshtopologywhich isrepresentedby a graph

�p�T�����

�where

�is thesetof nodes,and

is thesetof unidirectionaledges.The

network consistsof nodeswith full, partial,or no wavelengthconversioncapabilities.Weassumethatsplittinganddelivery (SaD)nodesareavailableandhave full splitting capability. An SaDnodeis ableto perform

�-

way light splitting. This typeof devicesis becomingcommerciallyavailable. In our continuingwork, we willconsiderthecasewherenoSaDnodesareavailableandspace-timeschedulingof multicastsessions.Westudytheprovisioningof dynamicmulticastsessionsin WDM opticalnetworkswith sparsesplitting capability(thatis, only a selectedsetof nodesis equippedwith splitting capability)with theobjective of minimizing networkresourcesused.

Theproblemof dynamicmulticastsessionprovisioningin WDM opticalmeshnetworks is to routethemulticasttraffic sessionfrom eachsourceto themembersof everymulticastgroup,andto assignanappropriatewavelengthto the session.Traditionally, routing andwavelengthassignmentareconsideredastwo separateproblems.To optimally provision multicastsessions,optimizingeachproblemseparatelyandthencombiningthemtogether, in general,do not yield an optimal solution to the completeproblem. To derive the optimalsolution, routing andwavelengthassignmentneedto be consideredsimultaneously. We thereforeformulatetheproblemasaninteger linearprogram(ILP). TheILP formulationis generalin that it only assumesthatthenetwork haspartiallight splitting capability.

We proposeandevaluateanefficient heuristicalgorithmfor routingandassigningwavelengthsto dy-namicallyarrived multicastsessionrequests.The solution to the ILP formulationservesas the baselineforevaluatingthe performanceof the proposedalgorithm. The basicideaof the proposeddynamicsessionpro-visioningalgorithmis to first find a setof minimumpaths(in termsof numberof hops)from thesourcenodeto thedestinationnodes.Uponfinding sucha set,the restof thealgorithmtries to merge thesepathsto forma light-treeor a setof light-trees(a light-forest) that spanto reachall the destinationnodes. The minimumhoppathsarefoundusingtheDijkstra’s algorithm. Thealgorithmtries to make full useof SaDnodesin thenetwork. NotethatdifferentSaDnodeassignmentpoliciescanbeusedwith ourproposedalgorithm.

We have evaluatedthe effectivenessof the proposedonline algorithmvia simulationin termsof theconnectionblockingprobabilityandtheresourcesusedby asession.All thesimulationresultsarebasedonanaverageof 20simulationruns.The14-nodeNSFnettopology(Fig. 8(a))is usedin thesimulationwith onepairof unidirectionalfibersbetweentwo directly connectednodes.Thenumberof wavelengthssupportedon eachfiber is 8. Nodesin thenetwork arerandomlyassignedto beequippedwith full rangewavelengthconvertersandtheothernodeshavepartialwavelengthconversioncapabilities.Multicastsessiondemands(e.g.,thesourcenodeandthedestinationnodes)arerandomlygenerated.

The first setof experimentswereconductedto checkfor efficiency of the heuristicdynamicsessionprovisioningalgorithm.Fig 6(a)shows theresultswhereaveragesessionlastingtime is setat

�timeunit (with

exponentialdistribution), andnetwork nodesarerandomlyassignedasSaDnodesin this setof experiments.As seenfrom Fig. 6(a), thecurvesshow a generaltendency of growth in thepercentageof sessionsroutedinthenetwork asthetotalnumberof SaDnodesincreases.Theproposeddynamicsessionprovisioningalgorithmperformswithin 10-20%of theILP solutions.Thegrowth rateis higherfor theheuristicalgorithm,indicatingthatthealgorithmperformsbetterwhenthenumberof SaDnodesbecomeslarger.

Fig. 6(b) depictsthe resultsfrom a setof experimentssimilar to the first set. Ratherthan randomly

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1 2 3 4 5 6 7 8 9 10 11 12 13 14

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% o

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ucc

essf

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ou

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g

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% o

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ucc

essf

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ou

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g

ILP Solution

Heuristic Solution

(a) (b)

Figure6: (a) Percentageof successfullyroutedsessionsversusthetotal numberof SaDnodesin thenetwork.The performanceof the heuristicalgorithm getsbetteras more SaD nodesare addedto the network. (b)Percentageof successfullyroutedsessionsversusthetotal numberof SaDnodesin thenetwork. Thesplittersareassignedto nodesbasedon thenodes’frequency of usein multicastrouting.

assigningSaDnodes,thesplitting capablenodesareassignedto nodesbasedon thenodes’frequency of useduring multicastrouting. By nodes’frequency of useduring multicastrouting, we meanthat the nodemostfrequentlyusedin multicastsessionroutingwhile thereareno splittingcapablenodesin thenetwork is chosenfirst to bea SaDnode,thenthenext frequentlyusednodeis chosen,andsoon. Theresultsof Fig. 6(b) showthatfor theILP solution,thisSaDnodeassignmentpolicy doesnot improvetheperformanceasmuchcomparedwith theprevioussetof experiments.However, theheuristicalgorithm,in this situation,performsmuchbetterwhenonly a few SaDnodesareavailablein thenetwork.

Fig. 7(a) illustratesthe resultsof our next set of experimentsconducted. We measurethe blockingprobabilityof multicastsessionsasmoreSaDnodesareaddedto thenetwork with varyingtraffic load.Splittingcapablenodesin thenetwork arerandomlyassigned.As seenfrom Fig. 7(a), themulticastsessionblockingprobabilitiesfor both the ILP solutionsandtheheuristicalgorithmincreaseastraffic load increases.We alsoobserve that theheuristicalgorithmperformsbetterandbenefitsmorefrom theaddedsplitting capablenodesthantheILP.

