Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 Article An Adaptive Beamforming Time With Round Robin MAC algorithm for reducing energy consumption in MANET VincenzoInzillo1,(cid:5),FlorianoDeRango1,•,AlfonsoArizaQuintana2,† andAmilcareF. Santamaria1,(cid:63) 1,(cid:5) UniversityofCalabria,DIMES;[email protected] 1,• UniversityofCalabria,DIMES;[email protected] 1,(cid:63) UniversityofCalabria,DIMES;[email protected] 2,† UniversityofMalaga;[email protected] VersionOctober24,2018submittedtoPreprints Abstract: TheuseofSmartAntennaSystems(SAS)inpervasiveenvironmentssuchtheMobileAd 1 hocNetworks(MANET)hasbeenpromotedasthebestchoicetoimproveSpatialDivisionMultiple 2 Access(SDMA)andthroughput. Althoughdirectionalcommunicationsareexpectedtoprovidegreat 3 advantagesintermsofnetworkperformance,directionalMAC(MediumAccessControl)protocols 4 introduceseveralissues. Oneofthemostknownproblemsinthiscontextisrepresentedbythefact 5 that, attemptingtosolveoratleastmitigatetheproblemsintroducedbythesekindsofantennas 6 especiallyatMAClayer,alargeamountofenergyconsumptionisachieved;forexample,dueto 7 excessiveretransmissionsintroducedbyveryfrequentlyissuesuchasdeafnessandhandoff. The 8 expedientsproposedinordertoreducethesedrawbacksattemptingtolimitbeamformingtimeof 9 nodesincooperationwithaRound-Robinscheduling,cangranthighperformanceintermsoffairness 10 andthroughput. Howevertheoverallenergyconsumptioninthenetworkisnotefficentduetothe 11 staticapproach. Inviewofthis, weproposeanAdaptiveBeamformingTimewithRound-Robin 12 MACprovidingforadynamicassignmentofthebeamformingtimewiththepurposetolimitthe 13 wasteofenergyofnodes. 14 Keywords: SmartAntennaSystems,MANET,MAC,EnergyConsumption,Beamforming,Round 15 Robin 16 1. Introduction 17 Inthelatestresearchstudies,relatingtowirelessnetworkenvironments,oneofthemostsignificant 18 and,atthesametime,criticalissueisrepresentedbythemanagementofenergyconsumptionofnodes 19 thatcouldhighlylimittheoverallnetworkperformancewithreferencetoprotocolsandapplication 20 fields. Inthisregard,severalaspectsshouldbeconsideredinordertoaddresstheproblemsimpliedby 21 mainfeaturesofthiskindsofnetworksthatsignificantlyaffectthebehavioursatphysical,Medium 22 Access Control (MAC) and routing layers. For instance, let us consider Mobile Ad hoc Networks 23 (MANET); they are self-organized networks in which mobile nodes can move independently; the 24 nodesusuallymoveaccordingtoacertainmobilitypatternmodelandthemovementofanodeisnot 25 necessarilyrelatedtothemovementofothernodesinthenetwork.Usually,inMANET,omnidirectional 26 antennasareusedforcommunicationamongnodesbothfortransmissionaswellasforreception; 27 thisapproachresultsinverylimitedperformancerelatingtophysical,linkandroutinglayerstatistics 28 [1-3]. Omnidirectionalantennas,alsoknownasisotropicantennas,radiateandreceiveequallywell 29 inalldirections. Mainadvantagesofomnidirectionalantennasinclude: easeofconfigurationand 30 implementation,lowdesigningcost,veryandsimplearchitecture(hardware-less). Forinstance,in 31 cellularsystems,theyallowtoamplifycellsignalsfrommultiplecarrierswithdifferentcelltowersin 32 multiplelocations.Nevertheless,despitefromthesefewbenefitstheyintroduceaconsiderablenumber 33 ofdrawbackssuchas: limitedrangeandcoverage(impliedbylowgain),highenergyconsumption, 34 © 2018 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 2of17 highinterferenceprobability(especiallyindensenetworks),veryhighperformancedependencyonthe 35 environmentsinwhichtheyareemployed(indoororoutdoor);nonetheless,omnidirectionalantennas 36 cannotexploitthebenefitsofcross-polarizationbecausetheyareverticallypolarized. Morespecifically, 37 thislastissue,contributestoincreasetheprobabilityofinterferencebetweencommunicatingnodes 38 inthechannel[4]. Fromatopologicalpointofview,thisapproachimpliesthat,thesignalgenerated 39 fromthetransmitterT,reachdesireduserswithonlyasmallpercentageoftheoverallenergysentout 40 intotheenvironment. Duetothishugenumberoflimitations,omnidirectionalantennasmaynotbe 41 efficientduetointerferencecausedbythetransmissionofpacketsinalldirections(otherthantarget 42 direction)andlimitedrangeofcommunications. 