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University of Southern California Dissertations and Theses
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Energy latency tradeoffs for medium access and sleep scheduling in wireless sensor networks
(USC Thesis Other)
Energy latency tradeoffs for medium access and sleep scheduling in wireless sensor networks
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ENERGYLATENCYTRADEOFFSFORMEDIUMACCESSANDSLEEP SCHEDULINGINWIRELESSSENSORNETWORKS by GangLu ADissertationPresentedtothe FACULTYOFTHEGRADUATESCHOOL UNIVERSITYOFSOUTHERNCALIFORNIA InPartialFulfillmentofthe RequirementsfortheDegree DOCTOROFPHILOSOPHY (ElectricalEngineering) December2005 Copyright 2005 GangLu UMI Number: 3219822 3219822 2006 UMI Microform Copyright All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 by ProQuest Information and Learning Company. Dedication Tomydearwifeandparents, Foryourloveandsupport! ii Acknowledgements First,Iamdeeplygratefulformyadvisor,Prof. BhaskarKrishnamachari. Heismymentornotonlyin career,butalsoinlifeandpersonality. Ithankhimforhisguidanceandsupport. IwouldliketothankothermembersonmydefenseandqualifycommitteeincludingProf. Raghaven- dra,Prof. Ghandeharizadeh,Prof. HelmyandProf. Psounis,fortheirusefulfeedbackduringmyqualify examanddefense. Especially,IwouldliketothankProf. CauligiRaghavendra,underwhichIspentmy first3yearsinUSC,forhisgenerousguidanceandsupport. IhavebeenworkinginbothProf. Krishnamachari’sAutonomousNetworkResearchGroup(ANRG) and Prof. Raghavendra’s group. Both groups are excellent groups, in terms of both academic and life. I feel really lucky to be a member of the groups and would like to thank all the members in the group, includingDongjinSon,ThrasyvoulsSpyropulos(Akis),AvinashSridharn,RahulUrgaonkar,KiranYe- davli, Yang Yu, Narayanan Sadagopan, Marco Zuniga, Sundeep Pattem, Shyam Kapadia, Caimu Tang, Eric Coe. I would like to thank Yang Yu and Narayanan Sadagopan specially for the insightful discus- sionsIhavewiththem. iii TableofContents Dedication ii Acknowledgements iii ListofTables vii ListofFigures viii Abstract xi 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 SensorNetworkMACProtocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 PerformanceMetrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 EnergyLatencyTradeoffsinMediumAccessControl . . . . . . . . . . . . . . . . . . 6 1.3.1 EnergyConsumptionSources . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.2 MACEnergySavingTechniques . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.3 Energy-LatencyTradeoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 ResearchContributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4.1 Data-GatheringMAC(DMAC)inatree . . . . . . . . . . . . . . . . . . . . . 7 1.4.2 DelayEfficientSleepScheduling(DESS)inarbitrarynetwork . . . . . . . . . 8 1.4.3 MinimumLatencyJointSchedulingandRouting(MLSR) . . . . . . . . . . . 8 1.4.4 EnergyEfficientJointLinkSchedulingandPowerControl . . . . . . . . . . . 9 1.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 RelatedWorks 12 2.1 EnergyEfficientMAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.1 EnergyEfficientContention-basedMAC . . . . . . . . . . . . . . . . . . . . 12 2.1.2 EnergyEfficientScheduling-basedMAC . . . . . . . . . . . . . . . . . . . . 14 2.1.3 OtherMACprotocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.3.1 IEEE802.15.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.3.2 ARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.3.3 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 EnergyefficientJointScheduling,PowerControlandRouting . . . . . . . . . . . . . 18 3 DMAC:Tree-basedDataGatheringMAC 21 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 DataForwardingInterruptionProblem . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.3 DMACProtocolDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.1 StaggeredWakeupSchedule . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3.2 DataDeliveryandDutyCycleAdaptioninMultihopchain . . . . . . . . . . . 27 iv 3.3.3 DataPrediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.4 MTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4 PerformanceEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.1 Multihopchain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.4.2 RandomDatagatheringTree . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.3 Energy-Throughput-LatencyTradeoffs . . . . . . . . . . . . . . . . . . . . . 40 3.4.4 ExperimentalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4 DESS:DelayEfficientSleepScheduling 44 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 ProblemScenarioandAssumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.3 ProblemDefinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.3.1 AlltoAllCommunication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.3.2 WeightedCommunication . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.4.1 OptimalAssignmentonSpecificTopologies . . . . . . . . . . . . . . . . . . . 50 4.4.1.1 OptimalAssignmentonaTree . . . . . . . . . . . . . . . . . . . . 50 4.4.1.2 OptimalAssignmentonaRing . . . . . . . . . . . . . . . . . . . . 51 4.5 HeuristicApproaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.5.1 CentralizedAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.5.2 LocalizedAlgorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.5.3 Randomization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.5.4 ConcentricRingfortheGridtopology . . . . . . . . . . . . . . . . . . . . . . 61 4.6 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.6.1 GridNetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.6.2 RandomNetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5 MLSR:MinimumLatencyJointSchedulingandRouting 67 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 SchedulingandRoutinginWirelessSensorNetwork . . . . . . . . . . . . . . . . . . 68 5.2.1 ApplicationScenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2.2 RoutingandScheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.3 MinimumLatencyJointSchedulingandRouting . . . . . . . . . . . . . . . . . . . . 74 5.3.1 DelayGraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.3.2 FDMAinterferencemodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.3.3 MLSRunderTrafficchange . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3.3.1 AddingaFlow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3.3.2 RemovingaFlow . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.3.4 MLSRunderTopologychange . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.3.5 Otherissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3.5.1 Energyefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3.5.2 Distributedsolution . . . . . . . . . . . . . . . . . . . . . . . . . . 82 5.3.6 Heuristicsolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4 MLSRunderInterference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.5 NumericalResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 5.5.1 FDMAchannelModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.5.2 SingleChannelInterference . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 v 6 EEJSPC:EnergyEfficientJointSchedulingandPowerControl 90 6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 6.2 Energy,LatencyandThroughputTradeoffsinJSPC . . . . . . . . . . . . . . . . . . . 92 6.2.1 ApplicationScenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 6.2.2 InterferenceModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.2.3 PowerControl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.2.4 StateoftheArtofJointSchedulingandPowerControl . . . . . . . . . . . . . 94 6.3 TJSPC:TunableJointSchedulingandPowerControl . . . . . . . . . . . . . . . . . . 96 6.3.1 MathematicalFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.3.2 HeuristicApproaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.3.2.1 ExponentialComplexityGreedyApproximation . . . . . . . . . . . 99 6.3.2.2 PolynomialGreedyHeuristic . . . . . . . . . . . . . . . . . . . . . 101 6.4 JSPC-TR:JSPCwithTransmissionRequestConstraint . . . . . . . . . . . . . . . . . 102 6.4.1 ProblemFormulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.4.2 β ∗ -searchAlgorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 6.4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.5 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.5.1 SimulationResultsforTJSPC . . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.5.2 SimulationResultsforJSPC-TR . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7 Conclusions 112 7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.2 FutureDirections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 AppendixA WakeupRadio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 A.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 A.2 PreliminaryWakeupRadio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 A.3 PeriodicalActive/SleepWakeupRadio . . . . . . . . . . . . . . . . . . . . . . . . . . 118 A.4 UltraLowPowerWakeupRadio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 References 122 vi ListofTables 1.1 Comparisonofscheduleandcontention-basedMACprotocols . . . . . . . . . . . . . 5 1.2 ApplicationscenariosfortheDMAC,DESS,MLSRandEEJSPCstudies . . . . . . . 8 2.1 OverviewofMACprotocolsforsensornetworks . . . . . . . . . . . . . . . . . . . . 17 3.1 Radioparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 MICA2Radioparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.1 SummaryoftheNotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 A.1 ThemeasuredaveragepowerconsumptionoftheMiniBrick . . . . . . . . . . . . . . 117 A.2 TheaveragepowerconsumptionoftheLucentOrinocoWLANcard . . . . . . . . . . 118 A.3 TheaveragepowerconsumptionofCC1000inMica2 . . . . . . . . . . . . . . . . . . 118 A.4 Thewakeupradiotechnology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 vii ListofFigures 1.1 Powerspecificationofsomeradios. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Energy cost for communication and computation. The energy cost for computation is calculated by JouleTrack [90]. Communication cost is based on ORINOCO WLAN card[82]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Energy-latencytradeoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1 SMACwithadaptivelisteninginachain. . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 DMACinadatagatheringtree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 DMACinachain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4 Datapredictionschemereducessleepdelay. . . . . . . . . . . . . . . . . . . . . . . . 29 3.5 Interfencebetweentwosendingnodescausessleepdelay. . . . . . . . . . . . . . . . . 31 3.6 Meanpacketlatencyoneachhopunderlowtrafficload. . . . . . . . . . . . . . . . . . 32 3.7 Totalenergyconsumptiononeachhopunderlowtrafficload. . . . . . . . . . . . . . . 32 3.8 Meanpacketlatencyfor10hopschainunderdifferentsourcereportinterval.. . . . . . 33 3.9 Energyconsumptionfor10hopschainunderdifferentsourcereportinterval. . . . . . 34 3.10 Throughputfor10hopschainunderdifferentsourcereportinterval. . . . . . . . . . . 34 3.11 Arandomdatagatheringtree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.12 Meanpacketlatencyforadatagatheringtreeunderdifferenttrafficload. . . . . . . . . 36 3.13 Energyconsumptionforadatagatheringtreeunderdifferenttrafficload. . . . . . . . . 37 3.14 Datadeliveryratioforadatagatheringtreeunderdifferenttrafficload. . . . . . . . . . 37 3.15 Meanpacketlatencyfordatagatheringdifferentsourcenumber. . . . . . . . . . . . . 38 3.16 Energyconsumptionfordatagatheringdifferentsourcenumber. . . . . . . . . . . . . 39 3.17 Datadeliveryratiofordatagatheringwithdifferentsourcenumber. . . . . . . . . . . . 39 3.18 Tradeoffamongenergy,latencyandthroughputforadatagatheringtreeunderdifferent trafficload. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 viii 3.19 MeanpacketlatencyoneachhopunderlowtrafficloadinMoteexperiments. . . . . . 41 3.20 TotalEnergyconsumptiononeachhopunderlowtrafficloadinMoteexperiments. . . 42 4.1 Examples of slot assignment with k = 3. The dotted arrows show the delay on each linkinthecorrespondingdirection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2 Shortestdelaypathforasingleblockofmlinks. . . . . . . . . . . . . . . . . . . . . 