Ancestral Dynamic Voting Algorithm for Mutual Exclusion in Partitioned Distributed Systems

16 Pages·2015·1.64 MB·English

HindawiPublishingCorporation
InternationalJournalofDistributedSensorNetworks
Volume2013,ArticleID120308,15pages
http://dx.doi.org/10.1155/2013/120308
Research Article
Ancestral Dynamic Voting Algorithm for Mutual Exclusion
in Partitioned Distributed Systems
FaranehZarafshan,1AbbasKarimi,2S.A.R.Al-Haddad,1
M.IqbalSaripan,1andShamalaSubramaniam3
1DepartmentofComputerSystemsEngineering,FacultyofEngineering,UniversitiPutraMalaysia,43400Serdang,Selangor,Malaysia
2DepartmentofComputerEngineering,FacultyofEngineering,ArakBranch,IslamicAzadUniversity,Arak38453,Iran
3DepartmentofCommunicationTechnology&Networks,FacultyofComputerScienceandIT,UniversitiPutraMalaysia,
43400Serdang,Selangor,Malaysia
CorrespondenceshouldbeaddressedtoFaranehZarafshan;[email protected]
Received1April2013;Revised29July2013;Accepted4September2013
AcademicEditor:ChaseQishiWu
Copyright©2013FaranehZarafshanetal. This is an open access article distributed under the Creative Commons Attribution
License,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperly
cited.
Datareplicationisaknownredundancyusedinfault-tolerantdistributedsystem.However,ithastheproblemofmutualexclusion
ofreplicateddata.Mutualexclusionbecomesdifficultwhenadistributedsystemispartitionedintotwoormoreisolatedgroupsof
sites.Inthisstudy,anewdynamicalgorithmispresentedasasolutionformutualexclusioninpartitioneddistributedsystems.
The correctness of the algorithm is proven, and simulation is utilized for availability analysis. Simulations show that the new
algorithm,ancestraldynamicvotingalgorithm,improvestheavailabilityandlifetimeofserviceinfaultyenvironments,regardless
ofthenumberofsitesandtopologyofthesystem.Thisalgorithmalsoprolongsthelifetimeofservicetomutualexclusionfor
fullandpartialtopologiesespeciallyforthesituationswherethereisnomajority.Furthermore,itneedslessnumberofmessages
transmitted.Finally,itissimpleandeasytoimplement.
1.Introduction class,aparticularmessageknownastokencirculatesinthe
distributedsystem[5]andonlythesitethathasthetokenis
In distributed systems, the redundancy of data or data
permittedtoenterthecriticalsection(CS).Theotherclass,
replication is a well-known approach to achieve fault tol-
permission-based algorithms, utilizes the permission from
erance [1], increase availability of data base [2], decrease
multiple(usuallythemajority)sitessothatthefailureofone
the response time of service and communication costs [3],
site(ormore,dependingonthealgorithm)istolerable.
and to share loads by distributing the computational loads
Permission-based algorithms are categorized into cote-
over multiple sites rather than imposing them to a singular
rie-based and voting-based. Coterie is a set of sites which
site [4]. Besides these advantages, data replication allows
require permission to commit an update. Every site in the
distributed systems to have concurrent access to sites for
coteriemustissuepermissionsothatasitecanenteritsCS.
common data. If multiple sites simultaneously modify the
However,votingreliesonpermissionfromapredetermined
commondata,therearedifferentcontentsofthesamedatain
number of sites regardless of which site agrees on commit-
thedistributedsystemleadingtodatainconsistency.Mutual
exclusion(MutEx)aimstopreventdatainconsistencywhen ment.
multiple sites are persuaded to access the same data at the Nowadays, distributed systems face new requirements
sametime. as they migrate to large scale applications. Social networks,
SolutionsfordistributedMutExarecategorizedintotwo sensor networks, and Internet of Things are instances of
main classes [5] which are token-based algorithms [6–9] applicationsfordistributedsystemsinwhichlimitationson
and permission-based algorithms [5, 10–16]. In the first thenumberofsitesortypesoftopologyarenotacceptable.
2 InternationalJournalofDistributedSensorNetworks
Votinghasahigherdegreeofreplication,withnolimitations atleast𝑟votes(forread)or𝑤votes(forwrite)areobtained
onthenumberofsitesandnoneedforcomplicatedcomputa- from one or more sites [2]. Weighted voting commits an
tions.Thereisahigherabilitytofacedynamicchangesinthe updateifthecumulativevotesofagreedsitesareatleastthe
system[17]andeasierimplementationforlargescalesystems. majority.ItthenguaranteesMutExevenifnomajorityexists.
However, coteries are not suitable for large number of sites In order to guarantee serial consistency, weighted voting
becausethenumberofcoteriesbecomeslargewith5sitesor utilizeslocks.Therefore,thenumberofmessagestransmitted
more,unlesstheyuseheuristicsotherwise,votingisverytime is more than majority voting, that is, 3𝑛 + 3 messages in
consuming for six or more sites [18]. Therefore, the higher the worst case. However, 4 messages are transmitted in the
number of messages transmitted is an issue with voting best case (if the first site has the majority vote or quorum).
algorithms.Moreover,somevotingalgorithmsarelimitedby Somestaticvotingalgorithms[16,24–27]arisefromweighted
topologyissues,and,insomeotheralgorithms,nonrealistic votingalgorithminallsiteswiththelogicalstructurebeing
assumptionsareconsideredwhenusingsiteinformation. chosenforquorumselectionandconsensus.