Thelastsetof experimentslook at thesizeof routingtreesin termsof numberof links used.In Fig 7(b),theaveragenumberof links usedby amulticastsessionobtainedby theILP andthatby theheuristicalgorithmarecomputedasa ratio. The figureshows that theaveragenumberof links usedpermulticastsessionin theheuristicalgorithmincreasesuntil about50%of nodesin thenetwork areSaDnodes.Thereafter, asmorenodesareSaDnodes,thecurvesremainvery close.This shows that themulticasttreesconstructedby our heuristicalgorithmis veryefficientwhenonly a fractionof thenodesareSaDnodes.Theresultsandfindingshavebeensubmittedfor publicationto IEEE Globecom,2004.

3. Optimal Configuration of q -Cyclesin WDM Optical Networks with Partial WavelengthCon-version

In the future DOE network, delivery of terabytesof dataper transactionwill be thenorm ratherthantheex-ception. Sincea failure in a WDM opticalnetwork mayresult in a tremendousamountof dataloss,efficientprotectionof datatransportis thusvery important.Therearetwo typesof well-known approachesto protectingopticalnetworks: ring-basedprotection[3] andpath-basedprotection[21, 12, 20]. Ring-basedapproachesare

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io o

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er o

f L

inks

Per

S

essi

on

7% SaD

20% SaD

50% SaD

70% SaD

85% SaD

(a) (b)

Figure7: (a) The sessionblocking probability versusdifferentsessionloadsandnumberof SaDnodes. (b)Ratio of the averagenumberof links usedfor establishinga sessionin the heuristicalgorithm over that ofsolutionsobtainedby ILP.

easierto manageandoffer very fastprotectionswitching.However, they arerathercapacityinefficient. Mesh-basedapproaches,on theotherhand,requiremuchlesssparecapacity, but have thedrawbackof complicatedsignalingandnetwork managementfor protection.Thepre-configuredprotectioncycle (

�-cycle) basedtech-

niques[4] combinethebenefitsof both ring-basedandpath-basedapproachesin that it canachieve ring-likerecoveryspeedwhile retainingthedesiredcapacityefficiencyof path-basedprotectionapproaches. Note thatcost-effectivefast restoration is very much desirable for the DOE productionnetwork. This effort providesqualityprotectionoptionsfor thefutureDOE network shouldsuchneedsaredeemednecessary.

Whenwavelengthconversionis notavailable,a light-pathmustusethesamewavelengthonall thelinkstraversedin a WDM opticalnetwork. This requirementis known asthewavelengthcontinuityconstraint.Ontheotherhand,if wavelengthroutersarecapableof wavelengthconversion,anopticalsignalmaybeconvertedfrom onewavelengthto anotherwavelength.In somepreviouswork on

�-cycle basedprotection[15, 17, 16],

a light-pathfollowing thewavelengthcontinuity constraintis calleda wavelengthpath( �Mr ) while a virtualwavelengthpath(

� �Mr ) is definedto bea light-paththatuseswavelengthconvertersateachnodeon thepathandmay have differentwavelengthson different links that thepathtraverses.Therefore,a �Mr network hasno wavelengthconversioncapabilitiesat all while a

� �Mr network hasfull wavelengthconversionat everynode,i.e., therearesufficient convertersat eachnodeto convert any incomingwavelengthto any outgoingwavelength.

In this work [8], we studytheoptimalconfigurationof�-cyclesin survivableWDM opticalmeshnet-

workswith partialwavelengthconversionwhile 100%restorabilityis guaranteedagainstany singlefailures.Weformulatetheproblemastwo integer linearprogramsfor non-jointandjoint optimizationcases,respectively.In the non-joint approach,working pathsare known beforeprotectionconfigurationis processed.

�-cycles

andwavelengthconvertersarethenoptimally determined.In thejoint approach,working paths,�-cycles,and

wavelengthconvertersarejointly determined.Theobjectivesin bothcasesareto minimizethetotalcostof linkcapacityusedby workingpathsand

�-cyclesaswell asthecostof wavelengthconvertersrequiredto accommo-

dateasetof traffic demand.In theproposed�-cycleconfigurationarchitectures,wetake into accountconverter

sharing:(a) whenconvertersareusedfor accessing�-cyclesandfor wavelengthconversionbetweentwo ad-

jacenton-cycle spans;(b) whenconvertersareusedamongdisjoint straddlingspansincidentto thesamenodefor accessing

�-cycles.Convertersharingreducesnetwork costby requiringasfew convertersaspossible.Our

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Figure8: Two examplenetworksfor performanceevaluation.

simulationresultsindicatethat theperformancesof theproposedapproachesoutperformexistingapproachesin termsof total networkcostand total numberof converters required. In addition,our approachesresultsinmorebalancedconverterusein thenetwork.

Specifically, we evaluatetheperformanceof our proposedoptimizationmodelsagainstthatof theap-proachesfor

� �Mr networks andfor networks in which converterscanonly beusedto access�Mr � -cyclesfrom �Mr working paths[17, 16]. Two cases,non-jointoptimizationandjoint optimizations,areconsideredin eachof the threeapproaches.Therefore,overall six architecturesare investigatedin the simulationandabbreviatedasfollows:

! rd�`r sut : working pathsuse �Mr ; partial wavelengthconversionon � -cycles if required;non-jointoptimization;(ourapproach)

! rd�`r t : workingpathsuse �Mr ; partialwavelengthconversionon � -cyclesif required;joint optimiza-tion; (ourapproach)

! �Mr svt : working pathsuse �Mr ; protection� -cyclesuse �Mr ; � -cyclesareaccessedwith wavelengthconversionif required;non-jointoptimization