43 Figure1.Interferencecausedbyomnidirectionalantennas. The Figure 1 illustrates a wireless network scenario in which nodes use omnidirectional 44 antennas to perform communications. In particular, the transmitter node T sends to the receiver 45 Racommunicationsignalbyusinganomnidirectionalantenna;Rattemptstocapturethesignalwith 46 thesameantennamodel. Becausethetransmittersignalisradiatedinalldirectionswiththesame 47 intensity,iftherearesuchnodesintheneighboringofthetransmitter/receiver(N andN )ispossible 48 T R thattheradiatedsignaliscapturedbythesenodesthat, inturn, mayattemptacommunicationat 49 thesametime. Inthiscase,interferencesandcollisionscanoccur;theseissuescouldenhanceasthe 50 mobilityofnodesincreases. Nevertheless,inthiscase,becausenodesradiateinthesamewaytoward 51 alldirections,ahugewasteofthebatterylifeofnodesiscertainlyachieved. Themajorityofthese 52 issuescouldbepartiallymitigatedusingdirectionalantennas. Directionalantennasmaybeuseful 53 toincreasenetworkefficiencybydirectingthetransmittedpowerinthedesired/intendeddirection. 54 Directionalantennashaveagreatnumberofadvantagesoveromnidirectionalantennasinadhoc 55 networking. Byfocusingenergyonlyintheintendeddirection,directionalantennascanincreasethe 56 potentialforspatialreuseandcanprovidelongertransmissionandreceptionrangesforthesame 57 amount of power. Increased spatial reuse and longer range translates into higher ad hoc network 58 capacity(moresimultaneoustransmissionsandfewerhops),andlongerrangealsoprovidesimproved 59 connectivity[5-7]. Differentkindsofissueshavetobeinvestigatedwhendirectionalcommunications 60 occurwithrespecttothetraditionalomnidirectionalcase;problemssuchasthehiddenterminaland 61 thedeafnessproblemhavetobeproperlyhandledaswellashandoffissueimpliedbymobilityof 62 nodes. 63 (a) Deafnessproblem (b) Handoffproblem Figure2.DirectionalantennascommonissuesinMANET Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 3of17 ReferringtodirectionalMACcommunicationsinwhichDirectionalRequesttoSend(DRTS)and 64 Directional Clear to Send (DCTS) are used to perform a transmission/reception flow, a particular 65 node (deaf node) that is engaged in a certain communication, but at the same time is solicited as 66 receiverbyanothersourcenodearisesthedeafnessproblem(Fig. 2(a)). Thenodethatexperiencesthe 67 deafness(thenodeAinFig. 2(a))couldtrytoretransmitmanytimesMAClayerpackets,resulting 68 in a large amount of collisions and considerable increase of the network overhead. Furthermore, 69 due to the recurring retransmission attempts from deaf node, a large waste of energy could take 70 place, andconsequentlythisnodeconsumesitsbatterylifeinaveryshorttime, highlydegrading 71 theoverallthroughputofthenetwork. Anothercommonissuewhileusingdirectionalantennasis 72 given by the handoff problem that is usually implied by the mobility of nodes in the network. In 73 Fig. 2(b)anexampleofhandoffisillustrated: thetransmitternodeTiscommunicatingwithanode 74 R;duringthecommunicationRmovesinthepositionR’andexitoutofthetransmitterbeamand 75 consequentlythecommunicationfailsandthebeamsneedtobere-pointed. Inthiscase,ifthenode 76 in the position R’ can still be reached by T through a beam switching. If a proper mechanism of 77 synchronizationandnodepositionrefreshingisnotprovided,thedirectionalbeamremainstunedfor 