1 FelixGartnerandSvenKloppenburg DarmstadtUniversityofTechnologyGermanyfelixinformatiktudarmstadtdeSysteamEngineeringDarmstadtGermanysvensysengde 1 ConsistentDetectionofGlobalPredicatesund ID: 492035
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1 ConsistentDetectionofGlobalPredicatesunderaWeakFaultAssumption FelixGartnerandSvenKloppenburg DarmstadtUniversityofTechnology,Germany,felix@informatik.tu-darmstadt.deSysteamEngineering,Darmstadt,Germany,sven@syseng.de 1 ConsistentDetectionofGlobalPredicatesunderaWeakFaultAssumption FelixGartnerandSvenKloppenburg DarmstadtUniversityofTechnology,Germany,felix@informatik.tu-darmstadt.deSysteamEngineering,Darmstadt,Germany,sven@syseng.de Athene:Godessofwisdom,guardianofartsandcrafts(KeynotebyMikeMorgantiyesterday) 2 \Wearelookingforsoftwarewhichalsoworksinverylargeandveryopendistributedsystems." 3 Observationinfault-freeasynchronoussystems Distributedcomputationsinasynchronoussystems. p 1 p 2 3 Observationinfault-freeasynchronoussystems Distributedcomputationsinasynchronoussystems. p 1 p 2 m 1 m 2 Applicationandmonitorprocesses. Applicationandcontrolmessages. Predicatedetection:Latticeofconsistentglobalstates. Modalitiespossiblyandde nitely. 4 Predicatedetectioninfaultyasynchronoussystems crashfaultassumption=atmosttprocessessimplystopexecutingsteps. Forthemoment:restrictcrashfaultstoapplicationprocessesonly(monitorsalwaysstayalive). Predicateupireferstofunctionalstateofpi. Canbeusedinpredicates: { Processpicrashedafter4thevent::upi^eci=4 { Everyprocesseithercommitsorcrashes:8i::upi_commiti Idea: ndsuitableanalogiestopossiblyandde nitelyforthesetypesofpredicates. 5 Implementablefailuredetection Everymonitormustkeepupiuptodate(failuredetection,discussedindetailbyMikelLarreayesterday). Canensureeventualdetection,butcannotavoidfalsesuspicions. Terminology:failuredetectorssuspectandrehabilitateapplicationprocesses. Bestwecando:anon-crashingprocessisnotpermanentlysuspected[ 3 ]. Forobservationpurposes:addcausalityinformationtosuspicions: { \mjsuspectspiaftereventekonpi." { \mjrehabilitatespiaftereventekonpi." Assume:betweentwoeventsatmostonesuspicionandrehabilitation. 6 Latticeoverextendedstatespace Treatupiasavariableonpi. Suspicion/rehabilitationisasimplestatechangeofpi(extendedstatespace). Changeofupinconsistentstatesyieldsagainconsistentstates. Lemma:Integrationofsuspicions/rehabilitationsintostatelatticeyieldsnewlattice(overextendedstatespace). Usethislatticeforpredicatedetection. 7 Permonitorlattice Duetofalsesuspicionsmonitorsconstructdi erentstatelattices. possibly/de nitelynotobserver-invariant. p 1 p 2 m 1 s us pe c t s p 1 m 1 r e ha bi l i t a t e s p 1 p 1 p 1 p 2 m 1 m 2 p 2 8 Globalfailuredetectorsemantics Problem:falsesuspicions. Solution:de ne\global"failuredetectorsemantics. piis(globally)suspectedaftereki ... { (pessimistic)9amonitorwhichsuspectspiafterek. { (optimistic)8monitorssuspectpiafterek. Cande nepessimisticandoptimisticstatelattice(unionandintersectionofallmonitorlattices). 9 Newmodalities Givenpredicate'onextendedstatespace. negotiably(')holdsi possibly(')holdsonpessimisticstatelattice. discernibly(')holdsi de nitely(')holdsonoptimisticstatelattice. p 1 p 2 p 1 p 1 p 2 p 2 m 1 s us pe c t s p 1 a f t e r e 0 m 1 r e ha bi l i t a t e s p 1 a f t e r e 0 9 Newmodalities Givenpredicate'onextendedstatespace. negotiably(')holdsi possibly(')holdsonpessimisticstatelattice. discernibly(')holdsi de nitely(')holdsonoptimisticstatelattice. p 1 p 2 p 1 p 1 p 2 p 2 m 1 s us pe c t s p 1 a f t e r e 0 m 1 r e ha bi l i t a t e s p 1 a f t e r e 0 ' p 1 c r a s he s w he n p 2 i s i nbe t w e e n e v e nt s 1 a nd 2 ' p 1 c r a s he s w he n p 2 i s i