! �Mr t : working pathsuse �Mr ; protection� -cyclesuse �Mr ; � -cyclesareaccessedwith wavelengthconversionif required;joint optimization

! � �Mr svt : workingpathsuse �Mr ; protection� -cyclesuse � �Mr ; non-jointoptimization! � �Mr t : workingpathsuse �Mr , protection� -cyclesuse � �Mr ; joint optimization

In the non-joint optimizations(i.e., rw�Mr sut , �Mr sut and � �Mr sut ), we usethe shortestpathrouting algorithmto find a working pathwith the shortesttotal link length for eachdemand,andapply theFirst-Fit strategy to assignrequirednumberof wavelengthsto thepath. For the joint optimizationcases(i.e.,rw�Mr t , �Mr t and � �Mr t ), on theotherhand,we take all shortestroutesasthesetof eligible routes.Inbothcases,eachworkingpathis a �Mr (i.e., thesamewavelengthis assignedto all spansalongthepath)andasetof candidate

�-cyclesis givenasinput for optimal

�-cycleconfiguration.

Two examplenetworksshown in Fig. 8 areusedfor performanceevaluationandcomparison.We firstevaluatethe performanceof threenon-joint approachesusingthe NSFNETtopology(Fig. 8(a)). Due to therelatively high computationalcomplexity of thejoint methods,especiallyfor rw�Mr t and �Mr t , we chooseto comparetheperformanceof thesix architecturesusinga smaller

�x�-nodenetwork shown in Fig. 8(b). We

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Figure9: Total costversusrelative costof asingleconverter.

usedemandsetscontaining' � and % � bidirectionalpairsfor theNSFNETtopologyandthe �x� -nodenetwork,respectively. The sourceanddestinationof traffic requestsarerandomlygenerated.In addition,we assumetwo fibersperspanand % � wavelengthsperfiber in theNSFNETtopologywhile the �x� -nodenetwork has �x�wavelengthsperfiber. Moreover, themaximumnumberof convertersplacedateachnodeis fixedto ' � and ey�in thetwo networks,respectively. However, the �Mr and � �`r approachesdo not follow this constraint,i.e.,thenumberof convertersusedat eachnodeis unlimitedin the �Mr and � �Mr approaches.Total CostComparisonThetotalcostrequiredto accommodatethetraffic demandsincludesthecostof wave-lengthconvertersandlink capacitycostsincurredby all working pathsand

�-cycles.Fig. 9(a)shows thetotal

costsrequiredby thethreenon-jointapproaches,respectively, asthecostof onewavelengthconverteris variedrelative to thecostof onewavelength-linkin theNSFNETtopology. We expresstheconvertercostin termsofthecostof a wavelength-linkof certainlengthin orderto figure in the factorthatwavelengthconversioncostmayvary greatlywith differenttechnologiesandadvancementof technologiesover time. Fromthefigure,weobserve thatour non-jointapproach( rw�Mr sut ) incursmuchlesscostthantheothertwo approaches.Whentheconvertercostis 60 units, for example,the total costincurredin our approach( rw�Mr sut ) is only about77%and70%of thatin �Mr sut and � �`r sut approaches,respectively.

Fig. 9(b) shows that the total costsof our proposedoptimizationmodelsaremuch lessthanthosein� �`r networks in both thenon-jointandjoint cases(i.e., � �`r sut and � �Mr t ), andeven lessthanthenon-joint �Mr approachin whichwavelengthconversionis only usedfor �Mr workingpathsto access�Mr � -cycles(i.e., �Mr sut case).Themainreasonis thata smallernumberof convertersis usedin ourapproaches.Although the total costrequiredby �Mr t is closeto that of rw�Mr t , we observe that �Mr t needsmorewavelengthsoneachspanto satisfyall demands.In otherwords,asetof demandswhichcanbeaccommodatedby rw�Mr t may not necessarilybe satisfiedby �Mr t if the numberof wavelengthson eachspanin thenetwork is not large enough.We alsoobserve from the figure that the performanceof joint optimizationsindifferentarchitecturesperformmuchbetterthanits correspondingnon-jointcounterpartsasreportedin [17, 16].

Impact of ConvertersOurapproachesdeploy workingpathsand�-cyclessothatthetotalcostof link capacities

andwavelengthconvertersusedin theentirenetwork isminimizedtoaccommodateasetof traffic demands.Ouroptimizationmodelstake convertersharinginto considerationto reducecostsby requiringasfew convertersaspossible. In our approaches,in caseof a failure, the convertersat a nodecanbe usedeither for workingpathsto access

�-cycleswhenwavelengthconversionis necessaryor for wavelengthconversionbetweentwo

adjacentlinks on thesame�-cycle. Theconverterscanalsobesharedamongdisjoint straddlingspansincident

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Figure10: Total numberof convertersusedversusrelative costof asingleconverter.

to thesamenodefor working pathsto access�-cycles. In contrast,convertersharingis not consideredat all

in [17, 16]. In their partial conversionapproach,converterscanonly be usedfor working pathsto access�-

cycles. In their� �Mr case,on the otherhand,convertersareusedexclusively for working pathsto access�

-cyclesor for wavelengthconversionbetweentwo adjacenton-cycle spans.At the commonnodeto whichstraddlingspansareincident,moreover, acertainnumberof dedicatedconvertersareneededfor eachstraddlingspan. Therefore,their approachesneedmuchmoreconvertersto accommodateall traffic demandsasshownin Fig. 10. The resultsindicatethat our approachesin generalperform much betterthan other approachesexcept that rw�Mr t slightly outperforms�Mr t asshown in Fig. 10(b). For example,when the convertercost is 40 units, rd�`r sut usesabout42% and 30% converterscomparedwith �Mr svt and � �Mr svtapproaches,respectively, in Fig.10(a)while rw�Mr t usesabout50%and2%converterscomparedwith �Mr tand� �Mr t approaches,respectively, in Fig. 10(b). However, �Mr t needsmorewavelengthson eachspan

to accommodateall traffic demands.