78 alongtimeinanundesireddirectionduetonodemovement;forthisreason,again,alotofenergy 79 consumptionoccurs. Mostresearchers,inordertomitigatetheseundesiredphenomenaindirectional 80 contexts,demonstratedthat,throughtheemploymentofSmartAntennaSystems(SAS)insteadofthe 81 moretraditionaldirectionalantennas,itispossibletocreateanefficientsystem,exploitingtheSpatial 82 DivisionMultiplexing(SDMA)techniquethatthiskindofdeviceswellprovided. UsingSAS,higher 83 spatialreuseandbetterlinkreliabilitycanbeachieved[8-9]. IncontextsinwhichdirectionalSmart 84 AntennaSystemsareused,thebeamformingissuehavetobedeeplyinvestigated.TheuseofDRTSand 85 DCTSframesinassociationwithaDirectionalNetworkAllocatorVector(DNAV)information,helps 86 todecreasethelargeamountofcollisionsthatusuallyoccurswhenusingomnidirectionalantennas, 87 butinenvironmentsinwhichSASareemployeditmightnotbeenoughtoprovidetheseexpedients 88 [10-12]. Inthepresentpaper,weproposetoreducetheseissuesbyenhancingtheworksproposedin 89 [13-14]usingSASalongwithaRound-Robinschedulinginordertoaddressmoredetailedchallenges 90 such as the queue and the time slice problem involved by the use of the Round-Robin. The main 91 purposeoftheworkistolimitthemassiveenergyconsumptioninthenetworkand,simultaneously 92 toimprovetheoverallperformancewhenDirectionalMACprotocolsareexecutedinmedium-high 93 mobilityenvironments. 94 2. StateofArt 95 RelatingtoMAClayercommunications, themostcausesofexcessiveenergyconsumptionin 96 mobilenetworkscenariosincludetheuseofomnidirectionalantennas,dataprocessing,highprotocol 97 overhead,highlevelofinterferencesinthechannel. DataprocessingimpliesthelargeusageofCentral 98 ProcessingUnit(CPU),memory,harddrive,etc. Topartiallysolvethisissuethemostactualsolution 99 istofindatradeoffonenergyconsumptionbetweendataprocessingandradiocommunication[16]. 100 Forexample,datacompressiontechniquesareintroducedin[15]tominimizepacketlengthandsoto 101 obtainanenergysavinginradiocommunication,butthecostofcomputationisincreased. Inwork 102 [17]authorsalsohighlightthelargeprotocoloverheadintroducedbythiskindofsystems. Generally, 103 tomakeaMACprotocolenergyefficient,atleastoneofthefollowingguidelinesareused: 104 • Reducingcollisionsandretransmissions:OneofthemostcommonobjectiveofMACprotocols 105 inordertoavoidcollisionssothattwointerferingnodesdonottransmitatthesametime. The 106 simplestwaysforcollisionavoidanceinageneralnetworkincludecodedivisionmultipleaccess 107 (CDMA),timedivisionmultipleaccess(TDMA),andfrequencydivisionmultipleaccess(FDMA). 108 Sincecollisionavoidancemaytranslateintoasubstantialoverhead,whichwillburnmoreenergy, 109 tradeoffsmustbeexploredtoachievereasonablesolution. 110 • Reducing overhearing: Wireless mobile nodes deplet battery life because they overhear the 111 transmissionsoftheirneighbors. Therefore,themobilenodesreceiveallpacketsthathittheir 112 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 4of17 receivers. One possible solution to this problem is the introduction of a control channel for 113 the transmission of control signals that will wake up the nodes only when needed. Authors 114 in[18]proposetobroadcastaschedulethatcontainsthedatatransmissionstartingtimesfor 115 eachmobilenodes. Inwork[19]twoschemesareproposedinordertomitigatethedeafness 116 causedbypersistenthearingofdataandforhandlingtheShortRetryLimit(SRL)indirectional 117 environments. 118 • Minimize control overhead: Protocol overhead should be reduced as much as possible, 119 especiallyfortransmittingshortpackets[20-22]. Duetothelargechannelacquisitionoverhead, 120 smallpacketshavedisproportionatelyhighenergycosts. Whenmobilenodesrequestmultiple 121 transmissionslotswithasinglereservationpacket,thecontroloverheadforreservationcanbe 122 reduced[23]. ApacketdeliveryschedulingalgorithmandtwoMACprotocolsinwhichnodes 123 usesdirectionalsectorizedantennasareproposedin[24]. Theschedulerandtheprotocolsare 124 designedwiththepurposetopreventtheco-siteinterferenceproblemthatcouldariseinsome 125 directionalcontextsalsobylimitingtheoveralloverheadinthenetwork. 