52 4.3 Shortestdelaypathfork blocksofmlinkseach. . . . . . . . . . . . . . . . . . . . . 53 4.4 Pathsfromnode0tonodemk−m−x . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.5 Pathsfromnodem+2tonode0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.6 Shortestdelayforxblocksofm+1linkseach . . . . . . . . . . . . . . . . . . . . . 56 4.7 (a) The sequential slot assignment f obtained for a ring with n = 8 nodes and k = 4 slots(n =mk). HereD f = 6. (b). Aslotassignmentf obtainedforaringwithn = 8 nodeswithk = 6usingtheoptimalconstructionfor(n =mk+t). HereD f = 9which matchesthelowerboundinequation4.9. . . . . . . . . . . . . . . . . . . . . . . . . 58 4.8 Concentric ring allocation for a grid of 4× 4 nodes with k = 5. The dotted lines illustratetheconcentricringsateachlevel. . . . . . . . . . . . . . . . . . . . . . . . . 61 4.9 The delay diameter of the heuristic algorithms versus grid size for the number of slots fixedatk = 15. ThegridisgivenasX×X. . . . . . . . . . . . . . . . . . . . . . . 62 4.10 Thedelaydiameteroftheheuristicalgorithmsversusthenumberofslots(k)forafixed gridsizeof9×9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.11 The delay diameter oftheheuristicalgorithmsversusthenumberofslots(k)fornodes randomlydeployedina10×10area. Thetransmissionrangeis2. . . . . . . . . . . . 63 4.12 The delay diameter oftheheuristicalgorithmsversusthenumberofslots(k)fornodes randomlydeployedina3×33area. Thetransmissionrangeis2. . . . . . . . . . . . . 64 4.13 The delay diameter of the heuristic algorithms versus the radio transmission range for nodesrandomlydeployedina10×10area. Numberofslotsisfixedatk = 10. . . . . 64 4.14 The delay diameter of the Random-Min algorithm versus radio transmission range for nodes randomly deployed in a 10×10 area withN = 50 andN = 100. The number ofslotsk = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.1 Adatagatheringapplicationinawirelesssensornetwork. . . . . . . . . . . . . . . . . 68 5.2 Twoschedulingandroutingschemesinwirelesssensornetworks. . . . . . . . . . . . 70 5.3 Exampleofschedulingandroutingfortwoactiveflows. . . . . . . . . . . . . . . . . 71 ix 5.4 DelayGraph: Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5 DelayGraph: Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.6 Anexampleoffindingminimumlength2nodedisjointpaths. . . . . . . . . . . . . . 76 5.7 Anexamplenetworkwithoriginalarc-length . . . . . . . . . . . . . . . . . . . . . . 77 5.8 Anexamplenetworkafternode-splittingandlinkreverse. . . . . . . . . . . . . . . . . 78 5.9 Averagedelayunderdifferentframelength . . . . . . . . . . . . . . . . . . . . . . . 86 5.10 Averageloadperactivenodeunderdifferentframelength . . . . . . . . . . . . . . . . 86 5.11 TotalDelayofNaiveD heuristicunderdifferentflowjoinorder . . . . . . . . . . . . 87 5.12 TotaldelayofNaiveD heuristicandMLSRforflowjoinsandleaves . . . . . . . . . 87 5.13 TotaldelayofNaiveD heuristicandMLSRundertopologychange . . . . . . . . . . 88 5.14 TotaldelayofNaiveD heuristicandMLSRundertopologychange . . . . . . . . . . 88 5.15 AverageDelayunderdifferentframelengthandnumberofflows . . . . . . . . . . . . 89 6.1 Illustration of energy efficient scheduling. ~ b is the number packets need to be trans- mitted for each link. S are all possible feasible transmission scenarios. C are the total transmissionpowerofthetransmissionscenarios. . . . . . . . . . . . . . . . . . . . . 95 6.2 Anexampleoftwodifferentschedulesunderβ = 0andβ = 10. . . . . . . . . . . . . 96 6.3 Thefourcharacteristicregionsinthenumberofusedslot,energyvs. β. . . . . . . . . 102 6.4 JSPC-TRprotocoland β ∗ -searchalgorithm. . . . . . . . . . . . . . . . . . . . . . . . 106 6.5 EnergycostreducesaslatencyconstraintincreasesasafunctionofT withvaryingβ. . 107 6.6 PerformanceofMIMSR,GreedyandDiGreedyasafunctionofβ withT = 100. . . . 109 6.7 Performanceundervarioustrafficrequestload. . . . . . . . . . . . . . . . . . . . . . 110 A.1 Energyandcommunicationabilitiesofradios . . . . . . . . . . . . . . . . . . . . . . 119 A.2 Wakeupprocessintheperiodicalactive/sleepwakeupchannel . . . . . . . . . . . . . 119 x Abstract Wirelesssensornetworksareexpectedtobeusedinawiderangeofapplicationsfromenvironment monitoringtoeventdetection. Thekeychallengeistoprovideenergyefficientcommunication;however, latencyremainsanimportantconcernformanyapplicationsthatrequirefastresponse. The central thesis of this work is that energy efficient medium access and sleep scheduling mech- anisms can be designed without necessarily sacrificing application-specific latency performance . We validate this thesis through results from four case studies that cover various aspects of medium access andsleepschedulingdesigninwirelesssensornetworks. Ourfirsteffort,DMAC,istodesignanadaptivelowlatencyandenergyefficientMACfordatagath- eringtoreducethesleeplatency. Weproposestaggeredschedule,dutycycleadaptation,dataprediction andtheuseofmore-to-sendpacketstoenableseamlesspacketforwardingundervaryingtrafficloadand channel contentions. Simulation and experimental results show significant energy savings and latency reductionwhileensuringhighdatareliability. Thesecondresearcheffort,DESS,investigatestheproblemofdesigningsleepschedulesinarbitrary networkcommunicationtopologiestominimizetheworstcaseend-to-endlatency(referredtoasdelay diameter). We develop a novel graph-theoretical formulation, derive and analyze optimal solutions for thetreeandringtopologiesandheuristicsforarbitrarytopologies. Thethirdstudyaddressestheproblemofminimumlatencyjointschedulingandrouting(MLSR).By constructing a novel delay graph, the optimal joint scheduling and routing can be solved by M node- disjoint paths algorithm under multiple channel model. We further extended the algorithm to handle dynamictrafficchangesandtopologychanges. AheuristicsolutionisproposedforMLSRundersingle channelinterference. In the fourth study, EEJSPC, we first formulate a fundamental optimization problem that provides tunable energy-latency-throughput tradeoffs with joint scheduling and power control and present both exponential and polynomial complexity solutions. Then we investigate the problem of minimizing xi totaltransmissionenergywhilesatisfyingtransmissionrequestswithinalatencybound,andpresentan iterativeapproachwhichconvergesrapidlytotheoptimalparametersettings. xii Chapter1 Introduction 1.1 Overview Awirelesssensornetworkisadistributedsensingnetworkcomprisedofthousands,oreventensofthou- sandssmalldevicesthatsense,collectanddisseminateinformationabouttheenvironment[1,104,103]. With each node equipped with radios of wireless communication capability and sensors that can sense certain physical phenomena such as acoustics, light, temperature, humidity and vibrations, wireless sensor networks (WSN) enable a wide range of applications, such as target tracking [72], habitat sensing [106, 105] and fire detection. The capability of sensor nodes [35, 71, 72] are very differ- ent from traditional nodes in computer networks. These devices have very limited energy, processing power, storage, communication range and rate. For example, in a Mote [35], the processor is Atmega 128L [2], a low-power micro-controller; its memory is less than 1MB. The radio used in MICA2 Mote isCC1000[3],withradiorateofonly38.4Kbaudandrangelessthan500feetrange. Wireless sensor networks require a new set of protocol stacks because of new features of wireless sensor networks [1, 104, 103]. First, most nodes in sensor networks are likely to be battery powered and it is not feasible to recharge or replace the batteries. Second, sensor networks are in large scale with hundreds or even thousands nodes randomly deployed in an ad hoc fashion with little human management[83, 87]. Third, thetraffic patterninsensor networksvaries with differentsensor network applications. Majortrafficcouldbein-networklocalcommunicationorfromsensorstoacommonsink inatreetopology[96,92]. Therearemanyresearchchallengesforthedevelopmentofawirelesssensornetwork. First,Energy efficiencyisacriticaldesignissueinwirelesssensornetworksinordertoprolongthenetworklifetime. Measurements show that wireless radio consumes a significant amount of energy [4, 5]. Hence energy efficient communication protocols are required for the success of wireless sensor network technology. 1 Figure1.1: Powerspecificationofsomeradios. Figure 1.2: Energy cost for communication and computation. The energy cost for computation is cal- culatedbyJouleTrack[90]. CommunicationcostisbasedonORINOCOWLANcard[82]. Latency remains an important concern for many event-driven applications such as fire detection, en- vironment surveillance. Depending on application scenarios, packets may be required to be delivered eitherassoonaspossible,orwithinapredefinedlatencybound. Asthebasiccommunicationbuildingblock,mediumaccessandsleepschedulingprotocolsarecru- cialindecidingtheenergyandlatencyperformanceofthenetwork. PreviousworksonMACprotocols in this domain generally either provide energy efficiency at the cost of high latency or provide low la- tency at the cost of energy. These observations motivate us to analyze the inherent tradeoff and design energy efficient and low latency medium access and sleep scheduling algorithms suitable for sensor networks. 2 1.2 SensorNetworkMACProtocol 1.2.1 PerformanceMetrics Typically in WSNs, nodes coordinate locally to perform data processing and deliver messages to a commonsink. ThedesireddesignfeaturesformediumaccesscontrolprotocolsinaWSNare: 1. Self-organization: Inmanyenvisionedscenarios,thesensordeploymentdistributionwillbevery dense, in order to provide higher accuracy and fine-grained information about the environment andalsobecausealargeraggregateamountofenergyisavailableinadensedeployment. Because of the environment and large scale of nodes, the nodes are usually randomly deployed and there can be little human management. Thus the MAC protocol must be able to self-organize the communicationinfrastructurefordatatransfer. 2. Energy efficiency: Sensor nodes operate on battery and it is often not feasible to replace or recharge batteries for sensor nodes. Energy efficiency is a critical issue in order to prolong net- work lifetime. Measurements show that wireless radio consumes a significant amount of en- ergy [4, 5]. Figure 1.1 shows the power specification of some current radios. Figure 1.2 shows thatthecommunicationenergycostcanbemuchhigherthancomputationenergycost. Inpartic- ular,MACprotocolsmustminimizetheradioenergycostsinsensornodes. 3. Lowlatency: Latencyrequirementsdependontheapplication. Intargettrackingapplications[72], aneventdetectedneedstobereportedtoasinkinrealtimesothatappropriateactioncanbetaken promptly. In other applications, sensor nodes can store data in the network waiting for sink to queryandlatencyisnotanissue. 4. High throughput: Throughput requirements vary with different applications too. Some appli- cations need to sample the environment with fine temporal resolution. In such applications, the more data the sink receives the better. In other applications, such as fire detection, it may suffice for a single report to arrive at the sink. Typically in sensor network applications such as fire de- tection, traffic may be light most of the time; when the environment changes abruptly due to a significant event (fire detected), for a short period the traffic may be very intense [1, 11]. MAC protocolsshouldbeabletohandlebothcasesefficientlywithhighdeliveryratio. 5. Fairness: Fairness requirements depends on the application too. In many applications, particu- larly when bandwidth is scarce, it is important to ensure that the sink receives information from 3 all sources in a fair manner [79]. In other applications, per-node MAC level fairness is not im- portant as long as application-level performance is not degraded [60]. For example, the sink can onlyprocessdataafterreceivingallpacketsfromtwosensors,whichcanletonenodesendallof itspacketsfirst,thenletthesecondnodetransmit. Theperformanceinapplicationlevelissame. 6. Reliability and Robustness: Because of the harsh channel quality, frequent nodes failures and dynamic topology changes, the MAC protocols must be robust and reliable to enable efficient communication. 7. Scalability MAC protocols must be able to handle large networks with dynamic changes since wirelesssensornetworkscanhavehundredsoreventhousandsofnodes[1]. Among these important requirements for MACs, energy efficiency is typically the primary goal in WSN.ItisoftendifficulttoachievegoodperformanceonalltheabovefeaturesforaMACprotocol. It is important to trade off secondary requirements to the most important factors when designing a MAC protocolforaspecificsensornetworkapplication. 