Inadditiontoconsistencyissuesfordistributedsystems, Staticvotingalgorithms[2,4]usepredeterminedinfor-
partitiontoleranceandavailabilityareotherconcerns(refer mationonsitesanddistributedsystems.Thisinformationis
to [19] for more details). In this study, a new algorithm fixed during the system’s life time. In case of emergency or
is introduced for partitioned distributed systems, based on failure,thealgorithmisnotabletochangeitspolicy.Thereare
dynamic voting algorithms. Similar to other voting based somesituationswherethedistributedsystemsarepartitioned
algorithms, every single site that wishes to access CS must intotwoormoreisolatedgroupsofsites[5,11]withnointer-
issueandbroadcastitsrequesttoagroupofconnectedsitesor section between isolated groups. These groups are known
distinguishedpartition(DP).ThesiteentersitsCSifnositein as partitions. All sites inside a partition can communicate
theDPsendsarejection.ThisalgorithmguaranteesMutEx. withoneanother,buttheycannotcommunicatewithother
Itisdeadlockfreeandneedsfewermessagestransmitted.It sitesinotherpartitions[28].Ifstaticalgorithmsareusedfor
alsocantolerateahighernumberoffaultsandhasahigher thesesituations,thepartitionscanhaveparallelaccesstoCS
availability when facing consecutive failures. Furthermore, becausethesitesinsideeachpartitionlookatthepartitionas
thisnewalgorithmissimulated.Itsavailabilityandnumber anintegratedsystem,wheninfacttheybelongtoapartition
ofmessagesarecomparedtomajorpartitiontolerantvoting amongmultiplepartitionsofadistributedsystem.
algorithms. Inapartitioneddistributedsystem,ifthereisnomajority
The remainder of this paper is organized as follows. partition,everysitemustrejectincomingupdaterequeststo
Section2hasbackgroundandliteraturereviewonstaticand avoiddatainconsistency.Inthiscase,thedistributedsystem
dynamicvotingalgorithmsfordistributedMutEx.Section3 is halted until a recovery or repair process is executed and
dealswiththenewproposedvotingalgorithm;proofofcor- aDPisfound.Thisinterruptiondecreasestheavailabilityof
rectnessisdiscussedinSection4,whileSection5presentsthe MutExandisknownastheproblemofhaltedstates[5,29].
experimental results and performance analysis of dynamic This problem cannot be solved by static voting algorithms
voting algorithms. The number of messages transmitted is becausetheydonothaveadaptabilitywithdynamicchanges
also discussed in this section. Finally, the conclusions and ofsystemconnectivity.
futureworksareexplainedinSection6. Dynamic voting algorithms [30–32] are the main solu-
tionstoavoidhaltedstates.Theyincreasetheavailabilityof
distributed MutEx in partitioned distributed systems [29]
2.BackgroundandLiteratureReview and utilize two main mechanisms to prolong MutEx either
by increasing the vote (or the priority) of a partition to be
Two types of voting-based algorithms, static and dynamic, higherthantheotherpartitionsorbyenablingthealgorithm
are utilized for MutEx in distributed systems. The simplest to service noncritical applications during the halted state
formofstaticvotingalgorithmismajorityvotingpresented (e.g.,[33]).Inthisstudy,thefirstmechanismisdiscussedin
by Thomas [4]. This algorithm performs a majority voting terms of the most successfully referred partition becoming
amongallthesitesinthedistributedsystemandusesadif- the DP and when the problem of halted states is prevented
ferentstrategytolockthemechanism(includingsemaphore or decreased. Major dynamic voting algorithms are group
[20]andmonitor[21])ortimestamps[22,23].Asiterequests consensus [29], autonomous reassignment [29], dynamic
to enter the CS to update replicated copies of data if and linear[30,31],hybrid[31,34],anddynamicweightedvoting
only if it gets the permission from the majority of 𝑛 sites, [32], all of which have been designed based on majority
thatis,⌈(𝑛+1)/2⌉.Otherwise,itmustrejecttherequestand voting,eitherdirectlyorindirectly.
waituntilitbecomeseligibletoentertheCS.Thisalgorithm Group consensus requires a coordinator to assign each
transmits 2𝑛 + 2 and ⌈𝑛/2⌉ + 𝑛 + 3 messages in the worst site a number of votes and allows only the group with the
andbestcases,respectively[4].Majorityvotingisthegeneral majority of votes to perform the requested operation [29].
formformanystaticanddynamicvotingalgorithms.Some Once a site has discovered the failure of the coordinator,
staticgenerationsarerelativeconsensusvoting[15]inwhich it initiates itself as a candidate for coordination. This site
multipleupdaterequestsareconsideredandorderedinone becomes the new coordinator and installs new votes if and
voting process based on some priority measures. Weighted only if at least the majority of sites sends consensus. A
voting,aspresentedbyGifford[2],occurswhensomevotes sequencenumberisassignedtoeachsite.Thesiteswiththe
areassignedtoeachsite.Eachread/writerequestproceedsif latest data always have the greatest sequence number. Vote
InternationalJournalofDistributedSensorNetworks 3
reassignment [18, 35, 36] is done by using the information repairrate[31].However,theresultsofthesealgorithmshave
sent by other sites on the topology of the system [29] in not been taken into account for environments with high
suchawaythatatthemostonepartitionformsthemajority probabilityoffailure.Theterm“hybridvoting”differsfrom
partition. “hybridmutualexclusion”(asusedin[37,38])whichhasthe
Autonomous reassignment [29] solves the problem of ideaofbothtoken-basedandpermission-basedalgorithms.
group consensus for the single coordinator by having the In dynamic weighted voting [32], each site has a pre-
distributionofthealgorithmoneverysiteinthedistributed defined weight and a DP with greater accumulative votes
system. Therefore, each site is responsible for managing its (weights) in comparison with the sum of corresponding
vote [29]. A mechanism is required to restrict a site from associatedweightstothesite(s),withthemaximumversion
changing its vote arbitrarily and making the MutEx at risk. number [32]. Every site keeps the information on version
To do so, each site must obtain an approval of a certain numbersandweightsofothersitesatthetimeofpartitioning.
number of sites prior to every assignment. Autonomous A coordinator is responsible for forwarding the update
reassignment is more flexible, simpler, and quicker than requesttothesitesinthemajoritypartitionandtodetermine
group consensus; however, it has a lower degree of fault thecommitmentorrejectionofanupdate[32].Asaresult,
tolerance [29]. Although this algorithm has some benefits dynamic weighted voting is a centralized algorithm which
including a lower number of messages, faster action, and has a lower degree of fault tolerance in comparison with
flexibility,itrequiresknowingtheglobalinformationonthe distributedalgorithms.Adifficultywiththisapproachisthe
total number of votes (including the votes of sites in other obtainingoffairandpropervaluesfortheweights.Ifaweight
partitions).Thisrequirementisnotrealisticasitcontradicts ofasiteisverygreat,thepartitionincludingthesiteisalways
theconceptofisolatedpartitions[11]. consideredasaDP.Hence,evenfailedsitesgetrepairedand
As a pessimistic technique to deal with partitioning, can rejoin the partition even if they are not useful for the
dynamic linear algorithm [30] is proposed with the aim of consensus.