126 • Reducingbeamformingtime: In[25]authors,proposeaToneDMACmechanismthatenable 127 thetransmissionofspecialpackets(Out-ofbandtones)bynodesinomnidirectionalmode;these 128 tonescanbeprocessedbyneighborsreducingconsiderablythelargebackofftimeintroducedby 129 deafness. In [14] a sectorized antenna model based on a round-robin scheduling algorithm 130 is presented in order to reduce the impact of the deafness in directional communication 131 environments. TheRound-Robinmechanismwasimplementedbyanalgorithm,thatmanages 132 theassignmentofthebeamtowardacertainsectoralsohandlingtheincomingframesthatcould 133 nottemporallybetransmittedinthechannel(incasetheyareoutsidefromthecurrentactive 134 sector)byusingwaitqueues. 135 Figure3.Round-RobinMACprinciple. TheFigure3illustratestheRound-RobinMAC(RR-MAC)principle. TheplaneisdividedintoN 136 equalsectors,eachonehavingacertainamplitudew(sectorwidth)andabeamformingduration 137 time T (sectortime)withi = 1...N; N isthenumberofsectorsinwhichtheplaneisdivided. 138 i Notethatallsectorshavethesamewidthaswellasthesamesectortime;eachnodethatbelongs 139 toacertainsectorbeamformswithanangleα untilthesectortimeisreached,thenitswitchesto 140 i thenextsector. Thesectorinwhichthebeamiscurrentlyactiveisdefinedcurrentactivesector. 141 2.1. MobilityissuesdirectionalMACworks 142 Otherapproaches,suchasthework[26],attempttoreducethehandoffissuethroughanefficient 143 beamsystemcontrol; asimilarworkispresentedin[27]; inthispaper, authorstrytomitigatethe 144 handoffproblembyproposingapredictivelocationmodelinordertoadvancethefutureposition 145 movements of the nodes. Nevertheless, these works are suitable for Vehicular ad Hoc Network 146 (VANET)environmentsanddonotproperlyaddressthedeafnessproblemwhichisveryrelevantin 147 MANET.In[28]weintroduceapredictivelocationmechanismthatalsoprovidesforaframescheduler 148 withpriorityinordertoreducethehandoffproblem. However,inthiscase,theenergyconsumption 149 ofnodesisnotconsidered. 150 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 5of17 3. OmnidirectionalandDirectionalantennasvsRound-RobinMAC 151 As largely mentioned in the previous sections, networks containing nodes equipped with 152 omnidirectionalantennasarepronetohighwasteofenergybecausetheshapeoftheradiationpattern 153 thatdoesnotbeamformonlyaspecificdirection. Althoughdifferentproposalsthereexistwiththe 154 aimtosolveoratleast,mitigatetheissuesderivedfromtheuseofomnidirectionalanddirectional 155 antennasatMAClayer,amoredeeplyanalysisisrequiredforhighlightingtheissuesthatneedtobe 156 addressed. Forexample,letusconsiderthework[14],thatattemptstomitigatetheoverallnetwork 157 energyconsumptionusingaSASantennamodulealongwithaRound-Robinscheduleralgorithm. 158 Basically,itworksfineundertwomainassumptions: 159 Assumption1. nodesareequippedwithhigh-efficienthardwareantennas(SAS). 160 Assumption2. datatrafficandnodesareuniformlydistributedamongsectors. 161 Assumption3. thesizeofthesectorqueuesarefixedandequalsforallsectors. 162 Inordertoevaluatetheimplicationsofthefirstassumptionitcanbeusefultoanalyzethebehavior 163 oftheRR-MACincasetheomnidirectionalantennaisusedinplaceofdirectionalorSAStechnologies. 