1.2.2 Taxonomy Generally there are two kinds of MAC protocols in wireless sensor networks: contention-based and schedule-based MAC. The typical contention-based MAC is the standardized IEEE 802.11 distributed coordination function [78]. It is very successful in current wireless LAN market because of its sim- plicity and robustness. However it is not energy efficient because the nodes spend a lot of time in idle listening mode, which consumes similar energy as the receiving mode [4, 5]. There are two important components in contention-based MAC: the listening mechanism and the backoff scheme [79]. The lis- tening time can be random or constant. There are four choices for backoff mechanism: no backoff, fixed window, exponential increase and exponential decrease. Simulation results in [79] show that the constant listening periods are energy-efficient. However, the traffic in sensor network can be highly synchronized, so a random delay is introduced before transmission to make it robust against repeated collisions. A contention-based MAC protocol has to monitor the channel activity before transmission. If the channel is busy, the sender has to back off a random period. In the backoff period, the node also monitorsthechanneltodecidewhetheritcandecreasethebackofftimer. Sothenodeisinidlelistening modewhichconsumeenergy. Contentionandcollisioncouldresultwastedpackettransmissionswhich are waste of energy. There are also overheads due to control packets to reduce contention. To save energy, the key idea is to turn off the radio when a node does not participate in data communication. 4 Table1.1: Comparisonofscheduleandcontention-basedMACprotocols MAC Self- organization Energy Latency Throughput Schedule- based poor good poor medium Contention- based good poor medium medium MAC Fairness Robust Scalability Schedule- based good poor poor Contention- based medium good good The advantage of contention-based MAC is its simplicity and robust which is very useful in wireless sensornetworks. Schedule-based MAC protocols rely on channel reservation. A typical schedule-based MAC is TDMA[10,67,93]. Itisstraightforwardtoemployenergyefficienttechniquesinschedule-basedMAC since a node can turn on its radio only in its reserved time slot and turn off radio in other slots. There is also no overhead due to contention and collision. However, schedule-based MAC protocols need synchronizationwhichmayposesignificantoverhead. Schedule-basedMACismorecomplicatedthan contention-based MAC, and is worse in terms of self-organization. When there is change in network topology, the schedule has to been adjusted which results in poor scalability and less robustness. An- other disadvantage of schedule-based MAC is its possible low channel utilization. A node is fixed to communicate in its reserved slot which means a node has only limited channel capacity while another node may waste its reserved slot when it has nothing to send/receive. This will also result in low throughputandhighlatency. Becausecontention-basedandschedule-basedMACbothhaveadvantagesanddisadvantages,there areeffortstocombinethemtogether,suchasMACinIEEE802.15.4. InIEEE802.15.4,asuperframeis dividedintoaContentionAccessPeriod(CAP)andaContentionFreePeriod(CFP).Anodecandecide touseeitherCAPorCFPbasedontherequirementofitsdatacommunication. Detailwillbediscussed innextsection. Table1.1summarizesthecomparisonofscheduleandcontention-basedMACusingtheperformance metrics. 5 1.3 EnergyLatencyTradeoffsinMediumAccessControl 1.3.1 EnergyConsumptionSources Wefirstidentifythefollowingmajorsourcesofenergywaste. 1. Collision: when a transmitted packet is corrupted it has to be discarded, and the follow-on re- transmissionsincreaseenergyconsumption. Collisionincreaseslatencyaswell. 2. Overhearing: whenanodereceivespacketsthataredestinedtoothernodes. 3. Control packet overhead: sending and receiving control packets consumes energy too, and less usefuldatapacketscanbetransmitted. 4. Idlelistening: listeningtoreceivepossibletrafficthatisnotsent. Thisisespeciallyofconcernin many sensor network applications. If nothing is sensed, nodes are in idle mode for most of the time. However,inmanyMACprotocolssuchasIEEE802.11orCDMAnodesmustlistentothe channel to receive possible traffic. Many measurements have shown that idle listening consumes 50%to100%oftheenergyrequiredforreceiving[4,5]. Forexample,StemmandKatzmeasured that the idle:receive:send ratios are 1:1.05:1.4, while the Digitan 2 Mbps Wireless LAN module (IEEE802.11/2Mbps)specificationshowsidle:receive:sendratiosis1:2:2.5[5]. 5. Transmissionpower: SomeradioshavefixedtransmissionpowerorMACprotocolsdonotutilize themultipletransmissionpowers. Whentwonodesarenearby,thenecessarytransmissionpower may be much smaller than the maximal transmission power of the radio. If the radio only uses themaximalpowertotransmit,itisasignificantenergywastage. 1.3.2 MACEnergySavingTechniques Corresponding to the source of energy wastage, there are several energy saving techniques in MAC layer: 1. Low duty cycle: In order to reduce the energy wastage due to idle listening, a node turns on its radioperiodicallytoseeifthereiscommunicationrequest,andgoesbacktosleepafterwards. 2. TDMA link scheduling: In TDMA link scheduling, a node can turn on its radio only in its reserved time slot and turn off radio in other slots. There is also no overhead due to contention andcollision. 6 3. Powercontrol: Anodecouldhavedifferentdistancetoitsneighbornodes. Itisnotnecessaryto alwaysusethemaximumtransmissionpowertoreachthenearbynodes,aslongastheSINRre- quirementissatisfiedatthereceivernode. Manyexistingradioscansupportmultipletransmission power. For example, CC1000 used in MICA2 motes can support 31 different transmission pow- ers. Power control techniques have been widely used in topology control in wireless networks. Recentlythereareworksonjointlyschedulingandpowercontroltosaveenergy. 1.3.3 Energy-LatencyTradeoffs Previous works (in particular [60], [26], [62],[28], [63], [33], [66]) have identified idle listening as a majorsource ofenergy wastage. To designan energyefficient MAC,it isessential toturn theradio off when a node does not participate in any data delivery. However, a node that is sleeping is no longer partofthenetwork,andthuscannothelptodeliverthesensordatafromitsneighborstoitsdestination. When a node has a packet for its neighbor which is in asleep, it has to wait until its neighbor is active. Thiscreatesafundamentaltrade-offbetweenenergyandlatency. 1.4 ResearchContributions Contention-based MAC protocols are particularly suitable for applications where the traffic load is un- predictable or varying rapidly, because of their low overhead requirements and flexibility. The SMAC protocol[60]proposedalowdutycycleschemewhichputstheradiotosleepperiodically(sleepsched- ule) to save energy. However, this approach increases the packet delivery latency significantly due to synchronized duty cycles for all nodes. In the first two studies, DMAC and DESS, we investigate how to minimize latency in such sleep scheduled contention-based MAC protocols without increasing the energycost. 1.4.1 Data-GatheringMAC(DMAC)inatree DMAC is an adaptive low latency and energy efficient MAC for data gathering in wireless sensor net- works[46,47]. Inthisstudy,wefirstshowthe Data Forwarding Interruption Probleminsynchronized sleep schedule protocols, whereby not all nodes on a multihop path are notified of data delivery in progress,resultinginsignificantsleepdelay. Thenweproposeastaggeredschedulefortree-baseddata gathering to solve the interruption problem by giving the sleep schedule of a node an offset that de- pendsuponitsdepthonthetree. DMACalsoadjuststhedutycyclesadaptivelytokeepthelatencylow 7 Table1.2: ApplicationscenariosfortheDMAC,DESS,MLSRandEEJSPCstudies Study DMAC DESS MLSR EEJSPC AccessMethod Contention- based Contention- based Contention-free Contention-free Traffic Unpredictable Lighttraffic Predictable, Longlived Predictable, low dynamics Topology Data gathering tree Any to any communication multiple sinks Datagathering Arbitrary topol- ogy Energy Effi- ciency By sleep scheduling By sleep scheduling By sleep scheduling Besides sleep, by power control Source of La- tency sleepschedule sleepschedule sleepschedule linkschedule Latency objec- tive Minimizing average latency (besteffort) Minimizing la- tencydiameter Minimizing av- eragelatency Maintaining per hop latency bound evenundervaryingtrafficloadconditions. Wefurtherproposeadatapredictionmechanismandtheuse of more-to-send packets in order to alleviate problems pertaining to channel contention and collisions. Simulation and experimental results show that DMAC provides significant energy savings and latency reductionwhileensuringhighdatareliability. 1.4.2 DelayEfficientSleepScheduling(DESS)inarbitrarynetwork In the second study, called DESS, we take an algorithmic approach and study a more general ver- sion of the problem: how should the sleep schedule be designed in arbitrary network communication topologies, in order to minimize the worst case end-to-end latency while providing energy efficiency through periodic sleep? We develop a novel graph-theoretical formulation of the problem and prove thatminimizingtheworst-caseend-to-endcommunicationlatency(referredtoasthedelaydiameter)is in general NP-hard. However, we are able to derive and analyze optimal solutions for the tree and ring topologies. Several heuristics for arbitrary topologies are also proposed and evaluated by simulations. Our simulations suggest that distributed heuristics may perform poorly because of the global nature of theconstraintsinvolved. 1.4.3 MinimumLatencyJointSchedulingandRouting(MLSR) Inthethirdstudyweaddresstheimportantproblemofminimizingcommunicationlatencywhileprovid- ingenergy-efficiencyfornodesinwirelesssensornetworks. DifferentfromDESS,wheretheobjective istominimizetheworstcaselatencygiventhefixeddutycyclingrequirementforeachsensor,inMLSR the interest is in the average latency for only the current active flows. As the flows in some wireless 8 sensor network can be long-lived and predictable, it is possible to design schedules for sensor nodes so that nodes can wake up only when it is necessary and asleep during other times. The routing layer decisionisalsoclosedcoupledtothewakeup/sleepscheduleofthesensornodes. Weformulatedajoint scheduling and routing problem with the objective of finding the schedule and route for current active flows with minimum average latency. By constructing a novel delay graph, the problem can be solved optimallybyusingaM node-disjointpathsalgorithmunderaFDMAchannelmodel. Wefurtherextend thealgorithmtohandledynamictrafficchangesandtopologychangesinwirelesssensornetworks. We also propose a heuristic solution for the minimum latency joint scheduling and routing problem under singlechannelinterference. 1.4.4 EnergyEfficientJointLinkSchedulingandPowerControl TDMA-based contention-free medium access protocols [6, 7, 8, 12, 9, 10, 13] can be more energy efficient than random access, particularly when traffic is predictable or slowly changing. In most prior studies of TDMA-scheduling, typically a simple model for interference is used where a receiving node sees interference from another transmitter if and only if it is within some nominal range R I . This model, while useful in providing a simple graph-coloring approach to TDMA scheduling, can be quite misleading in practice for two reasons. First, simultaneous wireless transmissions within the nominal rangedonotnecessarilycollideifthesignaltointerferenceplusnoiseratios(SINR)atthecorresponding receivers are sufficiently high. Second, aggregate interference from multiple out-of-range transmitters can be high enough to cause collisions. Another concern with many studies of TDMA in wireless ad hoc and sensor networks is that they ignore the possibility of variable transmission power. In practical systems this can be an important tunable parameter for reliable and energy-efficient communication, becausehighertransmitpowerscanincreasetheSINRatthereceivertoenablesuccessfulreceptionon alink,andlowertransmissionpowercanmitigateinterferencetoothersimultaneouslyutilizedlinks. In the third study, TJSPC [50], we study the problem of TDMA link scheduling using a realistic SINR- basedinterferencemodel,explicitlytakingtransmissionpowercontrolintoaccount. In the fourth study, we investigate the problem of energy efficiency in TDMA link scheduling with transmission power control using a realistic SINR-based interference model, given packets of a set of links to be transmitted within a latency bound. First, we formulate a fundamental optimization problem (TJSPC) that provides tunable tradeoffs between energy, throughput and latency through a single parameterβ. We present both exponential and polynomial complexity solutions to this problem andevaluatetheirperformance. Ourresultsshowthatformoderatetrafficloads,withappropriatetuning 9 Figure1.3: Energy-latencytradeoffs of parameters, major energy savings can be obtained without significantly sacrificing throughput. We then investigate the scheduling and power control problem with the objective of minimizing the total transmissionenergycostundertheconstraintthatalltransmissionrequestsaresatisfied(JSPC-TR).We present an iterative approach to solve JSPC-TR that leverages the heuristics for TJSPC and converges rapidlytothesettingofβ whichachievesenergyefficiencywhileguaranteeingdatadelivery. 