In additionto thetotalnumberof convertersused,wealsoconsiderthemaximumnumberof convertersrequiredamongall thenodesin thenetwork whenevaluatingtheperformancesof differentapproaches.Thisquantityindicatesthefairnessof differentapproachesin converterrequirementanduse.A smallernumberim-pliesthatthedifferencein thenumbersof convertersusedatvariousnodesmaybesmaller. Therefore,converterusemay be morebalancedin the network. Fig. 11 shows that our approachesrequirea muchsmallermaxi-mumnumberof convertersamongall thenodesandthereforeoutperformotherexistingapproaches.Whentheconvertercostis 40 units,for example,themaximumnumberof convertersamongall thenodesin rw�Mr svtapproachis only about33% and8% of that in �Mr svt and � �Mr sut approaches,respectively, while themaximumnumberof convertersamongall thenodesin rw�Mr t approachis only about6%of thatin � �Mr tapproach,asshown in Fig. 11(b). The resultshave beensubmittedfor publicationto IEEE/SPIEBroadNets,2004(previously known asOptiComm).

4. Impact of Working Path Routing Algorithms on Cost-Effectivenessof q -Cycle basedProtec-tion for WDM Optical Networks

To dynamicallyprovisionservicesin futuresurvivableDOEnetwork (assumefor example�-cyclesareusedfor

protection),we needto studytheimpactof routingalgorithmson thecost-effectivenessof theentirenetwork.

In�-cycle basedprotectionfor optical networks, especiallyin the caseof non-joint optimal working

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Figure11: Maximumnumberof convertersusedateachnodeversusrelative costof asingleconverter.

capacityroutingand�-cycle configurationstudiedby variousresearchers,whereworking capacityof a traffic

demandis routedbefore�-cyclesareoptimallyconfigured,theroutingof workingcapacityof a traffic demand

hasinvariablybeenassumedto usetheshortestpathrouting. However, shortestpathsfor routingworking ca-pacitiesmaynotnecessarilyresultin thebestoverallnetwork resourceoptimizationwhen

�-cycleconfiguration

is figuredin. In this work, we conductsimulationbasedstudiesof the impactof accommodatingworkingca-pacitiesusing " different routingalgorithmson theoverall networkresourceoptimizationin � -cycle protectedoptical WDM networks. The overall resourceoptimizationproblemis solved basedon the work reportedin[15, 17], wheretheproblemsof optimal

�-cycle configurationin survivableWDM opticalmeshnetworkswith

no wavelengthconversion,full wavelengthconversion,andpartialwavelengthconversionareformulated.Ourresultsshow thatwhenwavelengthconversionis allowed, thewidestshortestpathrouting, in general, outper-formsotheralgorithmsfor routingworkingcapacitiesto achievetheleastoverall networkcostunderdifferentoptimizationmodels,networkconfigurations,andworkloads. Thedetailsof simulationresultsarereportedin[10] andsubmittedfor publicationto IEEE/SPIEBroadNets,2004(previouslyknown asOptiComm).Thefind-ings provide a preferredrouting algorithmto achieve cost-effectivenessin future survivablenetworks should�-cyclebasedmechanismis usedfor network protection.

FUTURE CHALLENGES

Wehave identifieda few futurechallenges:

! Refining demand model: An expressive, flexible, and accuratemodel that capturesthe applicationresourcedemandcharacteristicsis crucialfor dynamicresourceschedulingandserviceprovisioning.Wehave an initial modelwhich is to be refinedover time with inputsfrom theapplicationcommunitiesaswell asthe UltraNet researchers.We alsoplan to adaptthe modelby usinga moving time window tohandledynamicallyarrived demands,i.e., demandsarenot given by a known set � ; rather, a demanddynamicallyarriveswith a requestedlastingtime.

! Terabit traffic grooming: Recognizingthat resourcedemandsvary greatlyover differentapplications,e.g.,multi-resolutionon-demandbandwidths,agroupof channels(e.g.,acontrolchannelandadatachan-nel) with differenton-demandbandwidths,thePI will tacklethis problemby designingtraffic groomingalgorithmsin the proposedspace-timedemandschedulingframework. Our initial work on multicasttraffic groomingis reportedin [1]. Variousprovisioning modesmustbesupportedso that applications

14

requiringmultiple channelswith a combinationof requirementscanbe effectively supported.The ca-pabilitiesof provisionedchannelsmustaccommodateburst, real-timestreams,aswell aslower prioritytraffic.

! Burst and long sessionscheduling:Sincethespeedof configurationdeterminesroutingandconnectionefficiency, long configurationtimesareespeciallynot efficient for shortburst datatransfer. Therefore,until configurationtimescanbesignificantlyreducedasthetechnologiesadvance,anintelligentschedul-ing shouldbedesignedto hide therelatively long configurationtime. We proposeto adaptour proposedspace-timeschedulingalgorithmsandtechniquescurrentlybeingdevelopedin theopticalburstswitchingarenato theschedulingof burstdatatransfersanddynamicon-demandbandwidths.

! Multicast demand scheduling: Theprovisionedchannelsmustalsoprovide for multi-point or shareduseto enableincreasinglypopulardistributed large-scalecollaboration. A receiver initiated approachis likely to be the mostsuitablesolution. A closelyrelevant problemis the space-timeco-schedulingof unicastchannelsandmulticastchannels,andefficient traffic groomingof multi-resolutionresourcedemands.We have donesomepreliminarywork on multicasttraffic groomingin [1] asdescribedin theaccomplishmentsection.