164 Forthispurpose,weevaluate,throughtheuseoftheOmnet++Networksimulator[29],theenergy 165 consumptionofnodesofthreedifferentrunconfigurationsusingthesamesimulationparameters 166 describedin[14](themostofthethemareillustratedintable1insubsection5.2ofthepresentpaper); 167 inordertoaccomplishtheanalysis,energysimulationmoduleshavebeeninsertedintoeachmobile 168 nodeforallowingtheemulationofthebatterylifetimebehavior. Theinitialenergyvalueofeachnode 169 wassetto300J,theshutdownenergyvaluewassetto0J;inthisway, anodeshutdownswhena 170 nodecompletelydepletesitsbatterylife. Inthefirstconfigurationrunnodesareequippedwiththe 171 classicalomnidirectionalantenna;inthesecond,nodesusetheomnidirectionalantennatogetherwith 172 theRR-MACscheduling;thelatestrunconfigurationissimilartothesecondexceptfromthefactthat 173 inthiscasetheantennaistheSASmoduledesignedin[30]. 174 Figure4.Residualcapacityprogression. TheFigure4depictstheresidualcapacity(averagedbyallnodes)plotcomparisonbetweenthe 175 threeconsideredcases. Aswecanexpect,whenusingtheomnidirectionalantennawithoutanyenergy 176 savingmechanism,nodesdeplettheirbatterylifeveryquickly;whentheomnidirectionalantennas 177 areusedincooperationwithRR-MACtheaveragedepletiontimeisalmostdoubled(t=190s)and 178 improvessignificantlywhenSASareemployedbynodes. ThisismainlyduetothefactthatRR-MAC 179 limitsthebeamformingtimeforeachsectortranslatingintoareductionofthenumbercollisionsand 180 interferences. Then,weinvestigateabouttheassumptions2and3. Inparticular,theseassumptions 181 implythatthesystemcouldbeaffectedfromthequeuesizeandthewaitingqueuetimeproblems[31] 182 thatcanaffecttheoverallnetworkconsumptioninthenetwork. Weanalyzetheseissuesbycreating 183 twomorerunconfigurations: inthefirstonemobilenodesareuniformlydistributedinthenetwork 184 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 6of17 scenario;alsotheactivitydegreeofthenodesisuniformlydistributedamongsectors;inthesecond, 185 instead,nodesareperiodicallyconcentratedinacertainsector(randomlychosen)ofthesectorized 186 planeandtheactivitydegreeofnodesisunbalancedamongsectors. Thenumberofsectorsinthe 187 planevariesfrom3to8whilethequeuesizeisevaluatedbasedonthefollowingequation: 188 Queuesize = Q×[N+w (N )] w ∈W (1) Q s Q Q ThequeuesizeisfunctionofthenumberofnodesNandthenumberofsectorsN intheplane. 189 s Qisavaluechosenintheinterval0.1 ≤ Q ≤ 0.25inordertomaximizethePacketDeliveryRatio 190 performanceof[14]. Thenumberofsectorsisweightedbythetermw thatvariesfrom1to6asthe 191 Q numberofsectorvalueincreases. Inparticular,giventhenumberofsectorarrayS = [3,4,5,6,7,8],the 192 weightvectorW isexpressedby: 193 Q W = [1,2,3,4,5,6] (2) Q Inordertoassesstheimpactofthetwosimulationscenariosrelatingtothequeueissues, we 194 comparethewaitingqueuetimeofthetworunningconfigurationsinfunctionofthenumberofsectors 195 andqueuesize. 196 (a) Averagewaitingqueuetimevsnumberofsectors (b) AveragewaitingqueuetimevsQueuesize Figure5.QueueissueswithRound-Robinscheduling. The Figure 5 illustrates the average waiting queue time in function of the number of sectors. 197 ThewaitingqueuetimeisaveragedbyvaryingtheQparameterfrom0.1to0.25. InFig. 3itcanbe 198 observedthatthewaitingqueuetimeinthecaseofnotuniformdistributednodesremainshigherthan 199 theuniformcaseindependentlyfromthenumberofsectorvalue;inparticular,thegapbetweenthe 200 waitingqueuetimeofthetwoconsideredcasesseekstogrowforsectornumbervalueshigherthan 201 5. ThecurvesinFig. 4areplottedinfunctionoftheQparameterthatrepresentsaproperlyindex 202 ofthequeuesize;asitcanbededucedfromeq. 1,thehigheristheQvalue,thehigheristhequeue 203 size. AsithappensinFig. 3thewaitingqueuetimeinthecaseofnotuniformtrafficliesabovethe 204 uniformcasecurveindependentlyfromthequeuesize. However,asopposedtoFig.3,thedifference 205 betweencurveshaskeptalmostconstantasthequeuesizeincreases. Intheuniformtrafficcaseitcan 206 benotedhowthewaitingtimeslightlydecreasesforthehighestvaluesofQwhile,inthenotuniform 207 case,thedecreasecorrespondingtothesamevaluesiscloselynegligible. Insummary,asthesizeof 208 thequeuegrowsupthewaitingtimeinthenotuniformcasedoesnottendtogetsmaller,orrather, 209 thedecreasingrelatedtohighqueuesizevaluesisnotsignificant. ThetrendsevaluatedinFig. 