1.4.5 Summary Table 1.2 shows the different application scenarios of DMAC, DESS, MLSR and EEJSPC, the four schemes we presented in this thesis, allowing for a high-level comparison between these studies. Both DMACandDESSarestudiespertainingtocontention-basedMACprotocolswhileMLSRandEEJSPC are contention-free schedule-based MAC. DMAC assumes a data gathering tree topology with unpre- dictable or fast changing traffic load. DESS, however, assumes a light traffic load with an arbitrary any-to-any communication model. MLSR assumes predictable long-lived traffic load in multiple-sinks datagatheringscenario. InEEJSPC,althoughcommunicationcanonanyarbitrarytopology,thetraffic load is expected to be more predictable. DMAC, DESS and MLSR provide energy efficiency only by putting nodes into sleep. In EEJSPC, besides the energy saving by sleeping during inactive slots, the focus is reduction of energy during packet transmissions in the active slots through the power control algorithm. The latency in DMAC, DESS and MLSR is due to the sleep schedule while in EEJSPC the latency is caused by the TDMA-link schedule. In DMAC, MLSR and DESS, the goal is to minimize the latency while keeping energy efficiency at a predetermined level. In EEJSPC, however, the goal is tominimizetheenergycostsubjecttoalatencyboundconstraint. 10 Figure1.3isanillustrationplacingthecontributionsofDMAC,DESS,MLSRandEEJSPCincon- text. It shows different operating points on an energy-versus-latency graph. Previous works generally eitheroperateatpointA,whichrepresentsareductionoflatencybysacrificingenergy(e.g. priorworks on joint link scheduling and power control), or at point B, which sacrifices latency to reduce energy (e.g. prior works on sleep scheduled MAC protocols). Our goal in this thesis is to show that MAC protocols can be carefully designed in many situations to operate at point C, which provides energy efficiency without necessarily suffering high latency – DMAC, DESS, MLSR and EEJSPC exemplify suchanoperatingpoint. 11 Chapter2 RelatedWorks AlotofMACprotocolsandschedulingalgorithmshavebeenproposedinthelastfewyearsforwireless sensornetworkswithdifferentsensornetworkapplicationassumptions. Thischapterprovidesasurvey ofthecurrentstateoftheartofMACprotocolswithanemphasisonenergyefficiency. Wealsoclassify and compare different schemes with several performance metrics. Then we briefly describe the works thatarecloselyrelatedtothisthesis. 2.1 EnergyEfficientMAC 2.1.1 EnergyEfficientContention-basedMAC PAMAS [33] is one of the earliest contention-based energy efficient MAC protocols. The goal of PA- MASistoreducetheenergycostinoverhearingamongneighboringnodes. Whenadatatransmissionis inprocessbetweentwonodes,allnearbynodesoverhearthepacketandcannotsendorreceive. Energy savingcanbeachievedtoputthosenearbynodestosleep. PAMASprotocolisbasedonMACAproto- col and modified to provide separate channels for RTS/CTS control packets and data packets. Channel monitoringisonthecontrolchannel. Thebasictechniqueisthatthereceivingnodetransmitabusytone overthecontrolchanneltoindicatethatthedatachannelisbusy. Theuseofaseparatecontrolchannel allows a node to determine when and for how long to power off the radio through the use of a probe protocol. Theoreticalanalysisisalsopresentedin[33]. Simulationresultsshowthat10%to70%power savingscanbeachievedforfullyconnectedtopologies. SMAC[60]triestoreduceallfourenergywastewiththreetechniques: periodiclisteningandsleep, collisionandoverhearingavoidanceandmessagepassing. Byperiodiclisteningandsleep,S-MAC[60] reduces the duty cycle of a sensor node by operate nodes in a periodic active/sleep schedule. During 12 sleep periods, nodes turn off radio completely to conserve energy. During active periods, nodes turn on radio to Tx/Rx messages. This will reduce channel capacity, however low traffic load is expected during most of the sensor network lifetime. So by default, nodes operate on low-duty-cycle mode to save energy. This, however, sacrifices latency. SMAC further argues that in sensor network, per-hop MAC level fairness is not an important issue since all nodes cooperates for a single common task. By trading off per-node fairness to efficiently transmit long messages, SMAC divides long message into several small fragments and transmit them in a burst. Only one pair of RTS/CTS is used to reserve the mediumfortransmittingallsmallfragments. Fragmentsareretransmittedseparatelyincaseofbiterror. By message passing, control overhead is reduced and the high cost of retransmitting a long packet is avoided. SimilartoPAMAS,SMACavoidsoverhearingbyputtingallimmediateneighborsofboththe senderandthereceivertosleepaftertheyhearanRTSorCTSpacket. NAVismaintainedateachnode toindicatetheactivityinitsneighborhood. AnodeshouldsleepuntilitsNAViszero. Although a low duty cycle MAC is energy efficient, it has three side-effects. First, it increases the packet delivery latency. An intermediate node may have to wait until the receiver wakes up before it can forward a packet. This is called sleep latency in SMAC [60], which increases proportionally with hop length by a slope of schedule length (active period plus sleep period). Second, a fixed duty cycle does not adapt to the traffic variation in sensor network. A fixed duty cycle for the highest traffic load resultsinsignificantenergywastagewhentrafficislowwhileadutycycleforlowtrafficloadresultsin low message delivery and long queuing delay. Third, a fixed synchronous duty cycle may increase the possibility of collision. If neighboring nodes turn to active state at the same time, all may contend for thechannel,makingacollisionverylikely. TosolvethefixeddutycycleprobleminSMAC,TMAC[26]proposesschemestoadjustdutycycle according to current traffic load. The basic idea of TMAC is that a node will keep active until no activation event hasoccurredforatime TA.Anactivationeventincludes: thefiringofaperiodicframe timer,thereceptionofanydataontheradio,thesensingofcommunicationontheradio,etc[26]. Anode will sleep if its not in an active period. The novel idea of TMAC is to transmit all messages in a burst intheactiveperiodsothatidlelisteningisreduced. TheauthorsofTMACidentifiedtheearlysleeping problem,inwhichanodegoestosleepwhenaneighborstillhasmessageforit. TMACemploysFRTS tosolvetheproblem. AnodeoverhearingaCTSpacketdestinedforanothernodesendsaFRTSpacket immediately. AnodethatreceivesanFRTSpacketwillwakeupafterthedurationinformationinFRTS and be ready to receive packets. Another solution proposed by TMAC is named “Taking priority on full buffers”. When a node’s transmit/routing buffers are almost full, it prefers sending to receiving by 13 immediatelysendsitsownRTSpackettoanothernode,insteadofreplyingwithaCTS.Theprobability ofearlysleepingproblemoccursisreduced. In scenarios where minimizing sleep latency is not important (non time critical applications), [36] presents an analysis on bounds on the delay of sending data from a node to a sink using a completely decentralizeddutycyclingscheme. Theauthorsshowthatifeachsensorturnsonandoffindependentof theothersensors,thedelayincurredisproportionaltothedistanceofthenodefromthesink. However the rate of this linear increase is not dependent on the locations of the nodes, but on the node density, transmissionrangeandtheaverageactiveandsleepdurations. The question arises whether energy-efficient duty cycling may be maintained while reducing sleep latency. One approach to this is the use of adaptive listening where nodes that lie one or more steps ahead in the path of a transmission can be kept awake for an additional length of time (present as an extension to the basic S-MAC in [24], as well as the T-MAC protocol [26]). This approach provides somereductioninsleeplatencyattheexpenseofgreaterenergyexpenseduetoextendedactivationand overhearing,butisnotsufficientforlongpaths. 2.1.2 EnergyEfficientScheduling-basedMAC TRAMA is a schedule-based protocol to provide energy efficient collision free MAC for sensor net- works. TRAMA divides time into slots and uses a distributed election scheme based on traffic infor- mation at each node to select the transmitter at each time slot. TRAMA reduces energy consumption byreducingcollisioncausedretransmissionsandbyputtingnodestosleepwhenevertheydonottrans- mit or receive. To solve the wasted slots problem of traditional TDMA-based MAC, TRAMA allows time slots to be reused by other nodes when the original owner nodes have no traffic to send. Time is organizedassignalslots(random-access)andtransmissionslot(scheduledaccess). TRAMAconsistsofthreecomponents: NeighborProtocol(NP),ScheduleExchangeProtocol(SEP) and Adaptive Election Algorithm. NP collects neighbor information by exchanging small signaling packets during signaling slots. Each node periodically sends ”keep-alive” beacons which contains in- cremental updates about its one-hop neighborhood. A node can then construct the topology of its two-hopneighborsbasedonthereceivedbeacons. SEPestablishesandmaintainstraffic-basedschedule information. A node can compute the number of slots in which it has the highest priority among its two hop neighbors. The node then need to announce the intended receiver for these slots, and gives up a slot if it does not have enough packets to send. The schedule is announced via schedule packet in a bitmap structure with each bit corresponds to one particular receiver ordered by their identifiers. The 14 Adaptive Election Algorithm uses a pseudo-random hash of the concatenation of node’s identity and timeslotnumbertocalculateitspriority. Thenodewiththehighestpriorityinatimeslotinthetwo-hop neighborhood is selected as the sender of the slot. However, if the selected node does not have any packetstosend,itcangiveuptheslotwhichcouldthenbeusedbyanothernode. EachnodewithAEA can decide its current state (transmit, receive or sleep) based on priorities from two-hop neighborhood andtheschedulesfromone-hopneighbor. 2.1.3 OtherMACprotocols 2.1.3.1 IEEE802.15.4 IEEE802.15.4isanewstandardtoaddresstheneedforlow-ratelow-powerlow-costwirelessnetwork- ing. The MAC protocol in IEEE 802.15.4 can operate on both beacon enabled and non-beacon modes. In the beaconless mode, the protocol is essentially a simple CSMA-CA protocol. In beacon mode, the IEEE 802.15.4 uses a superframe structure. A superframe begins with beacon frames sent periodically bythecoordinatoratanintervalthatcanrangesfrom15msto245s. Therearebothactiveandinactive portion in the superframe. Devices communicate with theirs PANs only during the active period and enter a low power mode during the inactive period. The active portion of each superframe is further divided into 16 equal time slots and consists of three parts: the beacon, a Contention Access Period (CAP)andaCollisionFreePeriod(CFP). ThechannelaccessinthetimeslotsinCAPiscontention-basedCSMA-CA.InCSMA-CA,alotof energyisgenerallyconsumedbythelongbackoffperiodwhichisrequiredduringhightrafficperiodsto avoidcollision. IEEE802.15.4supportsaBatteryLifeExtension(BLE)mode,inwhichtheCSMA-CA backoff exponent is limited to the range 0-2. This reduces the period of idle listening in low offered traffic applications. A network device can put its radio to sleep to conserve energy immediately after thereceptionofacknowledgementpacketifthereisnomoredatatobesentorreceived. TheIEEE802.15.4standardallowstheoptionaluseofCFPfordevicesthatrequirededicatedband- width to achieve low latencies. A device requiring dedicated bandwidth or low-latency transmission canbeassigneda Guaranteed Time Slots(GTS)inCFPbythePANcoordinator. EachGTSconsistsof someintegermultipleofCFPslotsandupto7GTSallowedinCFP.Whenadevicewishestotransmit aframeusingGTS,itfirstchecksalistonthebeaconframetoseewhetherithasbeenallocatedavalid GTS. If a valid GTS is found, the device enables its receiver at a time prior to the start of the GTS and transmitsthedataduringtheGTSperiod. TheMACofthePANcoordinatorensuresthatitsreceiveris enabledforallallocatedGTStimeslots. 