increasingtheavailabilityofMutExindistributedsystems,in Studies in [37, 38] introduce two forms of hybrid mu-
additiontoguaranteeingMutEx.Inthisalgorithmwith𝑛sites tual exclusion algorithms as a combination of token-based
owning replicated data, two parameters including version and permission-based algorithms. The study in [37] uses
number(VN)andthenumberofsitesorsitecopies(SC)are Maekawa’s quorums [24] for every site in the distributed
consideredinthelatestupdateandareassignedtoeachsite system. In the first phase, a site broadcasts messages to
𝑖 (1 ≤ 𝑖 ≤ 𝑛). A site is permitted to accept the request if its quorum asking for its permission. Once permission
andonlyifitbelongstoaDP.TodetermineaDP,messages is received, it creates a token message. Subsequently, the
arebroadcastbytherequestedsitetootherconnectedsites. algorithmneedstoformalogicaltreewiththetokenholderas
Then,thepartitionofconnectedsitessendsbackitsVNand itsroot.OncethetokenholderreleasesCS,itsendsthetoken
𝑆𝐶.Ifthemajorityofsitesinthepartition(i.e.,⌈𝑛/2⌉)hasthe tooneofitschildren inthetree.Thisalgorithmguarantees
maximumversionnumber,𝑀 = max(𝑉𝑁𝑗|𝑗 ∈ 𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛), MutEx as long as no failure of sites or links happens. It
thepartitionisaDP.Then,therequestedsiteispermittedto doesnotconsiderfaulttoleranceandpartitioningofnetwork.
accepttherequest,toinstallnewVNandSC,andtoaskthe Another hybrid MutEx algorithm is suggested in [38]. It is
otherstoupdatetheirdata.Thesitesofotherpartitionsare basicallyatoken-basedalgorithmwhichusestokenstogetthe
notallowedtochangetheirdata.Toavoidconcurrentaccess permissionofCSandutilizescoteries(similartoquorums)to
to CS, this algorithm uses lock mechanism [31]. This lock reducethenumberofcommunication.Itshouldbenotedthat
mechanism cannot solely guarantee MutEx in the systems hybridMutExisforgroupMutEx.
needingdynamicvotereassignment(partitioneddistributed Allvotingalgorithmsarecapableofenhancingtheavail-
systems)[11].However,themechanismcanbeutilizedwith ability of distributed systems to achieve MutEx. However,
differentformsofdynamicvotingalgorithms[29]asdynamic they are inefficient to keep the system available in case of
linearvotingisverysimpletounderstandandtoimplement. consecutive failures (e.g., Gifford’s weighted voting [2] and
Hybrid voting utilizes static voting for nonfaulty con- Thomas’smajorityvoting[4])orforcomplicatedcalculations
ditions and switches to dynamic voting once partitioning (e.g.,autonomousreassignment[29],hybridvoting[34],and
occurs. The aim of hybrid voting [31] is to increase the Davcev’s dynamic voting [32]) or for accurate knowledge
availabilityofdynamiclinearinsituationswherethenumber about the topology of the distributed system (e.g., group
of sites with the current copy of data is exactly 𝑛/2. In consensus [29]). A preliminary study [39] on ancestral
additiontothismechanism,hybridalgorithmusesapolicy dynamicvoting(ADV)algorithmshowsimprovementinthe
to keep the system up if two out of three sites participate availability of distributed systems where the sites or links
in the latest update, having the current data. To do so, a arevulnerabletofail.ADVguaranteesMutExinpartitioned
parameterdenotedasdistinguishedsite(DS)isaddedtothe distributed systems. It is simple and does not need special
informationstoredateachsite𝑖.Byusingthisparameter,the assumptions on the number of sites or topology of the
sites participating in the latest update can be recognized. It network. In this study, fault tolerance, lifetime of service,
hasbeenproventhathybridvotingincreasestheavailability and number of messages were investigated according to
ofMutExtobehigherthanthatforallstaticvotingalgorithms link failure and site failure, partially and fully connected
[31]. The results of the availability analysis of majority, topologies, and two different configurations of the system
dynamic linear, and hybrid algorithms demonstrate better (fresh start and consecutive);however, onlyavailabilityhad
performance for hybrid algorithm as systems with a high beendiscussedin[39].
4 InternationalJournalofDistributedSensorNetworks
Withtoken-basedandsomestaticalgorithmswhichuse query,readingpermissionfromonesiteisenough[11].This
logical topology structure, ADV does not need to know studyconcentratedonwritingonreplicateddataorupdate.
the topology. ADV uses the ancestor to give privilege to For simplicity, all the sites are supposed to have the same
a partition among multiple partitions. The sites are not priority.Iftwoormorerequestsarriveconcurrently,onlyone
required to obtain the permission from all the sites in DP is serviced based on the version numbers. If their version
toenterCS.Therefore,ADVisdifferentfromprimarycopy numbers are the same, one of them is chosen randomly. In
[40, 41] and coordinator cohort [42] in which one primary thisstudy,theissuesrelatingtoqueuingtheory,storage,and
site is set and permissions are issued for CS. The situation
synchronizationdelayarenottakenintoaccount.
is different to the extent of using a nonfixed coordinator
CS Flag announcesasitestatuswhenregardingtheCS.
in every cycle and voting technique for decision making.
Initially,allthesitesareinthenormalstate,thatis,CS Flag=
Furthermore, issues related to network partitioning are not
0.AsitegoestoCSstate,thatis,CS Flag=1,onceitreceives
pointedoutincoordinatorcohortandprimarycopy.
thepermissionfromothersitesforCS.CS Flag issetintwo
cases: when it is the establisher of the current voting cycle
orwhenasitehasbeenaskedbyothersitestoparticipatein
3.AncestralDynamicVoting(ADV)Algorithm
voting (i.e., received Msg1). In the first case, if CS Flag has
beenalreadyset,toavoiddatainconsistency,thesitehasto
Inthisstudy,ADVaimstoworkwithanytopology,whether
send back a rejection message to the sender. Therefore, the
the topology was partially or fully connected. To avoid
establisherfindstheconcurrentaccesstoCSandrejectsthe
parallelaccessofsitestoCS,CS Flag wasutilized.Ancestor
is a label for a site that establishes the latest successful request.