! Delay/jitter agile service provisioning: Circuit-switcheddedicatedchannelsofferstheminimumdelayanddelayjitter. Additional non-deterministicdelayanddelayjitter maybe introducedby hostprocess-ing (e.g.,operatingsystemandprotocolprocessing),network interfacecards,accessnetwork, andO-E-Oconversion.ThecontinentalUSroundtrip timeis about40ms.Toprovidedelay/jitteragileservicesto ap-plications,thePIbelievesthatanadaptivecross-layerapproachisneeded.Dedicatedchannels/guaranteedbandwidthsareneededto ensureminimumtransportdelay, especiallyfor instrumentcontrolandsteeringapplications.Residualdelayjitter mustbeabsorbedin theplayoutbuffer atthereceiving end.Weproposeto investigateanddevelopappropriatecross-layerdesignapproacheswhich will take threedirectionsinan integratedmanner:(i) low-latency sourcecodingandchannelcoding,(ii ) space-timeschedulingofon-demandresources,and(iii ) adaptive playoutbuffering andoutputscheduling.

! Integrated framework: To supportDOE’ssciencemissionthatincludefrom traditionaldataservicestoadvancedlarge scaledatatransport,a provisioning framework needsto integrateprovisioning,schedul-ing of IP services,non-IP(e.g.,dedicatedchannel)services,delay/jitteragile services,andso on. Inaddition,resourcesmustalsobedynamicallyprovisionedfor theproductionnetwork, researchnetwork,andexperimentalnetwork undertheintegratedframework.

! Cost-effective grade of protection: The network shouldprovide cost-effective gradeof protectionbyallowing theselectionfrom a variety of survivability options(with differentassociatedcost)asneeded[11, 7, 9, 8]. Theprotectionschemesshouldbeintegratedwith theserviceprovisioningframework.

Finally, wehopeto collaboratewith DOEandUltraNetpersonnelto designandimplementtheschedul-ing server, middleware,andinterfacewith thesignalingprotocol,testandvalidatethe implementationundercontrolleddeploymentin theDOEtest-bednetwork.

RESEARCH INTERACTIONS

Our interactionwith theDOE researchershave beenlimited sofar giventhatwe have beenfocusedondevelopingalgorithmsandconductingbasicresearch.ThePI madeinitial contactwith UtraNetpersonnel,inparticular, Dr. Nagi RaoandDr. Bill Wing at ORNL, on April 6 and26, seekingfeedbackon currentworkandcollaborationondynamicserviceprovisioning. Interactionswith DOEresearcherswill increasein thenear

15

futureoncethealgorithmsgetmorematureandarereadyto betestedin a test-bednetwork. ThePI alsoplanto interactwith theDOEapplicationcommunitiesto seekinformationonapplicationrequirementsandpatternsof network use. The goal is to comeup with a moresuitablemodel for demandsandresourceuseby DOEapplications.

The researchinteractionand collaborationwith Dr. Abdul A. S. Awwal of DoE lab hasbeenveryproductive. Together, we have identifiedandsolved several interestingproblemson unicast/multicasttrafficgroomingandnetwork protectionandrestoration[1, 2] thatcanpotentiallybeapplicableto relevant to futureDOE networks.

The PI hasalsostartedcollaborationwith Prof. BiswanathMukherjeeof University of California atDavis andProf. G. K. Changof Georgia Instituteof Technologyon issuesrelatedto multicastsupport,space-timescheduling,anddelay/jitteragileserviceprovisioning.Discussionswith Prof. MukherjeeandProf. Changhave beenvery thought-provoking. Feedbackon thePI’s currentwork from Prof. MukherjeeandProf. Changhasbeenvery positive andhelpful.

Finally, we attendedIEEE INFOCOM 2004 and 7th INFORMS conference,presentedsomeof ourresearchresultsandfindings[19, 11], andexchangedideaswith researchersfrom otherinstitutions.

References

[1] A. R.B. Billah, B. Wang,andA. A. S.Awwal. Multicasttraffic groomingin WDM opticalmeshnetworks.Proceedingsof IEEE Globecom:Optical NetworkingSymposium,SanFrancisco,CA USA, December2003.

[2] A. R. B. Billah, B. Wang, and A. A. S. Awwal. Efficient traffic groomingin SONET/WDM BLSRnetworks. OpticalEngineeringJournal, May 2004.

[3] A. FumagalliandL. Valcarenghi.IP restorationvs. WDM protection:Is thereanoptimalchoice? IEEENetwork, pages34–41,November/December2000.

[4] W. D. Grover andD. Stamatelakis.Cycle-orienteddistributed pre-configuration:ring-like speedwithmesh-like capacity for self-planningnetwork restoration. Proc. IEEE International Conf. Commun.(ICC’98), Atlanta, pages537–543,June1998.

[5] U. I. Gupta,D. T. Lee,andJ.Y. T. Leung.Efficientalgorithmsfor interval graphsandcircular-arcgraphs.Networks, pages459–467,1982.

[6] J. Kuri, N. Puech,M. Gagnaire,E. Dotaro,andR. Douville. Routingandwavelengthassignmentsofscheduledlightpathdemands. IEEE Journal on SelectedAreasin Communications, 21(8):1231–1240,October2003.

[7] T. Li andB. Wang. Cost-effective sharedpathprotectionin WDM optical meshnetworks with partialwavelengthconversion.Acceptedfor publicationin PhotonicNetworkCommunications(in press), 2004.

[8] T. Li andB. Wang. Optimalconfigurationof p-cyclesin WDM opticalnetworkswith partialwavelengthconversion.SubmittedOptiComm, 2004.

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[9] T. Li andB. Wang. Optimalconfigurationof p-cyclesin WDM opticalnetworkswith sparsewavelengthconversion.Submittedto IEEE Globecom, 2004.