15 With both CAP and CFP, IEEE 802.15.4 provides a flexible choice to accommodate the needs of differentapplicationsandnetworktopologies. 2.1.3.2 ARC Inmanysensornetworkapplications,fairnesscouldbeahighlydesirablemetric. Forexample,togeta whole picture of microorganism environment, roughly the same amount of data from all sensors in the environment is necessary. The authors of [79] proposed an adaptive transmission rate control (ARC) scheme to fairly distribute channel bandwidth between the originating and route-through traffic in the multihoparchitectureofsensornetworks. The successful injection of a originating packet indicates that there is still capacity available, so the node can increase its data rate. If the injection is failed, it indicates the channel is jammed so the nodedecreasesitsdatarate. Similarschemeisusedforroute-throughtraffic. Thefailtransmissionofa route-throughpacketwillcausetheupstreamnodetodecreaseitsdatarate. Thisimplicitsignaling can bepropagatedallthewaybacktothesourcenodetodecreasetheamountofroute-throughtraffic. ARC uses a linear increase and multiplicative decrease approach to adjust the data injection rate of both the originating and route-through traffic. The cost of dropping route-through traffic is higher thanoriginatingtraffic,soroute-throughtrafficisgivenpreferencebyhaving50%lessdecreasingrate. Simulationsin[79]showthatARCachievesfairnesswhilestillmaintaininggoodaggregatebandwidth energyefficiently. The author also investigate the listening and backoff mechanisms in the CSMA-based MAC. It is recommended that a fixed listening period and exponential decrease backoff period be used to save energy. In the backoff period, a node can be put to sleep instead of idle listening to further conserve energy. 2.1.3.3 Others The SMACS protocol [77], a schedule-based MAC, achieves network startup and link-layer organiza- tion, and the EAR algorithm enables seamless connection of nodes in a sensor network. The neighbor discovery and channel assignment phases are combined to reduce the network setup latency. Net- work wide synchronization is not needed but communicating neighbors in a subset need to be time- synchronized. SMACS achieves power saving by a random wakeup schedule during the connection phase and by turning the radio off during idle time slots. The authors of [76] proposed a hybrid TDMA/FDMA based centrally controlled MAC scheme. An analytical model is derived to find the 16 Table2.1: OverviewofMACprotocolsforsensornetworks Protocols ChannelAccess Energysavingtechniques Specificfeatures PAMAS Contention Overhearingavoidance Turning off radio of nodes nearbythesenderandreceiver SMAC Contention Low duty cycle, overhearing avoidance,messagepassing Tradeofflatencyandfairness TMAC Contention Lowdutycycle Adjustdutycycle IEEE802.15.4 Contention & schedule Lowdutycycle Both contention and contention- freeaccess NAMA Schedule None Distributedelectionalgorithm TRAMA Schedule Turnoffradioinidlestate Avoidwastetimeslots ARC Contention Fixedlisteningperiod Adaptive rate control to achieve fairness SMACS,EAR Schedule Random wakeup and turning ra- diooffwhenidle Large available bandwidth com- paredtosensordatarate Hybrid TDMA/FDMA Centralized schedule Hardwarebasedapproach Analysis to find optimal number ofchannels Multi-channel MAC Schedule Turnoffradiowhenidle Multi-channelassignment,sepa- ratelowpowerwakeupradio DMAC Contention Lowdutycycle Specific for data gathering tree, Dutycycleadaptation optimumnumberofchannelswhichismostenergyefficient. TDMAschemeisfavoredwhenthetrans- mitting power is larger while FDMA scheme is favored when receiving power is larger. The Node Activation Multiple Access [74] uses a distributed election algorithm to select only one transmitter per two-hopneighborhoodtoensurecollision-freereceptionsforallnodesintheone-hopneighborhoodof the transmitter. However, NAMA does not consider energy savings. The authors of [75] proposed a multi-channel MAC, in which each node records the channel used by its one-hop and two-hop neigh- bors,andmakesureitsownchannelisdifferentfromallitstwo-hopneighbors. Nodescanturnofftheir dataradiostosaveenergyandaseparatealwaysonradioisusedtowakeupnodesthathaveturnedoff theirmaindataradio. Thewakeupradioconsumesmuchlowerpowerthanradiosusedforregulardata communications. 2.1.4 Discussion To have a better understanding of current MAC protocols for sensor networks, we summarize the key features in Table 1. The energy saving techniques show the schemes used in each of these MAC to conserves energy. The specific features shows the novel and important features in each of these MAC protocols. From the table we can see that the key scheme to be energy efficient is to turn off radio to reduce idle listening. However, this trade off throughput, latency and fairness. Schedule-based MAC is more 17 energy efficient in nature than contention-based MAC, however with high overhead, thus is worse in termsofself-organizationandrobustness. Comparedtotraditionalcomputernetworks,sensornetworks applicationshaveverydifferentrequirementsonnetworktopology,trafficpattern,etc. ThusMACpro- tocols often have very different, sometimes contradictory assumptions. For example, SMAC trades off fairnesswhile[79]choosesfairnessasthemajorgoal. LowdutycycleMACprotocolsincreaselatency significantly to save energy, however, latency may be a very important metric in target tracking appli- cations. In terms of traffic pattern, some environment monitoring application need all sensors to report their samples back to the sink while in a fire detection application, traffic are mostly local to enable in-network processing and only one result is required to transmit back to the sink. Thus, we expect thatthereisnotageneralMACprotocolssuitableforallsensornetworkapplicationsandspecificMAC protocolsforaspecificapplicationcanbesimplewhilehavebetterperformanceinspecificmetrics. Previous sensor network MAC protocols tradeoff other performances, specifically the latency for energy savings. In this thesis, we are interested in designing energy saving MAC without sacrificing latency. InDMACandDESS,themediumaccessiscontention-based, thereforeweuselowdutycycle astheenergysavingtechnique. DMACprovidesbesteffortminimumaveragelatencyfordatagathering applicationwhileDESSworkstominimizetheworstcaselatencyforarbitrarynetworktopology. 2.2 EnergyefficientJointScheduling,PowerControlandRouting Scheduling is another effective approach to save energy. Other energy saving techniques at different layers,suchaspowercontrolinphysicallayerandpowerawareroutinginroutinglayer,canoftenaffect theenergysavings. Whileapplyingtheseenergysavingtechniquesseparatelyworks,jointoptimization approaches would achieve better performance. In this section, we discuss the related works on joint scheduling,powercontrolandrouting. Recently there have been several works ([15], [17], [18], [19], [20]) on jointly scheduling and power control in wireless sensor networks. ElBatt and Ephremides [15, 16] consider the problem of joint scheduling and power control in multi-hop networks. Their solution has two alternating phases: scheduling and power control. A transmission scenario (the selection of a particular set of links to transmit data) is defined as valid if no node is to transmit and receive simultaneously and no node is to receivefrommorethanoneneighboratthesametime. Anadmissibletransmissionscenariomeansthat a set of transmission power is available to satisfy theSNR constraints for all links in the scenario. In each slot the scheduling algorithm first searches a maximum valid scenario, which then is verified by 18 the distributed power control algorithm to see if it is admissible. If the valid scenario is not admissi- ble, the scheduling algorithm drops the link with minimum SNR and the power control algorithm is rerun. Once an admissible transmission scenario is found, the sources will transmit data packets using the computed transmission powers in current slot. They also proved that the power control algorithms proposedforcellularnetworkcanbeapplieddirectlyintowirelessmulti-hopnetworks. Astheschedul- ing algorithm schedules as many links as possible to be active at each slot, it can not guarantee energy efficiencyasdiscussedinEEJSPC. The authors in [17] proposed a distributed joint scheduling and power control algorithm for multi- casting in wireless Ad Hoc Networks. As in [15], the algorithm in [17] also tries to schedule all links withdatatransmissionrequirement. IfasetoftransmissionpowercannotbefoundtosatisfytheSNR constraints for all the links, the link with Maximum Interference to Minimum Signal Ratio (MIMSR, theratiobetweeninterferenceandsignalstrengthreceivedatthereceiverofthelink)isdeferreduntila feasible power control solution is available. In both [15] and [17], while the power control algorithm is optimal in minimizing the transmission power of a single transmission scenario, the scheduling al- gorithm which tries to find a maximum valid scenario may result in a non-optimal solution in terms of totalenergyconsumptioninmultipleslots. BhatiaandKodialam[18]deriveaperformanceguaranteedpolynomialapproximationalgorithmfor jointlysolvingrouting,schedulingandpowercontrol. Givenasourceanddestination,theyareinterested in making three decisions: the paths the data has to take between the source and the destination, the power with each link transmission is done and the time slots in which specific link transmissions have to take place. However, they consider a different interference model in which theSINR level impacts theaveragerateratherthanthesuccessorlossofindividualpackets. InourworkEEJSPC,asin[15,17], we will assume an interference model in which a radio can either successfully receive a packet or not dependingontheSINRthreshold. A closely related work by Cruz and Santhanam [19] proposes a joint scheduling and power control algorithm to minimize the total average transmission power in the wireless multi-hop network, subject to the constraints on average data rate per link and peak transmission power per node. Similar to [18], they assume an interference model that SINR affects the achieved data rate of the link in a slot. The long-term average rate of a link is then defined as the sum of the achieved data rate per slot dividedbynumberofslotswhennumberofslotsgoestoinfinity. Theyreducetheproblemtoaconvex optimization problem over a single slot using a duality approach. However, this prior work does not 19 consider the latency metric explicitly. Although the long-term average rate of a link is guaranteed, if therearelatencydeadlinerequirements,manypacketscouldbeuselesseveniftheyreachthesink. Theauthorsin[67]considertheproblemofpowercontrolledminimumframelengthschedulingfor TDMA wireless networks. Given a set of one-hop transmission requests, their objective is to schedule the transmission requests in a minimum number of time slots. The consider per-slot and per-frame versionsoftheproblemanddevelopmixedintegerlinearprogrammingmodels. Tominimizetheframe length, their approach is to schedule the maximal feasible active links in each slots, same as [15, 16]. Thusenergyefficiencycannotbeguaranteed. Sichitiu[59]proposesacross-layerschedulingforpowerefficiencyinwirelesssensornetworks. In order to conserve energy, sensor nodes are turned off. However, since an in active sensor node is no longerpartofthenetwork,thenetworkcanbecomedisconnected. Theauthorproposesadeterministic, schedule-basedenergyconservationscheme,inwhichtime-synchronizedsensorsformon-offschedules thatenablethesensortobeawakeonlywhennecessary. Theschemecanbedecoupledintotwodistinct phasesforeachflowinthenetwork: thesetupandreconfigurationphase,andthesteadystatephase. In the setup and reconfiguration phase, first a route from the node originating the flow to the base station is selected, then the schedules are set up along the chosen route. If a schedule can not be set up along the chosen route, the routing protocol will find an alternative route. In this scheme, the scheduling and routingschemesworkseparately. Previous related works mainly focused on the metrics of energy efficiency and did not explicitly consider the latency. In our work EEJSPC, we consider the energy efficiency of joint scheduling and power control under a specific latency bound. And in MLSR, we are interested in minimum latency joint scheduling and routing. In both works, we explicitly take latency into the design consideration. Ourapproachescanachievebettertradeoffsbetweenenergyandlatencythanpreviousworks. 