commitmentandthenumberofsiteswithreplicateddataof
between0and𝑛.Inadistributedsystemcomprising𝑛sites, 3.1.StructureoftheAlgorithm. Inthisstudy,ADVisexecuted
each site is labelled as 𝑆𝑘; 𝑘 = 1,2,...,𝑛 and keeps local bythreesubprocedures.Thefirstprocedureisforinitializa-
information on its version number (VN), ancestor (Anc), tionthatisperformedbyeverysinglesiteinthedistributed
and CS Flag, besides having the latest information of VN system. The second procedure is executed by a site which
and Anc of other sites in the partition. This information is
needs to update shared data and generates requests for CS.
dynamicallymodifiedaccordingtothesite’sreconnectionor
The third procedure is event handler and performs proper
disconnection,anditisinitiallyconnectedtoeverysiteinthe
actions once an event is triggered. The sites are normally
network.
waitingforincomingrequests,whetherfromanapplication
ADV is distributed among all the sites, and the failure
or from other sites. Therefore, ADV is an event triggered
of one or more sites cannot interrupt the service as long as
algorithm.
the ancestor of each voting cycle is up. A site is supposed
Each request carries at least the label of the sender or
to communicate with the others, unless it failed or is dis-
receiver(s) and the content of the message. Five types of
connected. For a single site, the failure of other sites is not
messagesaredefinedinADV.Theyareasfollows:
distinguishable from its corresponding links’ failure, unless
a special fault detector is utilized. However, in this study, Msg1:requesttoenterCS,
timeout for detection of failures (similar to [43]) is used. It
Msg2:permission,
isassumedthattheancestordoesnotfailduringCSing,but
itcandisconnectorleavethecurrentpartitiontoformanew Msg3: request to update data structures and release
DP. CS,
The main assumption of ADV is that the sites, update
Rejection: rejectionofaCSrequest,
their information the same way as what the establisher has
sentforthem.Theydonotbehavearbitrarilyasreportedin Failure:reportingasitefailuretoothersites.
general Byzantine problem. The definition of a partition is
similartoothervotingalgorithms;thatis,anisolatedgroup Figure1summarizestherelationsbetweenmessagesand
ofsitescannotcommunicatewiththesitesoutsidethegroup. sitestates.ThreemessagesasseeninFigure1aretransferred
Thereisnoassumptiononhowthesitesareconnected,and forasuccessfulupdateofCS.
there is no single coordinator in the system. Sites do not Therearetwotimersincludingrequest timerandrelease
need to know the information of other partitions and only timer which trigger the events of failure. The request timer
actbasedontheirpartitioninformation. is embedded in the ancestor’s routineand detects failure or
A distributed system initially forms one partition 𝑃; disconnection from other sites to which the request for CS
however, some sites or links may be timely disconnected hasbeensent,whereastherelease timer isutilizedtodetect
from the partition due to failures. Every single site 𝑘 sees disconnection or partitioning of a site from the ancestor.
this partition from its point of view as partition 𝑃𝑘, so that The value of the request timer is selected according to the
initially𝑃𝑘 = 𝑃.Inthecaseofpartitioning,somepartitions network communication delays. The release timer is longer
mayhaveoutdateddata(becausetheydonotreceiveupdates thantherequest timerbecauseitincludesatleasttwonetwork
fromtheDP),andreadingfromsuchpartitionsmayresultin communications delays and a longer time duration while
outdatedinformation.However,concurrentreadoperations the other site is in CS. The relation between these timers is
are allowed if the site belongs to a DP. Therefore, for each delineatedinFigure2.
InternationalJournalofDistributedSensorNetworks 5
Normal Void ADV initialize(𝑆𝑘){
𝐶𝑆 𝐹𝑙𝑎𝑔=0;
CSFlag=0
𝑃𝑘={𝑆1,...,𝑆𝑁};
𝐴𝑛𝑐=𝑆1;
Msg3 Msg1 𝑉𝑁=0;
}
Procedure 1: ADV Initialize(𝑆𝑘) sets initial local variables on
Vote reply, Update request, everysite𝑆𝑘.
CSFlag=1 CSFlag=1
site can access CS if and only if it belongs to a DP. Prior to
Msg2
that, it needs to communicate with all sites in its partition
Figure1:Relationbetweenmessagesandsitestates. by sending them Msg1. Once a site S𝑘 has received Msg1,
it checks its CS Flag. If CS Flag has been already set, the
siteparticipatesinotherupdatecommitment.Toavoiddata
inconsistency,itmustrejecttherequest.Thissiterejectsthe
3.1.1. Initialization of Sites. Procedure ADV initialize sets
CSrequestifthereisnoancestor;otherwise,itsetsitsCS Flag
initialvariablesoneverysiteinthenetworkandiscalledup
andparticipatesinvotingbysendingMsg2anditsVNtothe
beforeeventhandlingbyADV.Toavoidambiguity,thefirst
establisher.
timeancestorofthepartitionisassumedtobethefirstsite,
ftohrateivse,r𝑆y1.sThucceeasnsfcuelsCtoSreonfteevreinryg.siAtesinsoupprdeavteiodulsatueprdbayteAsDarVe receSivitieng𝑆𝑘Mpsge1rfforormmsthtehereqpuroecstedeustraeblUisphderat(eherreequ𝑆𝑖e)s,ta,suspeoenn
inProcedure4.
performedintheinitialstate,allVNaresetto0.
Aseverysitehasitsownviewofitspartition,itisgoodto 𝑆𝑖 mayfailafterreceivingthepermissionfrom𝑆𝑘,while
indicatetheviewofasite𝑆𝑘(𝑘 = 1,2,...,𝑛)foritspartition 𝑆𝑘iswaitingforjobaccomplishmentandCSreleaseby𝑆𝑖.In
by𝑃𝑘.Theprocedureforinitializationofasiteisasseenin this scenario, deadlock occurs when some sites are waiting
to enter CS, while no other site is in CS [5]. ADV benefits
Procedure1.
by having the release timer as 𝑆𝑘 does not have to wait for
infinity.Thistimershouldbelongenough.Ifitissettoashort
3.1.2. Generating CS Request. When a site needs to update value, MutEx may not be guaranteed because 𝑆𝑘 may think
replicateddata,itperformsprocedureADV CSingbysending that𝑆𝑖hasfailedwhileitisactuallyupanddoingitsjobinthe
its request to all its partition mates. Other sites may give
CSforalongertime.