5are 210 certainlyjustifiedbyoneofthemostcommonissuesimpliedbyaRound-Robinalgorithmscheduling: 211 thetimesliceproblem[32-33];basically,thetimeslicerepresentsthequantumassignedtoeachsector 212 (thesectortime)inequalportions;therefore,thecommunicationsarehandledinacircularwayamong 213 sectorswithoutpriority. Incaseofnotuniformdistributedtrafficifmostofmobilenodesarefocused 214 inaspecificsectoroftheplane,thecommunicationsrelatedtothatnodesareenqueueduntilthebeam 215 isallowedinthespecificsector;asconsequence,thelargestisthequantumassignedtoeachsectorthe 216 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 7of17 largestisthewaitingqueuetime. Inthesameway,asobservedin[14]ifthequantumassignedtoeach 217 sectoristoolow,thesystemwillprovidebadperformanceintermsofoverallthroughput;asimilar 218 behaviorisproducedifthequantumassignedtoeachsectorisaveragedinaspecificintervalwith 219 increasingthenumberofsectorswhichresultsinlargestwaitingqueuetimevaluesasseeninFig. 3. 220 4. Proposedmodel 221 4.1. ComparisonwithRR-MACandmotivations 222 Asexplainedinthesection3themainchallengesrelatedtotheRRapproacharereferredtothe 223 sizeofthequeuesandthedelayproducedbystatictimesliceswhichcannotbemodeledinfunction 224 ofthetrafficinthenetwork. However,asobservedin[13,14]thequantumoftimeassignedforthe 225 beamformingprocessisthesameforeachsectoraswellastheamplitudeofthewidth. Therefore, 226 inthework[14]emergesthatapropersetofthesectortimevalueaffectstheoverallperformance 227 morethanthesectorwidthchoice;thisimpliesthattimeslotassignedtosectorsneedstobecarefully 228 assignedinordertoimprovethesystemefficiency. Forthesereasonsweproposeanapproachthat 229 modifiestheoriginalRound-Robinalgorithmformulationrelativetotheevaluationofthesectortime 230 whilekeepingunchangedthesectorizationoftheplaneandthusthewidthofthesectors. Inorderto 231 understandthemodificationsintroducedwithrespecttotheRound-RobinMACalgorithmwebriefly 232 recallthemathematicalformulationofthislatter: 233 α = α =....= α i j T = T =....= T i j s (3) α (T) = α (T) =....= α(T) i i j j ∀i,j =1,2..N, i (cid:54)= j FromformulationgivenbyEq. 3itiseasytoobservethatallsectorshavethesamewidthand 234 thesamesectortimeT . TheuseofthisapproachhelpstoenhancetheMACperformanceintermsof 235 s reductionofcollisionsandfairnessimproving,resultinginaoveralldecreaseofthetotalamountof 236 energywastedbynodes. Unfortunately,RR-MACisastaticmodelanddoesnotadaptitselftothe 237 trafficchannelconditions;thiscouldrepresentalimitinscenariosinwhichnodesareconcentrated 238 inacertainsectorasverifiedintheprevioussection. Thegoalofthepresentworkistoimprovethe 239 efficiencyoftheRound-Robinschedulerintermsofenergymanagementbyprovidinganadaptive 240 beamforming time for each sector that takes into account the size of the waiting queue for each 241 sector. WedenotedthisnovelapproachasAdaptiveBeamformingTimewithRound-RobinMAC 242 (ABT-RRMAC).Tofigureouttherelevanceofusinganadaptivesectortimeassignmentletusconsider 243 thesituationdiscussedinsec. 3inwhichtwodifferentmobilenodestrafficdistribution(uniformand 244 notuniform)inthenetworkarecompared: 245 (a) Uniformnodedistribution (b) Notuniformnodedistribution Figure6.UniformnodedistributionvsnotuniformusingRound-Robinapproach. The Fig. 6(a) represents a network scenario in which mobile nodes are almost uniformly 246 distributedamongsectorsofthesectorizedplane;thecommunicationsareruledbytheRound-Robin 247 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 8of17 scheduling;therefore,thecurrentactivesectoristhesector2,thenthebeamisactiveinthatsector. As 248 noticedfromtheanalysisaccomplishedinsec. 