[10] T. Li, B. Wang,andC. Sowjanya. On theimpactof workingcapacityroutingon p-cycle basedprotectionin WDM opticalnetworks. Submittedto OptiComm, 2004.

[11] T. Li, B. Wang,andX. Zhang.Dynamicsharedpathprotectionin WDM opticalnetworks.7th INFORMSTelecommunicationsConference, BocaRatonFL USA, March2004.

[12] H. T. MouftahandP.-H. Ho. OpticalNetworks: ArchitectureandSurvivability. Kluwer AcademicPub-lishers, 2003.

[13] X. Hu S. Gao, X. Jia and D. Li. Wavelengthrequirementsand routing for multicastconnectionsinlightpathandlight-treemodesof WDM networkswith limited drops.IEE Proceedings, 148(6):363–367,December2001.

[14] L. H. SahasrabuddheandB. Mukherjee. Light-trees:Opticalmulticastingfor improved performanceinwavelength-routednetworks. IEEE CommunicationsMagazine, pages67–73,February1999.

[15] D.A. Schupke, C.G. Gruber, andA. Autenrieth. Optimal configurationof p-cycles in WDM networks.Proc. of IEEE International Conference on Communications(ICC), New York, USA, 5:2761–2765,April/May 2002.

[16] D.A. Schupke,M.C. Scheffel, andW.D. Grover. An efficientstrategy for wavelengthconversionin WDMp-cycle networks. Proceedingsof theFourth InternationalWorkshopon theDesignof ReliableCommu-nicationNetworks(DRCN2003),Banff, AB,Canada, October2003.

[17] D.A. Schupke,M.C. Scheffel, andW.D. Grover. Configurationof p-cyclesin WDM networkswith partialwavelengthconversion.PhotonicNetworkCommunications, pages239–252,June2003.

[18] N. SrinivasandC.S.R.Murthy. Designanddimensioningof aWDM meshnetwork to groomdynamicallyvaryingtraffic. PhotonicNetworkCommunications, 7(2):179–191,2004.

[19] B. WangandT. Mannan.Dynamicmulticastsessionprovisioningin WDM opticalnetworkswith sparsesplitting capability.7th INFORMSTelecommunicationsConference, BocaRatonFL USA, March2004.

[20] D. Xu, Y. Xiong, andC. Qiao. A New PROMISEAlgorithm in Networkswith SharedRisk Link Groups.IEEE Globecom,SanFrancisco,CA, December2003.

[21] H. Zang.WDM MeshNetworks: ManagementandSurvivability. Kluwer AcademicPublishers, 2003.

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APPENDIX A

PROJECT PUBLICATIONS

1. A. R. B. Billah, Bin Wang,andA. A. S. Awwal, “Multicast Traffic Groomingin WDM Optical MeshNetworks.” Proceedingsof IEEE Globecom:OpticalNetworking Symposium,SanFrancisco,CA USADecember2003.

2. Abdur Billah, Bin Wang,andAbdul A. S.Awwal, “Efficient Traffic Groomingin SONET/WDMBLSRNetworks.” Acceptedfor publicationin OpticalEngineeringJournal,May, 2004(in press),SPIE.

3. Tianjian Li, Bin Wang,andXinhui Zhang. “Dynamic SharedPath Protectionin WDM Optical Net-works.” 7th INFORMSTelecommunicationsConference,BocaRaton,FL March2004.

4. Bin WangandTowsif Mannan. “Dynamic Multicast SessionProvisioning in WDM Optical Networkswith SparseSplitting Capability.” 7th INFORMS TelecommunicationsConference,Boca Raton,FLMarch2004.

5. Tianjian Li andBin Wang,“Cost Effective SharedPath Protectionfor WDM Optical MeshNetworkswith Partial WavelengthConversion.” Acceptedfor publicationin PhotonicNetwork CommunicationsJournal.

6. TianjianLi andBin Wang,“Efficient OnlineAlgorithmsfor DynamicSharedPathProtectionin OpticalWDM Networks.” Submittedto PhotonicNetwork CommunicationsJournal.

7. Towsif MannanandBin Wang,“Dynamic Multicast SessionProvisioning in WDM Optical Networkswith SparseSplittingCapability.” Submittedto IEEEGlobecom,2004.

8. NandaLella andBin Wang,“DynamicContentionResolutionin OpticalBurstSwitchingNetworkswithPartialWavelengthConversionandFiberDelayLines.” Submittedto IEEEGlobecom,2004.

9. TianjianLi andBin Wang,“Optimal Configurationof�-Cyclesin WDM OpticalNetworkswith Sparse

WavelengthConversion.” Submittedto IEEE Globecom,2004.

10. TianjianLi andBin WangandChavaSowjanya,“On theImpactof WorkingCapacityRoutingon�-Cycle

BasedProtectionin WDM Optical Networks.” Submittedto IEEE/SPIEBroadNets,2004(previouslyOptiComm).

11. TianjianLi andBin Wang,“Optimal Configurationof�-Cyclesin WDM OpticalNetworkswith Partial

WavelengthConversion.” Submittedto IEEE/SPIEBroadNets,2004(previously OptiComm).

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APPENDIX B

Problem1. Space-Time DemandSchedulingOptimization: Non-blocking Case

Theobjective is to minimizethenetwork resourceuse.

(1) Thefollowing aregivenasprograminputs:

! s : thesetof nodesin thenetwork.! : thesetof links in thenetwork.! � : thesetof wavelengthson eachlink.!{0 = D ) F : thesetof scheduledtraffic demands;�5| , � | and � | arethesourceanddestinationnodesandthe

numberof requestedlight-pathsof demand) , respectively.!{} |~5 | ] D ��5� F : indicateswhetherdemands)� and )9 areoverlappingin time (=1) or not (=0) (�� ).! A ] : thelengthof link ( \ � ).! � : a largenumber(e.g.,maximumdemandlastingtime).