nbe t w e e n e v e nt s 1 a nd 2 ' ( or bot h) e x e c ut e a n e v e nt e i t he r p 1 or p 2 10 Intuitionbehindnewmodalities Optimistic/pessimisticlatticecanbeunderstoodinanalogytooptimistic/pessimisticnetworkprotocols: { pessimistic:becarefulallthetime,takeimmediateactionifsomethingbadhaspossiblyhappened. ) usenegotiablytotriggeraction. { optimistic:goaheadwithoutsynchronizationandhopeforthebest,dealwithcon ictsonlywhennecessary. ) usediscerniblytoignorespurioussuspicions. Understandableinanalogytopossibly/de nitely: { Safetyrequirement2':takeactionifnegotiably(:')isdetected. { Livenessrequirement3':validatedifdiscernibly(')isdetected. 11 Detectionalgorithmsinanutshell Letmonitorscausallybroadcasttheirsuspicionstoallothermonitors. Eventuallyallmonitorlatticesconverge. Canthendopossibly/de nitelydetectioninobserverinvariantstatelattices(usestandardalgorithms). Problem:howknowthattherewillbeno\late"failuredetectoreventsarriving? Solution: { Monitorspiggybackcoordinatesofmostrecentglobalstatetheyhaveseen:permonitorstableregion. { Takeintersectionofallmonitorregions:globallysettledregion. { Steadilyexpandsettledregion,extractoptimistic/pessimisticdataanddopossibly/de nitelydetectiononit. 12 Settledregionexample p 2 p 1 p 1 p 2 12 Settledregionexample p 2 p 1 p 1 p 2 m 2 s us pe c t s p 2 a f t e r e 2 a t a ppl i c a t i on t i m e (2 ; 2) m 2 s us pe c t s p 2 a f t e r e 2 a t a ppl i c a t i on t i m e (2 ; 2) a f t e r e 1 a t m 1 s us pe c t s p 2 a a ppl i c a t i on t i m e (3 ; 1) a f t e r e 1 a t m 1 s us pe c t s p 2 a a ppl i c a t i on t i m e (3 ; 1) no c ha nge t o be e xpe c t e d r e g a r di ng m 2 no c ha nge t o be e xpe c t e d r e g a r di ng m 2 no c ha nge t o be e xpe c t e d r e g a r di ng m 1 no c ha nge t o be e xpe c t e d r e g a r di ng m 1 s e t t l e d r e gi on 13 Advancedtopics Algorithmworksunderassumptionthatnomonitorsfail. Ifmonitorscanfail,detectionbecomesharder: { Canstilldetectnegotiablywithoutastableregion. { Detectiondiscerniblyimpossible,becauseaccuratefailuredetectionisneeded. { Aweakervariant(t-discernably)canbedetectedatthepriceofhavingamajorityofcorrectmonitors. 14 Complexityandrestrictedpredicates Complexity: { generalpredicatedetectionisNP-complete[ 1 ]. { Ourdetectionalgorithmsareonlywrappersaroundpossibility/de nitelydetection. { Studyrestrictedclassesofpredicates. Perfectfailuredetectorsavailable: { Nofalsesuspicions. { Optimistic/pessimisticlatticearethesame. Perfectfailuredetectorsandcrashpredicates: { Predicatesarestable. { possibly=de nitely!negotiably=discernibly 15 Overviewofresults Firstworktodealwithgeneralpredicatesinfaultysystems(onlyotherworkbyGargandMitchell[ 2 ]restrictstheclassesofpredicates). Observationmodalitiesnegotiablyanddiscernibly... { donotsolveallproblemsincrash-a ectedsystems. { re ectbytheirde nitiontheinherentproblemofcrashfailuredetection. { canbeunderstoodinanalogytopossiblyandde nitely. { canbedetectedinasynchronoussystems,evenifmonitorsmaycrash. Stillalotofworktodo. 16 References [1] CraigM.ChaseandVijayK.Garg.Detectionofglobalpredicates:Techniquesandtheirlimitations.DistributedComputing,11(4):191{201,1998. [2] VijayK.GargandJ.RogerMitchell.Distributedpredicatedetectioninafaultyenvironment.InProceedingsofthe18thIEEEInternationalConferenceonDistributedComputingSystems(ICDCS98),1998. [3] VijayK.GargandJ.RogerMitchell.Implementablefailuredetectorsinasynchronoussystems.InProc.18thConferenceonFoundationsofSoftwareTechnologyandTheoreticalComputerScience,number1530inLectureNotesinComputerScience,Chennai,India,December1998.Springer-Verlag.Acknowledgements Slidesproducedusing\cuttingedge"LATEXslideprocessor PPower4 byKlausGuntermann.