priority to concurrent incoming requests for CS by consid-
If no message arrives before the release timer’s timeout,
eringtherequesters’versionnumbers.Therefore,VN𝑘isalso 𝑆𝑘 labels 𝑆𝑖 as faulty and sends a message to other sites in
sent along with a request. The time when a site generates a 𝑃𝑘, announcing that it has released CS. In the normal case,
CSrequestdependsontheapplicationitperformsorthose 𝑆𝑖 executestheprocedureVote replyuponreceivingareply
performedbyothersites.
messageintheformofMsg2withineachsite’sVNbeforeits
𝑆𝑘 needstoupdatethereplicateddataandsendsMsg1to request timer’stimeout.
other sites in 𝑃𝑘. In this case, the replicated data is the CS. For procedure Vote reply, the establisher of CS request
To avoid inconsistency, only one site is eligible to write on
receivesreplies(i.e.,Msg2,VN,andAnc)fromothersitesin
this value in a mutually exclusive manner. The site sets the partition𝑃𝑖 and decides based on their and Anc, as seen in
request timerbeforesendingarequestforCS.Asiteextracts
Procedure5.
aofrerqequuesetstf.oWrtihmeneoruetqbuyesdt-etcimreearsihnagsthtiimsteiomuetrs,a𝑆n𝑘draealolicsaelsttihmaet 1,2,𝑆.𝑖.s.e,e𝑛kssiftoesrtihnepmaratxitiimonu.mAvseirtseiownitnhuVmNbe𝑘r=𝑀𝑀,amisofnogu𝑘nd=,
eitherothersiteshavefailedoritisdisconnectedfromother
anditchecksifitsancestorexistsinthepartition.Ifso,the
sites. Then, it can resend its requests for a limited number partitionisaDPand𝑆𝑖iseligibletocommittheupdate.Once
of times or reject the request if it previously has done that
theestablisherfindsitselfinsidetheDP,itacceptstheupdate
numberofunsuccessfulattempts,asseeninProcedure2.
request,increasesitsversionnumber,assignsitslabelasanew
ancestor,andasksothersitestoupdatetheirinformationby
3.1.3. Event Handling. All the sites are normallywaitingfor broadcastingMsg3.
aneventfromothersitesoreventhemselves.Whenanevent Every site that receives Msg3 updates its information to
arrives, an event handler decides on the event based on new𝑉𝑁and𝐴𝑛𝑐oftheestablisherandresetsitsCS Flag as
the type of message delivered to the site. Procedure ADV presentedintheprocedureCommitment release,asseenin
EventHandlerisexecutedoneverysite,asseeninProcedure Procedure6.
3. It is always possible for a repaired site to rejoin the
When 𝑆𝑖 has received an update request for CS, it is distributed system or to update if its data are obsolete.
consideredastheestablisherofthecurrentvotingcycle.This Obsoletenesscanoccurduetolinkfailuresorfailuresofsites
6 InternationalJournalofDistributedSensorNetworks
VoidADV CSing(𝑆𝑘){
If(𝑆𝑘wantstoenterCS){
Setrequest timer;
Setnumber-of-attempts;
Send(Msg1,𝑉𝑁𝑘)to𝑃𝑘;
While(number of attempts!=0)
While(request timer!=0){
request timer–;
If((request timer=0)
&&(number-of-attempts!=0))
{
Send(Msg1,𝑉𝑁𝑘)to𝑃𝑘;
Number-of-attempts–;
}
ElserejecttheCSrequest;
}
}
}
Procedure2
VoidADV EventHandler(void){
While(1){
Ifanyeventarrivestoasite𝑆𝑘
Switch(Event){
CaseMsg1:Update request();
CaseMsg2:Vote Reply();
CaseMsg3:Commitment release();
CaseFailure:
Removefailedsitefrom𝑃𝑘;
CaseReject:{
CS Flag=0;
Broadcastrejectionto𝑃𝑘;
}
}
}
}
}
Procedure3
duringupdatecommitment.Inthiscase,theobsoleteorfailed the coordinator. To detect and elect a new ancestor, some
site must send its update request to a site through which it techniquessuchas[29]canbeaddedonADV.
connectswiththepartition.
If a site 𝑆𝑗 wants to join partition 𝑃𝑖 through site 𝑆𝑖, it
sendsitsrequestto𝑆𝑖.𝑆𝑖 actsonbehalfof𝑆𝑗.Itchecksifits 4.ProofofCorrectness
partitionisaDPandifothersitesinthepartitionagreeona
new site joining. To ensure that the new site’s reconnection
ThissectionprovesthatADVcansolvetheproblemofMutEx
does not risk MutEx, 𝑆𝑖 must ensure that it is not a part in partitioned distributed systems and prevent deadlocks.
of a MutEx mission. If its CS Flag is set, it waits until its
The algorithm works correctly if every site updates its
CS Flag is released by the establisher. Then it establishes a
information.Thefollowingshowsthetheoremsandproofs.
procedure similar to MutEx and informs other sites that a
newsiteisaddedtothepartition𝑃𝑖.Inotherwords,thesame Theorem 1. ADV guarantees MutEx in a nonpartitioned
process to commit an application request must be followed distributedsystem.
forreconnectionorjoiningofasite.
TheconceptofDPinADVdependsontheexistenceof Proof. As long as no failure occurs, a distributed system is
theancestor.Iftheancestorfails,ADVinterruptstoservice nonpartitioned.Thisproofis discussed in two states: initial
othersites.Thisproblemiscommoninalgorithmsbasedon stateandnormalstates.
InternationalJournalofDistributedSensorNetworks 7
VoidUpdate request(void){
If(CS Flag==0&&Anc!=Null){
CS Flag=1;
Send(Msg2,VN,Anc)to𝑆𝑖;
Setrelease timer;
//ifasitedoesnotreceiveanyCSreleasebeyondrelease timer,
//itreleasesCSandbroadcastsittopartition𝑃
While(relase timer!=0)
release timer–;
If (release timer=0andCS Flag==1){
//noCSreleasehasarrivedfrom𝑆𝑖beforerelease timer
//time-out
Label𝑆𝑖asfaulty;
If(𝑆𝑖!=Anc)
Broadcast(Failure,𝑆𝑖)to𝑃𝑘;
Else
WaituntilAncreplies;
}
}
Else
Send(Reject)to𝑆𝑖;
}
Procedure4:ProcedureUpdate request().