3,assumingauniformactivitydegreeofnodes,inthis 249 case,thewaitingqueuetimeisacceptableaswellastheMAClayerperformance;inFig. 9bitcanbe 250 observedthattheoverallnodedistributionisunbalancedamongsectorsaswellastheactivitydegree 251 ofnodes. Morespecifically,mostofthemobilenodesaremainlydistributedinthesector1which, 252 asassumption,hasalsothehighestactivitydegreeamongsectors;supposingthatthecurrentactive 253 sectorisagainthesector2andthatsectorcontainsaverysmallnumberofnodeswithrespecttothe 254 sector1togetherwithaverylowburdenofactivecommunications,itmayoccuranunder-useofthe 255 allocatedresourcesinthatsector;inparticular,duetothestaticsectortimereservationassignment 256 provided by the Round-Robin algorithm (the assigned sector time is the same for all sectors), the 257 overallbeamformingprocessbecomesinefficientresultinginaconsiderabledecreasingoftheMAC 258 performanceespeciallyintermsofthroughputandenergyconsumption. Indeed,inFig. 6bitiseasy 259 toobservethat,duetounbalanceddispositionofnodesamongsectors,theenergyconsumptionin 260 sectorsS ,S ,S ,S ,S ,S (representingthe80%oftheoverallplane)isquiteinefficientbecausethe 261 2 3 4 5 7 8 beam,inthatsectorsisperformedforatimeT thatismuchhigherthantherequiredquantumoftime 262 s requiredforemptyingthequeues. Importanttohighlightthat,becauseweareanalyzingtheworst 263 conditioncase,weassumethatthescenariosillustratedinFig. 6(b)remainunchangedforalongtime 264 orchangeveryslowly. 265 4.2. ABT-RRMACformulation 266 InlightofthepreviousconsiderationsourABT-RRMACapproachmodifiestheoriginalRound 267 Robinalgorithmformulationregardingtheevaluationofthesectortimewithoutaffectingtheplane 268 sectorizationandthusthewidthofthesectors. Basically,theideaistoassignaportionoftimeforeach 269 sectorthatisproportionaltothesizeofthequeues,thatinthiscaseisnotfixedforeachsectorandcan 270 varydynamically. 271 Figure7.AdaptiveBeamformingTimeRR-MACexample. InFigure7,anexampleoftheABT-RRMACapplicationisshown.Theplaneisnormallysectorized 272 intoequalsamplitudesectorsaswellastheRoundRobinMAC.However,inthiscase,weconsider 273 trafficpatternthatisnotuniformlydistributedamongnodes;inFig.7,itisassumedthat,twoparticular 274 sectorsdenotedS andS respectivelyhavedifferentsizeoftheframewaitingqueues;inthisregard, 275 x y thetermsize denotesthesizeofthewaitingqueuerelatedtothei-thsector. Whileconsideringthe 276 qi situationinFigure7,assumingthatT andT arethebeamforming(sector)timesrelatedtothesector 277 X Y xandyrespectively,theABT-RRMACassignsthebeamformingtimesasfollows: 278 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 9of17  T1 = ∑iN=si1zseiqz.i.e.qi ×T (cid:54)= Ts ⇒ T (cid:54)= T (cid:54)=..(cid:54)= T ⇐⇒ size (cid:54)= size (cid:54)=..(cid:54)= size  TN = ∑iNs=.i.z1.esqiNzeqi ×T 1 2 N q1 q2 qN Where: 279 T = ∑N Ti (4) N i=1 ThetermTdenotesthemeanbeamformingtimeaveragedbyallsectors.Initially,thebeamforming 280 timesarethesameforallsectorsandsettoT (RR-MAC);afteratrainingphasesetto10s(thetime 281 s of convergence of the RR-MAC), the mean beamforming time and then sector times are updated 282 periodicallyinorderthatforeachsectorisassignedaquantumoftimethatisproportionaltothesize 283 ofthequeueofthatsectormultipliedbythemeanbeamformingtime. Inthisway,sectortimescanbe 284 differentandunbalancedamongthemandthemajorfractionoftimeisassignedtothesectorhaving 285 thebiggestqueuesize. Forinstance,ifweconsidertheexampleofFigure7,becausesize >size 286 qx qy thentheABT-RRMACwillassignsectortimessuchthat T > T . Themotivationofthischoiceis 287 X Y duetofactthatsize >size theservingqueuerateofS islowerthantheservingqueuerateofS ; 288 qx qy X Y consequently,S needsforabeamformingtimehigherthanS inordertoemptyitsqueue. Among 289 X Y otherthings,thischoicewilloptimizetheenergyconsumptionofnodesinthenetwork;infact,the 290 undesiredwasteofenergycausedbytheclassicRound-Robinduetothestaticmodelislimitedbythe 291 dynamicbeamformingtimeassignment. 