20 Chapter3 DMAC:Tree-basedDataGatheringMAC 3.1 Overview IntheIntroductionChapter1,wedescribedbrieflythefundamentaltradeoffsbetweenenergyefficiency and low latency. In this chapter, we will describe the tradeoff in detail. And in a typical data gather- ing application scenario, we employ the unique feature of the unidirectional communication pattern to proposeanadaptiveMACfortree-baseddatagatheringwhichcanprovidebotherenergyefficiencyand lowlatency. We know that in order to save energy, we need to turn off the radio to avoid energy waste of idle listening. Since in sensor network applications, traffic load is very light most of the time, it is often desirable to turn off the radio when a node does not participate in any data delivery. Prior work, e.g. [63] suggests putting idle nodes in power saving mode and switching nodes to full active mode when a communication event happens. However, even when there is traffic, idle listening still may consume most of the energy. For example, a sensor node reports its sensing reading one packet per second. Suppose the packet length is 100 byte, it takes 8ms for a radio of 100Kbps data rate, while the other 992ms is still wasted in idle listening. S-MAC [60] reduces idle listening energy cost by reducing the duty cycle of a sensor node in which a node follows a periodical active/sleep schedule. During sleep period, nodes turn off radio to preserve energy. During active period, nodes turn on radio to Tx/Rx messages. Although a low duty cycle MAC is energy efficient, it has three side-effects. First, it increases the packet delivery latency. At a source node, a sampling reading may occur during the sleep period and hastobequeueduntiltheactiveperiod. Anintermediatenodemayhavetowaituntilthereceiverwakes up before it can forward a packet received from its previous hop to the next hop. This is called sleep latency in SMAC [60], and it increases proportionally with hop length by a slope of schedule length 21 (active period plus sleep period). Secondly, a fixed duty cycle does not adapt to the varying traffic rate in sensor network. A fixed duty cycle for the highest traffic load results in significant energy wastage whentrafficislowwhileadutycycleforlowtrafficloadresultsinlowmessagedatadeliveryandlong queuing delay. Therefore it is desirable to adapt the duty cycle under variant traffic load. Thirdly, a fixed synchronous duty cycle may increase the possibility of collision. If neighboring nodes turn to activestateatthesametime,allmaycontendforthechannel,makingacollisionverylikely. There are several works on reducing sleep delay and adjusting duty cycle to the traffic load. Those mechanismsareeitherimplicit(e.g. [60],[26])inwhichnodesremainactiveonoverhearingofongoing transmission or explicit (e.g. [62]) in which there are direct duty cycle adjusting messages. SMAC [60] proposed adaptive listening to reduce the sleep delay. In adaptive listening, a node who overhears its neighbor’s transmission wakes up for a short period of time at the end of the transmission. In this way, if the node is the next-hop node, its neighbor is able to immediately pass the data to it instead of waitingforitsscheduledlistentime. AnongoingworktoimproveSMAC[30]pointsoutthatthephase differenceintheschedulecouldaffectthelatency. Itincludesasimpleanalysisfortwocases. Incase1 where the phase difference is in the same direction of the data flow, delay is reduced. In case 2 where phase difference is in the opposite direction, delay is increased. Then it proposes a scheme to design globalsynchronizationalgorithm. InTMAC[26],anodekeepslisteningandpotentiallytransmittingaslongasitisinactiveperiod. An active period ends when no activation event has occurred for a certain time. The activation time events include reception of any data, the sensing of communication on the radio, the end-of-transmission of a node’s own data packet or acknowledgement, etc. FRTS is employed to solve the early sleep problem. The authors of [62] propose a slot-based power management mechanism. If the number of buffered packets for an intended receiver exceeds a thresholdL, the sender signals the receiver to remain on for the next slot. A node requested to stay awake sends an acknowledgement to the sender, indicating its willingness to remain awake in the next slot. The sender can then send a packet to the receiver in the followingslot. Therequestisrenewedonaslot-by-slotbasis. However, in previous implicit or explicit mechanisms, not all nodes beyond one hop away from the receiver can overhear the data communication, and therefore packet forwarding will stop after a few hops. As we shall describe in section 3.2, this data forwarding interruption problem causes sleep latencyforpacketdelivery. After describing the data forwarding interruption problem, we will describe the proposed DMAC mechanisminsection3.3. DMACemploysastaggeredactive/sleepscheduletosolvethisproblemand 22 Figure3.1: SMACwithadaptivelisteninginachain. enable continuous data forwarding on the multihop path. In DMAC, data prediction is to used enable active slot request when multiple children of a node have packets to send in a same sending slot, while More to Send packet is used when nodes on the same level of the data gathering tree with different parents compete for channel access. In section 3.4 and 3.4.4, we evaluate the performance of DMAC bysimulationandrealmoteexperiments. 3.2 DataForwardingInterruptionProblem Thedata forwardinginterruption problem existsin implicitadaptiveduty-cycle techniquesbecause the overhearingrangeislimitedbytheradio’ssensitivitytosignalsonair. Nodesthatareoutofthehearing range of both the sender and the receiver are unaware of ongoing data transmissions, and therefore go tosleepuntilthenextcycle/interval. Thedataforwardingprocesswillthenstopatthenodewhosenext hoptowardsthesinkisoutoftheoverhearingrangebecauseitisinsleepmode. Packetswillthenhave tobequeueduntilthenextactiveperiodwhichincreaseslatency. Also,forexplicitmechanism,theduty cycle adjusting messages can only be forwarded limited hops in an active period. So nodes out of the rangegotosleepaftertheirbasicdutycycle,leadingtointerrupteddataforwarding. Assumeanactiveperiod(i.e. theportionoftimeineachintervalwhenanodeisactive,unlessthere is more data to be sent/received) is only long enough to transmit one packet each hop. In SMAC, only the next hop of the receiver can overhear the data transmission and remains active for a long period. Other nodes on the multihop path do not overhear the data transmission thus go to sleep after the basic active period, resulting in the interruption of packet forwarding to the sink till the next duty cycle. It is shown theoretically in [60] that the delay with adaptive listening still increases linearly with the numberofhopswithaslopethatishalfoftheintervallength. Therefore,comparedwiththecaseofno adaptive listening, the delay is only reduced by half. Meanwhile, nodes other than the next-hop in the 23 neighborhood of the sender and the receiver also overhear the data transmission and thus may remain active unnecessarily. Similarly, in TMAC [26], a node remains active if it senses any communication ontheair. Typically, aradio’sinterferencerangeislargerthanitstransmissionrange(e.g. inNS-2, the interference range is set to more than twice the transmission range). In TMAC, any neighbor nodes in the interference range of either the sender or the receiver will remain active. Many of the nodes do not participateinthedatadeliverybutremainactiveforanunnecessarilylongperiodwhichwastesenergy. Meanwhile only nodes in the interference range hear the communication, while other nodes out of the interference range on the multi-hop path still go to sleep after their basic active period. Thus packets still suffer from the data forwarding interruption problem. The use of the FRTS technique proposed in TMACcanonlyhelpforwardthepacketonehopfurther. Besidesthesleeplatency,thedutyadjustment alsosuffersfromthisearlysleepproblem. Thesameproblemhappenstothetechniquein[62],inwhich the request for a next active slot can be only received by the next hop. The nodes beyond that will still gotosleepaftertheirbasicactiveperiod. Figures3.1illustratesthisdataforwardinginterruptionproblemusingSMACwithadaptivelistening as an example. There is a chain of nodes with a single source on the far left and the sink on the far right. We assume an active period is only long enough to transmit one packet one hop. By adaptive listening, the next hop of the receiver overhears the receiver’s ACK or CTS packet, then remain active anadditionalslot. Butothernodesstillgotosleepaftertheiractiveperiods. Ifthesourcehavemultiple packets to send, those packets can only be forwarded two hops away every intervalT. Latency is also only reduced by half. Collision is also depicted in the figure. Suppose in slot between 2μ and 3μ, both node 0 and node 1 need to transmit packets, a collision could happen. Things will be even worse if between0andμ,allnodeshavepacketstosend. Thehearing/interferencerangealsocausesatradeoffbetweenthelatencyandenergy. Ifthehearing range is long, latency is reduced since more nodes on the path can overhear the communication and remain active. Meanwhile, more nodes not on the path also overhear the communication and waste energy in idle listening on the increased active periods. We need a MAC that can tell all nodes on the pathandnoothernearbynodestostayactiveand/orincreasetheirdutycyclestoenablecontinuousdata forwardingwithoutincurringenergywasteofunrelatednodes. 24 3.3 DMACProtocolDesign 3.3.1 StaggeredWakeupSchedule One can identify three main communication patterns in sensor network applications. The first involves localdataexchangeandaggregationpurelyamongnearbynodes(thesecanbehandledbyclusteringor simple medium access mechanisms). The second involves the dispatch of control packets and interest packets from the sink to sensor nodes. Such sink-originated traffic is small in number and may not be latencysensitive. Wecanreserveaseparateactiveslotperiodicallywithalargerintervallengthforsuch control packets. The third and most significant traffic pattern in WSN is data gathering from sensor nodes to sink. For a sensor network application with multiple sources and one sink, the data delivery pathsfromsourcestosinkareinatreestructure,andatagatheringtree[32]. Routesmaychangeduring data delivery, but we assume that sensor nodes are fixed without mobility and that a route to the sink is fairly durable, so that a data gathering tree remains stable for a reasonable length of time. Flows in the data gathering tree are unidirectional from sensor nodes to sink. There is only one destination, the sink. All nodes except the sink will forward any packets they received to the next hop (except local processing packets which are handled in cluster). Our key insight in designing a MAC for such a tree is that it is feasible to stagger the wakeup scheme so that packets flow continuously from sensor nodes to the sink. DMAC is proposed to deliver data along the data gathering tree, aiming at both energy efficiencyandlowlatency. In DMAC, we stagger the activity schedule of nodes on the multihop path to wake up sequentially like a chain reaction. Figure 3.2 shows a data gathering tree and the staggered wakeup scheme. An interval is divided into receiving, sending and sleep periods. In receiving state, a node is expected to receive a packet and send an ACK packet back to the sender. In sending state, a node will try to send a packettoitsnexthopandreceiveanackpacket. Insleepstate,nodeswillturnoffradiotosaveenergy. The