VoidVote reply(void){
StoreVNandAncofsites∈𝑃𝑖;
IfMsg2doesnotarrivefromasite𝑆𝑗∈𝑃𝑖&itsrequest timerhastime-outs{
Label𝑆𝑗asfaulty;
Broadcast(failure,𝑆𝑗)to𝑃𝑖;
}
If(Find𝑆𝑗∈𝑃𝑖|𝑉𝑁𝑗=max{𝑉𝑁∈𝑃𝑖})and𝐴𝑛𝑐𝑗 ∈𝑃){
𝑉𝑁𝑖=𝑉𝑁𝑗+1;
𝐴𝑛𝑐𝑖=𝑆𝑖;
Broadcast(Msg3,𝑉𝑁𝑖,𝐴𝑛𝑐𝑖)to𝑃𝑖;
}
}
}
Procedure5
1 rejects other CS requests. Therefore, two or more sites
VoidCommitment release(void){ cannot enter CS concurrently, and MutEx is guaranteed in
𝑉𝑁𝑗=𝑉𝑁𝑖; nonpartitioneddistributedsystem.
𝐴𝑛𝑐𝑗 =𝐴𝑛𝑐𝑖;
CS Flag=0; (2)InNormalStates.Foranonpartitioneddistributedsystem,
} MutEx is not guaranteed if the two sites 𝑆𝑖 and 𝑆𝑗 access
theCSsimultaneously.Themethodofcontradictionisused.
Procedure6 MutEx is not guaranteed when sites 𝑆𝑖 and 𝑆𝑗 have two
differentdatawiththesameversionnumbers.Asthedataare
different,twodifferentancestors(𝐴𝑛𝑐𝑖and𝐴𝑛𝑐𝑗)coordinate
twodifferentupdates.When𝑆𝑖 and𝐴𝑛𝑐𝑖 arenotconnected
to 𝑆𝑗 and 𝐴𝑛𝑐𝑗, the system is partitioned. This situation
(1) In Initial State. In a nonpartitioned distributed system, contradicts the assumption that the distributed system is
initially every site considers 𝑆1 as Anc. If a site 𝑆𝑖 needs to nonpartitioned.
accessCS,itissuesMsg1toallothersites.Othersitessettheir
CS FlagonceMsg1isreceived,andtheykeepitsetuntilaCS Theorem 2. ADV guarantees MutEx in partitioned distrib-
release message arrives from 𝑆𝑖. Every site with 𝐶𝑆 𝐹𝑙𝑎𝑔 = utedsystem.
8 InternationalJournalofDistributedSensorNetworks
Proof Node A Node B
(requester) (ancestor)
(1) In Initial State. Initially one site 𝑆1 is considered as the . .
. .
ancestor of initial partition. The initial partition is divided . .
into two partitions, 𝑃𝑖 and 𝑃𝑗, due to the failure of site 𝑆𝑘. SeSnedtrreeqquueesstt(tMimsegr11))
The method of contradiction is used to prove the theorem. Msg1
Th𝑃𝑖,eanadlg𝑆o𝑗riftrhommd𝑃o𝑗easccneopttgtuwaoraunptdeaetMeruetqEuxeswtshseinmsuitletasn𝑆e𝑖ofuroslmy. timer Send permission(Msg2)
In this situation, updates are coordinated by two DPs with est Setreleasetimer
u
two different ancestors, that is, 𝐴𝑛𝑐𝑖 and 𝐴𝑛𝑐𝑗. Based on Req
the algorithm, the repaired site 𝑆𝑘 is eligible to rejoin other Msg2
partitions,aslongasthedestinationisaDP.As𝑃𝑖and𝑃𝑗have Enter CS
theirownancestors(i.e.,𝑆𝑖and𝑆𝑗)andboth𝑃𝑖and𝑃𝑗areDPs, r
twopartitionsaremergedandtheinitialpartitionisformed, .. me
. ti
butwithtwodifferentancestors.Thissituationiscontraryto e
s
thebasicassumptions. Send release CS ea
el
R
(2)InNormalState.Whenadistributedsystemispartitioned (Msg3)
intotwopartitions𝑃𝑖 and𝑃𝑗,oneofthefollowingsituations Msg3
occurs.Formorethantwopartitions,MutExcanbeproved
inasimilarway.
Figure2:Relationbetweenrequest timerandrelease timer.
(a)𝑆𝑗disconnectspartition𝑃𝑖fromitsancestor𝐴𝑛𝑐𝑖.Site
𝑆𝑗 in 𝑃𝑗 receives a request for update. 𝑆𝑗 does not
detecttheancestor𝐴𝑛𝑐𝑖,and𝑃𝑗isnotDP.Therefore,
the site 𝑆𝑗 does not update the data, and MutEx is 1
satisfied.
2
(b)Site𝑆𝑖in𝑃𝑗receivesanupdaterequest.𝑆𝑖isconnected 5
to 𝐴𝑛𝑐𝑖. Therefore, 𝑃𝑖 is DP, and 𝑆𝑖 updates the
common data. As other sites in 𝑃𝑗 cannot enter the
CS,MutExissatisfied.
4 3
(c)Similar to Theorem1, by using the method of con-
tradiction, Theorem2 can simply prove that two Figure3:Adistributedsystemwithtwopartitions.
partitions with two different ancestors do not exist
in two different partitions 𝑃𝑖 and 𝑃𝑗. Since only one
ancestorexistsinthesystem,onlyoneDPisformed.
Furthermore,allthesitesinDPupdatetheir𝑉𝑁and Based on the philosophy of partitioned distributed sys-
𝐴𝑛𝑐tothesamevalues,beforereleasingtheirflags. tem,exceptforonepartition,therearesomepartitionswhose
sites should not enter CS. In fact, this definition indicates
thatthesitesinthenondistinguishedpartitionmuststarve!
Thus,inMutExalgorithmsforpartitioneddistributedsystem,
Theorem3. ADVisdeadlockfree. starvationfreedomisnotrealistic.Theonlyprivilegeforthese
typesofalgorithmsishigheravailabilityofMutEx.
Proof. One reason for deadlock to occur is waiting loops,
whensites𝑆𝑖,𝑆𝑗,and𝑆𝑘 arewaitingforbeingreleasedfrom
5.ExperimentalResults
one another in a chain fashion. ADV utilizes one ancestor
to issue release messages. By using the assumption that the
For more clarity, ADV algorithm is shown in Figure3
ancestor does not fail during CSing and other sites have to
which shows a distributed system with 5 sites. The links
wait for release messages from the ancestor, a chain cannot
which are displayed with dashed lines have already failed
beformed.