292 4.3. ABT-RRMACimplementation 293 The ABT-RRMAC algorithm is implemented in the Omnet++ Network Simulator in the 294 DcfUpperMACmodule,thatisthemainclassinwhichthemostimportantoperationsatMAClayerare 295 provided,suchasframeandcollisionsmanagement;therefore,asexplainedin[14]thesectorizationof 296 theplaneismanagedbytheSASantennamodule(PhasedArraymodule). Thefollowingpseudo-code 297 enhancestheoriginalRound-RobinMACformulation: 298 Algorithm1ABT-RRMACpseudo-code(part1) 1: procedureINIT(numSectors) 2: numQueues←numSectors 3: CREATEQUEUES(numQueues) 4: endprocedure 1: procedureASSIGNSECTORTIME(trainingPeriod,updatePeriod,numQueues) 2: ifSim.Time()<trainingPeriod||Sim.Time()<updatePeriodthen 3: averageSectorsTime=0; 4: fori=1;i<numQueues;i++do 5: sectorTime[i]=Ts; 6: endfor 7: else 8: averageSectorsTime=computeAverageSectorsTime() 9: fori=1;i<numQueues;i++do 10: sectorTime[i]= sizeqi ×averageSectorsTime; 11: endfor ∑iN=1sizeqi 12: endif 13: endprocedure Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 24 October 2018 doi:10.20944/preprints201810.0547.v1 Peer-reviewed version available at J. Sens. Actuator Netw. 2018, 7, 50; doi:10.3390/jsan7040050 10of17 Algorithm2ABT-RRMACpseudo-code(part2) 14: procedureSTARTTRANSMIT(frame) 15: intframeSector=getFrameSector(frame); 16: intcurrentActiveSector=getCurrentActiveSector(); 17: ifcurrentActiveSector!=frameSectorthen 18: queueSector[frameSector].insert(frame)//queuetheframe 19: else 20: transmissionQueue.insert(frame); 21: transmitFrame←queueSector[activeSector].front() 22: queueSector[activeSector].pop() 23: CONFIGUREANTENNA(activeSector) 24: endif 25: endprocedure 1: procedureSTARTRECEPTIONSTATE 2: CONFIGUREANTENNA(omnidirectional) 3: MACinreceptionMode 4: SCHEDULEEVENT(CSMATimer) 5: endprocedure 1: procedureRECEPTIONFRAME(frame) 2: orientation←GETORIENTATION(frame) 3: sector←GETSECTOR(orientation) 4: CONFIGUREANTENNA(sector) 5: endprocedure 1: procedureRECEIVEFRAMEFROMUPPERLAYERS(frame) 2: sector←GETSECTORFRAME(frame) 3: queueSector[sector].push_back(frame) 4: endprocedure 1: procedureMACPROCCESS 2: INIT(NumSectors) 3: STARTRECEPTIONSTATE 4: loop 5: WaitEvent 6: ifEventIsUpperFramethen 7: RECEIVEFRAMEFROMUPPERLAYERS(frame) 8: elseifEventIsLowerFramethen 9: RECEPTIONFRAME(frame) 10: elseifEndTransmissionthen 11: STARTRECEPTIONSTATE 12: elseifEndCSMA∧QueueSector(cid:54)=empty then 13: STARTTRANSMIT(frame) 14: else 15: STARTRECEPTIONSTATE 16: endif 17: endloop 18: endprocedure Atthebeginningoftheprocess,aftertheplaneissectorizedintoequalwidthsectors,thesame 299 quantum of time is assigned for all sectors (Round-Robin). If the trainingPeriod has elapsed the 300 averageSectorsTimedenotingthemeanbeamformingtimeaveragedbyallsectors,canbecomputed; 301 rememberthatthisparameterisupdatedperiodicallyafteranupdatePeriod(thatwesetto10s)has 302 passed;fromthefirsttimethattheaverageSectorsTimeiscomputed,thebeaformingtimesofthesectors 303 areassignedaccordingtoexpressiongivenbyEquation4. Thewholeoftheseoperationsareincluded 304 inAssignSectorTimefunction. ThetransmissionofframesisruledbyStartTransmitfunctioninwhich 305 thesystemchecksifthesectorforwhichisdestinedthecurrentframeisthecurrentactivesector. Iftrue, 306 itinsertstheframeinthetransmissionqueueandtransmittheframe,otherwisetheframeisqueuedin 307 itswaitingsectorqueue,anddelayeduntilitssectordoesnotbecomethecurrentactivesector. The 308