receiving and sending period have same length ofμ which is enough for one packet transmission andreception. Dependingonitsdepthdinthedatagatheringtree,anodeskewsitswakeupschemedμ ahead from the schedule of the sink. In this structure, data delivery can only be done in one direction towardstheroot. Intermediatenodeshaveasendingslotimmediatelyafterthereceivingslot. A staggered wake-up schedule has four advantages. First since nodes on the path wake up sequen- tially to forward a packet to next hop, sleep delay is eliminated if there is lost due to channel error or collision. Second, a request for longer active period can be propagated all the way down to the sink, so that all nodes on the multihop path can increase their duty cycle promptly to avoid data stuck in 25 Figure3.2: DMACinadatagatheringtree. intermediate nodes. Third, since the active periods are now separated, contention is reduced. Fourth, onlynodesonthemultihoppathneedtoincreasetheirdutycycle,whiletheothernodescanstilloperate onthebasiclowdutycycletosaveenergy. In a multi-hop wireless network, it is well known that contention-based MACs suffer from the hidden node problem. In MACAW [34], virtual and physical carrier sense and RTS/CTS exchange are utilizedtoreducehiddennodeproblem. Forlargepacketsizes,thesesmallcontrolpacketsareefficient in saving the possible high cost of a packet lost. However, for sensor networks where packet size is usually small, the overhead of RTS/CTS could be very high compare to the actual data transmission cost. ThereforewedonotadvocatetheuseofRTS/CTSinDMAC.DMAC,however,employslinklayer ARQthroughACKcontrolpacketanddataretransmission,andthehiddennodeproblemismitigatedto some extent through the manner in which active slots are scheduled so that nodes on the same path do not cause hidden node collisions. Although ACK packets consume energy and bandwidth, we believe theseareessentialforthelinkreliabilitytorecoverlostpacketduetoharshqualitywirelesschanneland contention(thoughthereisalwaysthepossibilityofusingimplicitACKs[61]incaseofhighlyreliable links). If a sending node does not receive an ACK packet from receiving node, it will queue the packet untilnextsendingslot. After3retransmission,thepacketwillbedropped. In DMAC, nodes with the same depth will have same offset, and thus a synchronous schedule. During the sending period, nodes will compete for the channel. To reduce collision during this period, everynodebacksofffordifsplusarandomtimewithinafixedcontentionwindowatthebeginningof asendingslot. Sincethelengthofasendingslotisonlyenoughforonepackettransmission,thereisno needforexponentialcontentionwindowincrease,andthereforeweemployafixedcontentionwindow. Basedontheabovechoices,thesendingandreceivingslotlengthμissetto: μ =DIFS +CW +DATA+sifs+ACK 26 Figure3.3: DMACinachain. whereDIFSistheDCFinter-framespace,CWisthefixedcontentionwindowsize, DATAisthepacket transmission time(We assume all packets are in the same length), sifs is Short inter-frame space and ACK istheACKpackettransmissiontime. Synchronization is needed in DMAC. However, local synchronization is enough since a node only needs to be aware of its neighbors’ schedule. There exist techniques such the reference broadcast synchronizationscheme(RBS)[27]thatcanachievetimesynchronizationprecisionof3.68±2.57μsec after 4 hops. Given that typical slot lengths are on the order of 10ms in length, we will assume that synchronizationisavailableinthefollowingdiscussions. 3.3.2 DataDeliveryandDutyCycleAdaptioninMultihopchain Figure 3.3 shows DMAC operation in a multihop chain. Every node periodically turns to receiving, sendingandsleepstates. Itisshownthatwhenthereisnocollision,apacketwillbeforwardedsequen- tiallyalongthepathtothesink,withoutsleeplatency. However when a node has multiple packets to send at a sending slot, it needs to increase its own dutycycleandrequestsothernodesonthemultihoppathtoincreasetheirdutycyclestoo. Weemployed a slot-by-slot renewal mechanism. We piggyback a more data flag in the MAC header to indicate the request for an additional active periods. The overhead for this is very small. Before a node in its sending state transmits a packet , it will set the packet’s more data flag if either its buffer is not empty or it received a packet from previous hop with more data flag set. The receiver check the more data flag of the packet it received, and if the flag is set, it also sets the more data flag of its ACK packet to the sender. With the slot-by-slot mechanism and the policy to set more data flag when buffer is not empty, DMAC can react quickly to traffic rate variation to be both energy efficient and maintain low datadeliverylatency. Anodewilldecidetoholdanadditionalactiveperiodif: 27 1. Itsendsapacketwiththe more dataflagsetandreceivesanACKpacketwiththe more dataflag set. 2. Itreceivesapacketwithmoredataflagset. In DMAC, even if a node decides to hold an additional active period, it does not remain active for thenextslotbutschedulesa3μsleepthengoestothereceivingstateasshowninFigure3.3. Thereason for a 3μ sleep is that it knows the following nodes on the multihop path will forward the path in the next 3 slots. In [25], it is shown that the maximum utilization of a chain of ad hoc nodes is 1 4 if the radio’s interference range is twice the transmission range. So the maximum sending rate for a node is one packet per 4 slots. However, to accommodate the possibility of short range between two neighbor nodes, a node will only send one packet every 5μ in DMAC in order to avoid collision as much as possible. Of course, this may reduce the maximum network capacity by about 20%, but if the traffic load is more than 80% of the maximum channel capacity duty-cycled mechanisms would not function efficientlyinanycase,makingthisamootpoint. A good result of the staggered wake up schedule is that the more data flag can be propagated to all the nodes on the multi-hop path. In Figure 3.3, suppose the source sets the more data flag of the first packet, since this packet can be forwarded to the sink without interruption, all nodes will receive the firstpacketwithmoredataflagsetthuswillholdanadditionalactiveperiod3μlateraftertheirsending slot. So at time 5μ, the second packet from the source can still be delivered to the sink with very short delay. However, there is a possibility of inconsistency on the new active period request. We may have a situation where the receiving node is awake, while the sending node is off. This could happen when the receiving node received a packet with more data flag, but the ACK packet sent by the receiver is not received by the sender. In this case, the receiving node will waste an active period in idle listening. However,theslot-by-slowrenewalmechanismwillmakesurethatanodewillonlywasteoneadditional active period, though packets will have a sleep delay. The situation where the sending node is awake butthereceivingnodeisoffisnotpossiblesincethesendingnodewillholdanadditionalactiveperiod only ifit successfully receivedan ACK packetwith more data which guaranteedthe receiver isawake. DMAC avoids this situation because transmission is more energy costly than receiving and a packet retransmissionchancewillbewasted. Measurements have showed that the cost for switching radio between active and sleep is not free. However, the overhead of this switching is likely to be small [29] compared to energy savings in a 3μ sleepperiodofaround30ms. 28 Figure3.4: Datapredictionschemereducessleepdelay. 3.3.3 DataPrediction Inlastsection, weassumeasinglesourceneedsahigherdutycyclethanthebasiclowerdutycycle. In a data gathering tree, however, there is a chance that each source’s rate is small enough for the basic dutycycle,buttheaggregatedrateatanintermediatenodeexceedsthecapacityofbasicdutycycle. For example, suppose a node C has 2 children A and B. Both children has only one packet to send every interval. At the sending slot of an interval, only one child can win the channel and send a packet to the node. Assume A wins the channel and sends a packet to C. Since A’s buffer is empty, the more data flag is not set in A’s packet. C then goes to sleep after its sending slot without a new active period. B’s packetwouldthenhavetobequeueduntilnextinterval. ThisresultsinsleepdelayforpacketsfromB. We propose a scheme called data prediction to solve this problem. If a node in receiving state receives a packet, it predicts that its children still have packets waiting for transmission. It then sleeps only3μafteritssendingslotandswitchesbacktoreceivingstate. Allfollowingnodesonthepathalso receivethispacket,andscheduleanadditionalreceivingslot. Inthisadditionaldatapredictionreceiving slot, if no packet is received, the node will go to sleep directly without a sending slot. If a packet is receivedduringthisreceivingslot,thenodewillwakeupagain3μlaterafterthissendingslot. Foranodeinsendingstate,ifduringitsbackoffperioditoverhearstheACKpacketfromitsparent inthedatagatheringtree,itknowsthatthissendingslotisalreadytakenbyitsbrotherbutitsparentwill hold an additional receiving slot 3μ later, so it will also wake up 3μ later after its sending slot. In this additional sending slot, the node then can transmit a packet to its parent. Figure 3.4 shows an example ofthedatapredictionscheme. Of course, this generalizes beyond the case of a node having two children. If a node has more children, in the additional receiving slot, the remaining children would compete for the channel again. Thisprocesswouldrepeatuntileventually,allchildrenwillbeabletotransmittheirpackettotheparent one by one with shortest delay. However if a collision happens, all children nodes have to wait until 29 next interval. But since those nodes have the same parent, they are at most two hops away. Hence they candetecteachother’stransmission,andthechanceofacollisionduetohiddennodeproblemissmall. Thereisanoverheadbroughtbythe data predictionscheme. Afterthereceptionofthelastpackets from its children, a node will remain idle for a receiving slot which waste energy in idle listening. Compared to the huge latency reduction by the data prediction, we believe this additional overhead wouldbeworthwhile. 3.3.4 MTS Althoughanodewillsleep3μbeforeanadditionalactiveperiodtoavoidcollision,thereisstillachance ofinterferencebetweennodesondifferentbranchesofthetree. ConsidertheexampleinFigure3.5;two nodes A and B are in interference range of each other but have different parents in the data gathering tree. Inthesendingslotofoneinterval,Awinsthechannelandtransmitsapackettoitsparent. Neither B nor its parent C holds additional active slots in this interval. Thus B can only send its packet in the sending slot of next interval, resulting a sleep latency ofT. Since C does not receive any packet in its receiving slot and B does not overhear ACK packet from C in its sending slot, data prediction scheme willnotwork. We propose a solution to mitigate this interference using an explicit control packet, that we refer to as More to Send (MTS). The MTS packet is very short with only destination’s local ID and a flag. A MTSpacketwithflagsetto1iscalledarequestMTS.AMTSpacketwithflagsetto0iscalledaclear MTS. AnodesendsarequestMTStoitsparentifeitherofthetwoconditionsistrue: 1. Itcannotsendapacketbecauseofchannelbusy. Afterthenode’sbackofftimerfires,itfindsthere isnotenoughtimeforittosendapacketanditdoesnotoverhearitsparent’sACKpacket. Itthen assumesthatitlostthechannelbecauseofinterferencefromothernodes. 2. It receives a request MTS from its children. This is aimed to propagate the request MTS to all nodesonthepath. ArequestMTSissentonlyoncebeforeaclearMTSpacketissent. AnodesendsclearMTStoitsparentifthefollowingthreeconditionsaretrue: 1. Itsbufferisempty. 2. AllrequestMTSsreceivedfromchildrenarecleared. 