The other reason for deadlock is waiting for infinity to because 𝑆3 has separated and formed an isolated group.
entertheCS.ADVbenefitsbyhavingtherelease timersothat Therefore,thedistributedsystemhastwopartitions{𝑆3}and
i𝑆s𝑘adwoaeistendobtywaaniottfhoerrisnifitenoitny.lyBiafsietdsCoSnFAlaDgVisaslegto.rHithowme,vCerS, t{h𝑆1e,la𝑆t2e,st𝑆e4s,ta𝑆b5}li,swhehrenwatwso𝑆4u.pdateshavebeencommittedand
ADVsetsarelease timeronceasitesetsitsCS Flag.Thesite Scenario1.Site4hasreceivedanupdaterequest(current𝑉𝑁
releasestheCS Flag.Itsendsamessagetoothersitesinthe is 2). Its lock is granted, and the ancestor of the establisher
partitionannouncingthatithasreleasedCSandasksthemto is S4 (S4 is the establisher and ancestor as well). Therefore,
do the same procedure. Therefore, waiting for infinity does based on the algorithm, partition 𝑃 = {𝑆1, 𝑆2, 𝑆4, 𝑆5} is a
notoccurinADV. DPand𝑆4 commitstheupdate bybroadcastingnew𝑉𝑁 =
InternationalJournalofDistributedSensorNetworks 9
3 and 𝐴𝑛𝑐 = 𝑆4 to sites in 𝑃. Once the commitment is InTest1,thesystemisintheinitialcondition.Whenthe
accomplished,thesitesareaskedtoreleasetheirlocks. version numbers are zero, there is no ancestor and the site
copies.Thedistinguishedsitereferstoalltheothersiteswith
tSoceintsarnioei2g.h𝑆b2ouesrtsab{𝑆li1s,h𝑆e3s,a𝑆4v}otainndgpwraoictsesfsobry𝑇s𝑤ensdecinognd𝑀s.𝑠𝑔A1s cAosmthmeosynstdeamtai.n𝑆i1tiraellcyefivoermsasroenqeupeastrttiotiounpdanatdetchoimspmarotnitidoantais.
𝑆3 has already failed, 𝑆2 does not receive any reply from 𝑆3 theDP,updateiscommitted.Theversionnumbersandother
after𝑇𝑤seconds.𝑆2thensupposesthat𝑆3isafailedsiteand indicesarethenupdatedinTest2.
roefptohretfsaiitletodostithee.rItsiitsensoanteddctohnattinifu𝑆e3sbitescoopmereasttihoensesrteagbalridshleesrs, apaWrtihtieonna{l𝑆i4n}k.Gfaiivlse,nsi𝑆te2𝑆a4sitshseepesatraabtelidsh.Ther,iAssDitVetchaennafcocrempst
itrejectseveryincomingrequestbecauseitdoesnotbelong theupdatebecausetheancestorof𝑆2,thatis,𝑆1,belongsto
toDP. partition {𝑆1,𝑆2,𝑆3}. Dynamic linear and hybrid algorithms
Scenario3.𝑆4receivestwolockrequestssimultaneouslyfrom alsocommittheupdatebecause𝑐𝑎𝑟𝑑 𝐼 = 3(numberofsites
sites𝑆2and𝑆5.Inthiscase,asitemaybechosenrandomlyto withmaximumversionnumber)ismorethan𝑁/2,thatis,2
beservicedfirst.Othersitesareaskedtorejecttheirupdate (𝑁asthemaximumSCofsitesinpartition).Theresultsof
requests.Ifaneighbourcannotsetitslockforanyreason,it updatecommitmentaredisplayedinTest3.
sendsbacktherejectionsothat𝑆4 canbeinformedtoreject InTest3,thesystem’sconditionissimilartotheformer
theupdaterequest. test,exceptthattheestablisherischangedto𝑆4.Noneofthe
algorithmscancommittheupdate.Therefore,toavoiddata
Scenario4.𝑆3isrepairedandfound𝑆2asitsneigh-bour,but inconsistency,therequestmustberejected.
itcannotarbitrarilyrejoinapartitiontowhich𝑆2belongs.In Another partitioning happens in Test 4 with 𝑆1 as
thiscase,𝑆3asks𝑆2forupdatecommitment.As𝑆2belongsto the establisher. Consequently, there are three partitions:
aDP,𝑆3isallowedtoconnect.Itcanreceivethelatest𝑉𝑁and {𝑆1,𝑆2},{𝑆3},and{𝑆4}.Withregardtothesites’information,
𝐴𝑛𝑐through𝑆2too.ADValgorithmisexpectedtoguarantee allthealgorithmshavetheconsensusandupdatetheassoci-
MutExandtoimprovetheavailabilityofMutExwhenfailures atedinformation.
occur. Hybrid algorithm improves the availability of dynamic
Forthepurposesofsimulationandexperimentalresults, linear algorithm if less than the majority of the current
ADV, dynamic linear, and hybrid voting algorithms are sitesremains.Thesiteshavehigherrepairrateversusfailure
discussed as follows. One effective point on fault tolerance rate (the probability of repair is thus much more than the
of an algorithm is coordination. A centralized coordinated failure).Since𝑐𝑎𝑟𝑑 𝐼equals𝑁/2,dynamiclinearalgorithm
algorithm is vulnerable to fail because the coordinator is cannot continue working and rejects the request in Test 5.
a single point of failure. Reliability and availability of the However, Test 5 has a major difference with other cases
systemarealwaysfunctionsofthereliabilityandavailability because only one site can remain in the partition. In this
of the coordinator. Therefore, these algorithms are avoided, particularcase,bothADVandhybridalgorithmsareableto
except when they are required due to the limitations of commit.Therefore,ADVandhybridimprovetheavailability
implementation or when the algorithms are utilized to of dynamic linear if less than the majority of the sites has
upgradeorimprovetheperformanceofold-fashionsystems. currentdata.
Forthisstudy,groupconsensusanddynamicweightedvoting In this section, the benefits and weaknesses of ADV
are ignored in the analysis and comparison. Autonomous versus hybrid and dynamic linear algorithm are analysed.
reassignmentcanbeagoodcandidateforanalysis;however,it Differentscenariosoffailureinjection,topology,andsimula-
needstoknowthetotalnumberofvotesincludingthevotes tion environment are presented. However, the performance
ofsitesinotherpartitions.Thisconditionisnotrealisticor measures used for the comparison and analysis should be
possible in many real situations. For this reason, it is also discussed,asinthefollowingsection.
neglectedinthisstudy.