(2) Theproblemsolvesthefollowing variablesgivenasetof connectionrequests0 :! | ] D ��5�y� LNLNL � | F : thenumberof light-pathsof demand) usingwavelength .!{2 | A ] D ��5� F : indicateswhetherthepathof demand) traverseslink � \ �� usingwavelength (=1) or

not (=0).

! A ] D ��5� F : indicateswhetherthepathof somedemandstraverselink � \ �[� usingwavelength (=1)or not (=0).

ObjectiveminimizeD_ A �y 

yy¡ A # A F (2)

Subject to ( ) ] 0 � ]&� �/� \ �[� ] , if not specifiedotherwise):Requestedcapacitiesof demand) : yy¡

| �� | (3)Flow conservationconstraintsat sourcenodes:

9¢¤£¥§¦©¨ ¢ �( 2 | ¦ ¨ ¢ � | � 2 | A ¦ ¨ ���Qª \�« � \ � �5| � ] (4)

Flow conservationconstraintsatdestinationnodes:

A £¥ A ¬ ¨ ( 2 | A ¬ ¨ � | � 2 | ¬ ¨ ¢ ���Qªb « ��� | ��b_� ] (5)

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Flow conservationconstraintsatothernodes:

A £¥ A ¤( 2 | A ® 9¢¤£¥ � ¢ �( 

2 | � ¢ ���Qª ]s �N&� � | ��� | � (6)Wavelength on link ( \ � ) shouldnotbeusedby two demandsif they areoverlappingin time:

2 |~9 A °¯ 2 |© A ±¯ } | ~ | R²% �aª ) � ) ] 0 �³��_� (7)Constraintsindicatingwhetherwavelength on link ( \ � ) is usedby somedemands:

A R |¤+´2 | A (8)

H 0 H# A ¶µ |+´2 | A (9)

Subject to ( ) ] 0 � ]&� �/� \ �[� ] , if not specifiedotherwise):Requestedcapacitiesof demand) : yy¡

| �� | (10)Flow conservationconstraintsat sourcenodes:

9¢¤£¥§¦ ¨ ¢ �( 2 | ¦©¨ ¢ � | � 2 | A ¦¨ ���Qª \�« � \ � � | � ] (11)

Flow conservationconstraintsatdestinationnodes:

A £¥ A ¬ ¨ ( 2 | A ¬ ¨ � | � 2 | ¬ ¨ ¢ ���Qªb « ��� | ��b_� ] (12)

Flow conservationconstraintsatothernodes:

A £¥ A ¤( 2 | A ® 9¢¤£¥ � ¢ �( 

2 | � ¢ ���Qª ]s �N&� � | ��� | � (13)Constraintsindicatingwhetherdemand)� anddemand)9 overlapsin time:

� # 3 | ~ | * µ � |© ® � |�~ �aª )� � )/ ] 0 �³��_�¤� 3·* �¸� if � |¶¹ � |~ ��� otherwise (14)� # �� ® 3 |�~5 |* � ¹ � | ~ ® � | �aª ) � ) ] 0 �³�º�»+� 3 * �¸� if � | ¶¹ � | ~ ��� otherwise (15)� # 3 |~5 |. µ � | ~ ® � | �Qª )� � )/ ] 0 �³��_� 3¼. �¸� if � | ~ ¹ � | ��� otherwise (16)

� # �� ® 3 | ~ | . � ¹ � | ® � | ~ �aª )¤ � )9 ] 0 �³�º�»+� 3¼. �¸� if � | ~ ¹ � | ��� otherwise (17)} | ~ | R 3 | ~ | * � } | ~ | R 3 | ~ | . � } | ~ | µ 3 | ~ | * ¯ 3 | ~ | . ® �y�Qª )¤ � )9 ] 0 �³��»+� (18)Wavelength½�¾ ¿ � ¾ on link ( \ � ) shouldnotbeusedby two demandsif they overlapin time:

2 |~9 A ¯ 2 |© A ¯ } | ~ | R²% �aª )� � )/ ] 0 �³��_� (19)Constraintsindicatingwhetherwavelength on link ( \ � ) is usedby somedemands:

A R |¤+´2 | A (20)

H 0 H# A µ |+´2 | A (21)

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Problem2. Space-Time DemandSchedulingOptimization: Blocking CaseI

Theobjective is to minimizethenumberof demandsto berearranged.If thereexist severalsolutionsthatresultin rearrangingthe minimum numberof demands,theonethat usestheminimum network resources,i.e., theminimumnumberof wavelength-links(or cost),is selected.

(1) Thefollowing aregivenasprograminputs:

! s : thesetof nodesin thenetwork.! : thesetof links in thenetwork.! � : thesetof wavelengthson eachlink.!{0 = D ) F : thesetof scheduledtraffic demands;0 | �S� � | ��� | ��� | ��� | ��� | ��� | � is atuplerepresentingdemand) where� | , � | , � | , � | , � | and� | arethesourcenode,thedestinationnode,thenumberof requestedlight-

paths,thesetupandtear-down dates,andthepriority of demand) , respectively. Whendemand) hasahigh priority (

� | =1), it mustbe scheduledbetween� | and � | , i.e., it cannotbe rearranged.Otherwise,demand) mayberearrangedif its priority is low (� | =0).! A ] : thelengthof link ( \ � ).! � : a largenumber.

(2) Theproblemsolvesthefollowing variablesgivenasetof connectionrequests0 :! | ] D ��5�y� LNLNL � | F : thenumberof light-pathsof demand) usingwavelength .!{2 | A ] D ��5� F : indicateswhetherthepathof demand) traverseslink � \ �� usingwavelength (=1) or

not (=0).