The remainder of this paper discusses dynamic voting
algorithms including hybrid and dynamic linear which are 5.1. Performance Measures. Two main measures are used
utilized for analysis and comparison. Table1 displays the for the analysis and comparison of dynamic voting algo-
results of 5 consecutive tests on ADV, hybrid, and dynamic rithms including the number of messages transmitted and
linearvotingalgorithms. availability of MutEx. Availability has widely been used in
Test numbers are presented in the first column. System analysis and comparisonof dynamic voting algorithmsand
configuration, and information required by each voting is defined as the probability that an update request can be
algorithm is perceived in the second column, including the servicedatanytime,𝑡[34].Thismeasurerequiresnotonly
site that has received the update request (establisher). A a partition existence but also the capability of at least one
requestcanbeexaminedifandonlyifanonfaultyestablisher site in the partition to be operational in order to service
has obtained the request. The version numbers (VN), site therequest.Aseconddefinitionmeasuresavailabilityasthe
copies(SC),distinguishedsites(DS),andtheancestorofeach proportionoftimeduringwhichadistributedsystemservices
site(Anc)havebeenpresentedinthesystemconfiguration.If the requests either as critical or noncritical. By using this
dynamiclinearvotingistakenintoaccount,SCandVNneed definition,synchronizationdelaysarethetimeduringwhich
to be known, whereas ADV needs VN and Anc. Obviously, aprocessenterstheCS,tillthenextprocesscomingintothe
VN,SC,andDSareessentialforhybridvoting. CS[16].Interruptionperiodsduringconnectivitychanges(as
10 InternationalJournalofDistributedSensorNetworks
Table1:ComparisonofADV,dynamiclinearandhybridvotingalgorithmsfor5consecutivetests.
Testno. Systemcondition Dynamiclinear Hybrid ADV
S1 S2 S3 S4
Accept Accept Accept
VN 0 0 0 0
1
Anc — — — —
SC 4 4 4 4
DS S1,⋅⋅⋅S4 S1,⋅⋅⋅S4 S1,⋅⋅⋅S4 S1,⋅⋅⋅S4
S1 S2 S3 S4
2 VN 1 1 1 1 Accept Accept Accept
Anc 1 1 1 1
SC 4 4 4 4
DS S1,⋅⋅⋅S4 S1,⋅⋅⋅S4 S1,⋅⋅⋅S4 S1,⋅⋅⋅S4
S1 S2 S3 S4
VN 2 2 2 1 Reject Reject Reject
3
Anc 2 2 2 1
SC 3 3 3 4
DS S1,⋅⋅⋅S3 S1,⋅⋅⋅S3 S1,⋅⋅⋅S3 S1,⋅⋅⋅S4
S1 S2 S3 S4
VN 2 2 2 1 Accept Accept Accept
4
Anc 2 2 1 1
SC 3 3 3 4
DS S1,⋅⋅⋅S3 S1,⋅⋅⋅S3 S1,⋅⋅⋅S3 S1,⋅⋅⋅S4
S1 S2 S3 S4
VN 3 3 2 1 Reject Accept Accept
5
Anc 1 1 1 1
SC 2 2 3 4
DS S1 S1 S1,⋅⋅⋅S3 S1,⋅⋅⋅S4
discussedin[17])shouldalsobetakenintoaccount.However, messages(i.e.,3𝑗messages)intheworstcase,where1 ≤ 𝑗 ≤
issues relating to synchronization and delays are not taken 𝑁.
intoaccountinthisstudy.Inthispaper,asimplifiedversion Dynamic linear and hybrid algorithms require 4𝑗 − 2
of the first definition is used. Availability is measured by messages(1≤𝑗≤𝑁)forcommitmentand2𝑗+1forrejecting
thenumberoftimesthatadistributedsystemcanservicea therequest.Itisnotedthatthedifferencebetweenthesetwo
requestandupdatereplicateddatasuccessfully[39]. algorithmsisthewayofchoosingDP,notintheprotocolof
Though the availability improvement of MutEx is the sendingmessages.Obviously,ADVneedsfewernumbersof
mainobjectiveofthisstudy,itcanbecompromisedbyhigh messagescomparedtodynamiclinearandhybridalgorithms.
messagetransmissions.Forahighernumberofsites,ahigher
number of messages are required to be transmitted. A high
number of message transmissions for every commitment 5.2.SimulationofTestHarness. Softwaresimulationsareused
cause extra communication cost, more time for sites to in this section to study the availability of dynamic voting
process messages, and traffic increase in the network. The algorithmsdealingwithhighrateoffailures.Inthesimula-
effectivetimededicatedtoserviceupdatesandqueryrequests tion environment, the issues related to interruption during
isthenaffected.Therefore,thereshouldbeatradeoffbetween connectivity changes [17] are not taken into account. The
thesetwomeasures. simulationofvotingalgorithmsisconsideredasevent-driven.
At least 3 messages are required for ADV algorithm to An event-driven simulation implies that the algorithm acts
commitorrejectanupdaterequest,with2outof3messages orreactsifachangeoccurs,whetheramessageisreceivedor
forcommunicationbetweentheapplicationandestablisher. required to be sent. This assumption already has been used
Theestablishercanbeanyofnonfaultysitesinthedistributed inthesimulationofprotocolsinthedistributedsystems[44–
system.Onemoremessageisenoughforupdatecommitment 46]andindynamicvotingalgorithms[29].MATLABcanbe
orrejectioniftheestablisheristheancestororifitdoesnot usedeffectivelyforthepurposeofsimulation.Thetoolboxes
agree on an update. Otherwise, 𝑗 − 1 messages should be ofdistributedcomputingandrealtimealsocanbeutilizedor
sent to other 1 ≤ 𝑗 ≤ 𝑁 sites for lock activation. 𝑗 − 1 linkedtothisstudy’ssimulatorforfutureworks.
messagesfromthesitestotheestablishercanannouncethat Simply,allsitesareassumedtohavecommondata.The
lockisgrantedandotherinformationordisagreement.More sites are labelled as 𝑆𝑖, 𝑖 = 1,2,...,𝑛, where 𝑛 presents the
𝑗messagesarerequiredforthecommitmentorrejectionand numberofsitesinthedistributedsystem.Tohavethesame
lock release. Hence, ADV algorithm transmits 3𝑗 − 2 + 2 simulation assumptions, the information on the simulation