! A ] D ��5� F : indicateswhetherthepathof somedemandstraverselink � \ �[� usingwavelength (=1)or not (=0).

!ÀÂÁ| ] D ��5�y� % LNLNL F : thetime differencebetweenactualscheduleandrequestedscheduleof demand) (foreithersetupor tear-down date)if demand) is rearrangedaheadof schedule.!À | ] D ��5�y� % LNLNL F : thetime differencebetweenactualscheduleandrequestedscheduleof demand) (for

eithersetupor tear-down date)if demand) is postponed.!{Ã_Á| ] D ��5� F : indicateswhetherdemand) is rearrangedaheadof schedule(=1) or not (=0).!{à | ] D ��5� F : indicateswhetherdemand) is postponed(=1) or not (=0).!3 | ~ | * ] D ��5� F : indicateswhethertheactualtear-down dateof demand)/ (=� | ¯ À | ® ÀÄÁ| ) is laterthan

theactualsetupdateof demand)� ( � | ~ ¯ À |~ ® À Á|�~ ) (=1) or not (=0) (�º� ).!3 |~/ |©. ] D ��5� F : indicateswhethertheactualtear-down dateof demand) (=� | ~ ¯ À | ~ ® ÀÄÁ| ~ ) is later

thantheactualsetupdateof demand)/ ( � | ¯ À | ® ÀÂÁ|© ) (=1) or not (=0) (�� ).!{} | ~ | ] D ��5� F : indicateswhetherdemands) and ) areoverlappingin time (=1) or not (=0) (�� ).

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ObjectiveminimizeD � # |y´

� Ã Á| ¯ Ã | � ¯ _ A �(  +y¡ A # A F (22)

Subject to ( ) ] 0 � ]&� �/� \ �[� ] , if not specifiedotherwise):Requestedcapacitiesof demand) : yy¡

| �� | (23)Flow-conservationconstraintsat sourcenodes:

9¢¤£¥§¦ ¨ ¢ �( 2 | ¦©¨ ¢ � | � 2 | A ¦¨ ���Qª \�« � \ � � | � ] (24)

Flow-conservationconstraintsatdestinationnodes:

A £¥ A ¬ ¨ ( 2 | A ¬ ¨ � | � 2 | ¬ ¨ ¢ ���Qªb « ��� | ��b_� ] (25)

Flow-conservationconstraintsatothernodes:

A £¥ A ¤( 2 | A ® 9¢¤£¥ � ¢ �( 

2 | � ¢ ���Qª ]s �N&� � | ��� | � (26)Constraintsindicatingwhetherthe actualtear-down dateof demand)9 is later than the actualsetupdateofdemand)� : � # 3 |�~/ |* µ �Å� | ¯ À | ® À Á| � ® �� | ~ ¯ À | ~ ® À Á| ~ �¤�

� # � 3 |~/ |©* ® �/� I �Å� | ¯ À | ® À Á| � ® �� | ~ ¯ À | ~ ® À Á| ~ �¤�ƪ )� � )/ ] 0 �³��_� (27)Constraintsindicatingwhetherthe actualtear-down dateof demand)¤ is later than the actualsetupdateofdemand)/ : � # 3 | ~ | . µ �Å� |�~ ¯ À | ~ ® À Á| ~ � ® �� | ¯ À | ® À Á| �¤�

� # � 3 | ~ | . ® �/� I �Å� |~ ¯ À | ~ ® À Á| ~ � ® �� | ¯ À | ® À Á| �¤�ƪ )� � )/ ] 0 �³��_� (28)Constraintsindicatingwhetherdemands)� and )9 areoverlappingin time (both 3 | ~ | * and 3 | ~ | . are1):

} | ~ | R 3 |~5 |©* � } | ~ | R 3 |~5 |©. � } | ~ | µ 3 |~/ |©* ¯ 3 |~5 |©. ® �y�Qª ) � ) ] 0 �³��»+� (29)Wavelength on link � \ �� shouldnotbeusedby two demandsif they areoverlappingin time:

2 |~9 A °¯ 2 |© A ±¯ } | ~ | R²% �aª ) � ) ] 0 �³��_� (30)Constraintsindicatingwhetherwavelength on link � \ �� is usedby somedemands:

A R |+´2 | A � H 0 H# A ¶µ |¤+´

2 | A (31)Constraintsindicatingwhetherdemand) is rearrangedaheadof schedule:

� # Ã Á|{µ À Á| �5� ® Ã Á| ¹ ® À Á| (32)Constraintsindicatingwhetherdemand) is postponed:

� # à |{µ À | �5� ® à | ¹ ® À | (33)Demand) canonly berearranged(advancedor postponed)whenits priority is low (� | �»� ):

à Á| ¯ à | ¯ � | R �y� (34)22

Problem3. Space-Time DemandSchedulingOptimization: Blocking CaseII

Theobjective is to minimizethetotal schedulelength(i.e., from theinstantwhenthefirst demandis scheduledto the instantwhen the last demandfinishes). If thereexist several solutionswhich result in the minimumschedulelength,theonethatusestheminimumnetwork resources,i.e., theminimumnumberof wavelength-links (or cost),is selected.However, significantnumberof low priority demandsmaypotentiallyberearrangedin orderto minimizethetotal schedulelengthin thisproblemformulation.

(1) Additionalvariables:

! �ÆÇ A§È : theearliestsetupdateamongall thedemands.! �ÄÇÊÉ�Ë : thelatesttear-down dateamongall thedemands.

ObjectiveminimizeD � # �Å� ÇÊÉ�Ë ® � Ç AÌÈ � ¯ _ A �y 

yy¡ A # A F (35)

(2) Additionalconstraints: �aÇ A§È R � | ¯ À | ® À Á| � (36)� ǼÉ�Ë µ � | ¯ À | ® À Á| L (37)

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