30 Figure3.5: Interfencebetweentwosendingnodescausessleepdelay. Table3.1: Radioparameters Radiobandwidth 100Kbps RadioTransmissionRange 250m RadioInterferenceRange 550m PacketLength 100bytes TransmissionPower 0.66W ReceptionPower 0.395W IdlePower 0.35W 3. ItsentarequestMTStoitsparentbeforeandhasnotsentaclearMTS. AnodewhichsentorreceivedarequestMTSwillkeepwakingupperiodicallyevery3μ. Itswitches back to the basic duty cycle only after it sent a clear MTS to its parent or all previous received request MTSfromitschildrenwerecleared. Same as the slot-by-slot renewal scheme and data prediction scheme, the higher duty cycle request by MTS packets are forwarded through the staggered schedule to all nodes on the multihop path. The difference from the slot-by-slot renewal scheme is that only two MTS packets are sent for a MTS request/clear period. This is due to the overhead of the MTS packets. If a MTS packet need to be transmittedineachadditionalactiveperiod,theoverheadofMTSpacketswillbehigh. InconsistentscheduleispossibleduetothelossofMTSpackets. Asofttimerismaintainedtoclear requestMTSifnodatareceivedortransmittedafteracertainnumberofreceivingslotinordertoavoid unnecessaryactiveslotsbecauseoflostofclearMTSpackets. SlotlengthhastobeincreasedtoenablethetransmissionofMTSpacketsafteradatatransmission. Since the MTS packet is very short, the increase will be very small. Energy consumption will increase too because the overhead of MTS packets and the increase of slot length. In the simulation section, we show that MTS can significantly reduce latency in a sensor network at only small overhead of energy cost. 31 Figure3.6: Meanpacketlatencyoneachhopunderlowtrafficload. Figure3.7: Totalenergyconsumptiononeachhopunderlowtrafficload. 32 Figure3.8: Meanpacketlatencyfor10hopschainunderdifferentsourcereportinterval. 3.4 PerformanceEvaluation We implemented our prototype in the ns-2 network simulator with the CMU wireless extension. For comparison, we also implement a simple version of SMAC with adaptive listening, but without its synchronizationandmessagepassingscheme. WewillalsocomparewithafullactiveCSMA/CAMAC without periodical sleep schedule. This will serve as the baseline of latency, energy and throughput performance. We choose 3 metrics to evaluate the performance of DMAC: Energy Cost is the total energy cost to deliver a certain number of packets from sources to sink. This metric shows the energy efficiency of theMACprotocols. Latencyistheendtoenddelayofapacket. ThroughputorDeliveryratioisthe ratioofthenumberofpacketsarrivedatthesinktothenumberofpacketsentbysources. TheradiocharacteristicsareshowninTable3.1. TheenergycostsoftheTx:Rx:Idleradiomodesis setto1.67:1:0.88. Thesleepingpowerconsumptionissetto0. AMTSpacketis3byteslong. Accordingtotheparametersoftheradioandpacketlength,thereceivingandsendingslotμissetto 10msforDMACand11msforDMAC/MTS.Theactiveperiodissetto10msforSMACwithadaptive listening. All schemes have the basic duty cycle of 10%. This means a sleep period of 180ms for DMAC,198msforDMAC/MTSand90msforSMAC. All simulations are run independently under 5 different seeds. All sources generate packets at con- stantaveragedratewithrandomizationininter-packetinterval. 33 Figure3.9: Energyconsumptionfor10hopschainunderdifferentsourcereportinterval. Figure3.10: Throughputfor10hopschainunderdifferentsourcereportinterval. 34 Figure3.11: Arandomdatagatheringtree. 3.4.1 Multihopchain To reveal the fundamental performance of DMAC, we first perform a test on a simple multihop chain topologywith11nodes. Thedistancebetweenadjacentnodesis200meters. Firstinordertoshow the capability of reducing the sleep delay in DMAC, we measure the end-to-end latency of packets under very light traffic rate of source report interval 0.5s. In this light traffic load, there is no queuing delay butonlyasleepdelaythatiscausedbyperiodicalsleep. Figure 3.6 shows the averaged packet latency with different hop length. In both DMAC and full activeCSMA/CA,thelatencyincreaselinearlywiththenumberofhopswithalmostthesameslop. The additionallatencyofDMACisatthesourcewhenasensingreadingoccursduringthesleepperiodand has to wait until the node wakes up. The SMAC with adaptive listening, however has higher latency. Especially, the latency has a jump every 3 hops. This is because by adaptive listening, a packet can be forwarded two hops instead of one hop without adaptive listening. However the packet has to queued forascheduleintervalforthethirdhop. Thisisshownclearlyinthefigure. Figure 3.7 shows the energy cost with different hop length. In all MAC protocol, the energy cost increase linearly with the number of hops. However, the energy cost of the full active CSMA/CA increases much faster than other two MAC protocols. DMAC consumes less energy cost than SMAC. ThisisduetotheadditionalactiveperiodinSMACfornodesthatarenotthenexthopofadatapacket (butarewithinhearingrange). We then test the rate adaption of these MAC protocols. We vary the traffic load by changing the sensorreportintervalonthesourcenodefrom0.05sto0.55s. Thehoplengthisfixedat10hops. 35 Figure3.12: Meanpacketlatencyforadatagatheringtreeunderdifferenttrafficload. Figure 3.8 shows the averaged packet latency under different source report interval. Clearly full active CSMA/CA has the lowest latency. DMAC has a slightly higher latency due to the initial latency at the source. SMAC, however, has much higher latency, especially when traffic load is heavy at small source report interval. The reason is that since packets can be forwarded two hops every one interval, thosepacketssufferedfrombothsleepdelayandqueuingdelay. Whentrafficloadisveryhigh,collision wouldsignificantlyincreasepacketlatencyasaretransmissioncanonlybedoneafteronetotalschedule interval. Whensourcereportislessthan0.05s, thetrafficloadwillbemorethan80%ofthemaximum channelcapacity. OnlyfullactiveCSMA/CAcanhandlesuchahightrafficload. Figure 3.9 shows the total energy cost under different source report interval. Energy cost decreases as traffic load decreases. For full active CSMA/CA, however, the decrease is small since without radio off, the idle listening still consume significant energy. DMAC has a less energy cost due to the same reasonasabovethatnodesotherthannexthopofadatapacketremainactiveunnecessarily. Figure 3.10 shows the throughput achieved for different MAC protocols. All MAC schemes have quitegooddatadeliveryrationear1underthesimplemultihopchaintopology. 3.4.2 RandomDatagatheringTree Inthistopology,50nodesaredistributedrandomlyina1000m×500mareasshowninFigure3.11. The sinknodeisattherightbottomcorner. Adatagatheringtreeisconstructedbyeachnodechoosingfrom its neighbor the node closest to the sink as its next hop. In order to show the different packet latency, a 36 Figure3.13: Energyconsumptionforadatagatheringtreeunderdifferenttrafficload. Figure3.14: Datadeliveryratioforadatagatheringtreeunderdifferenttrafficload. sourceshouldbeatleast3hopsawayfromthesink. Fivemarginnodesarechosenassourcestotestify themechanismofdatapredictionandMTS.Allsourcesgeneratereportsatthesamerate. The packet latency under different source report intervals is shown in Figures 3.12. Full active CSMA/CA has small delay for all traffic load. However, other three MAC schemes’ latency increases significantly when the traffic load is larger than a certain threshold. DMAC/MTS can handle the high- est traffic load with small delay among the three MAC schemes with periodical sleep. Compared to mulithop chain under the same heavy traffic load, the latency in a data gathering tree is much higher. Thisisduetotheinterferencebetweennodesinthesamedepthofthetree. Theinterferencecouldresult indatalost,scheduleinconsistencyandMTSpacketlostwhichincreasethesleeplatency. 37 Figure3.15: Meanpacketlatencyfordatagatheringdifferentsourcenumber. Figure 3.13, 3.14 shows the energy and throughput performance. We collect the energy costs of all the 50 nodes in the network because some MAC schemes could cause unrelated nodes to maintain higher duty cycle. It is shown in the figure that DMAC and DMAC/MTS are the two most energy efficient MAC schemes. DMAC/MTS, however, consumes higher energy than DMAC because of the overhead of MTS packets and more active period requested by MTS packets. In terms of end-to-end throughput, DMAC/MTS has a good delivery ratio while SMAC and DMAC’s delivery ratio decreases whentrafficloadisheavy. We further evaluate the scalablity of DMAC under a dense network, in which 100 nodes are ran- domly placed in a 100m× 500m area. A data gathering tree is constructed rooted at the sink on the right bottom corner. All sources generate traffic at one message per 3 seconds. We vary the number of sourceswhicharechosenrandomlyfromthemarginnodesinthenetwork. Figure 3.15 shows the averaged delay under different number of sources. As source number in- creases, inteference increases which results in increased latency for SMAC and DMAC without MTS. DMAC/MTS, however, can still maintain quite low latency. This low latency is achived at very small overhead in energy compared to DMAC without MTS, which is shown in figure 3.16. DMAC/MTS also has the second delivery ratio next to full active CSMA. This clearly shows the effectness of DMAC/MTS. 38 Figure3.16: Energyconsumptionfordatagatheringdifferentsourcenumber. Figure3.17: Datadeliveryratiofordatagatheringwithdifferentsourcenumber. 39 Figure 3.18: Trade off among energy, latency and throughput for a data gathering tree under different trafficload. 3.4.3 Energy-Throughput-LatencyTradeoffs To understand the tradeoffs among energy, throughput and latency, Figure 3.18 shows the number of packets can be sent per unit resource measured in terms ofEnergy×Latency for scenario in Figure 3.11. Fromthefigure,weseethatbecauseSMACachievesenergyefficiencyatthesacrificeoflatency, it sends the least number of packets per Joule× Second. This suggests that for applications that can tolerate message latency, SMAC is a reasonable solution. But for applications that require real- time data delivery, SMAC is not feasible due to the data forwarding interruption problem. DMAC and DMAC/MTS, however, can achieve both energy efficiency and low message latency. DMAC/MTS can operate with even smaller base duty cycle to save more energy when traffic is light and can still adapt to traffic bursts with high throughput, low latency and small energy consumption. However, this figure also shows that when traffic load exceeds a certain threshold, a full active MAC is most suitable when takingbothenergyanddelayintoaccount. SinceDMACcanadjustdutycycletotrafficloadwithsmalllatency,wecansetthebasicdutycycle even smaller. But a lower duty cycle could have longer initial sleep delay at the source node when a sensing reading occurs during the source’s radio is off. So there is a limitation on lowest basic duty cycle DMAC can operate on. However, with the same application latency bound requirement, DMAC canoperateonalowerbasicdutycyclethanSMACorTMACtobemoreenergyefficient. Finally, we should note that this comparison between DMAC and SMAC is only applicable under the specific data gathering tree scenario for unidirectional communication flow from multiple sources toasinglesink. SMACisinfactageneral-purposeenergy-efficientMACthatcanhandlesimultaneous 40 Table3.2: MICA2Radioparameters Radiobandwidth 19.2Kbps PacketLength 36bytes TransmissionPower 25mW ReceptionPower 28mW IdlePower 18mW Figure3.19: MeanpacketlatencyoneachhopunderlowtrafficloadinMoteexperiments. datatransmissionsandflowsbetweenarbitrarysourceanddestination. Forapplicationsthatrequiredata exchangebetweenarbitrarysensornodes,DMACcannotbeusedwhileSMACwillbeagoodchoice. 3.4.4 ExperimentalResults To further evaluate DMAC performance on a real system, we have implemented DMAC on MICA2 Mote [35]. The basic radio features of the MICA2 Mote is shown in table 3.2. We have thus far tested DMAC on the multi-hop chain topology to reveal its fundamental performance and validate the corresponding simulation results 1. The distance between two adjacent nodes is 0.6m. We configured the MICA2 radio [3] to transmit using the smallest transmission power (output power .20dBm) so that anodecanonlyreachitsdirectonehopneighbornodes. InDMAC,thereceiveandtransmitslotlength is set at 200ms, the sleep period is 3600ms, so the total duty cycle is 10%. To have a fair comparison, the active slot length of SMAC is also set at 200ms but the sleep length is only 1800ms to have 10% dutycycle. First,inordertoonlyshowthereducedsleeplatencyofDMAC,wemeasuretheend-to-endlatency of each packet under a very light traffic setting of one packet per 12 seconds. Each packet is 36 bytes 41 Figure3.20: TotalEnergyconsumptiononeachhopunderlowtrafficloadinMoteexperiments. long including physical layer header. In this light traffic, there is no queueing delay but only sleep latency. Figure3.19showsthemeanpacketlatencywithdifferenthoplength. Similartothesimulation results,thelatencyofbothDMACandfullactiveCSMA/CAincreaselinearlywiththenumberofhops withalmostthesameslop. ThelatencyofDMACisabout2100mslongerthanthefullactiveCSMA/CA which is about half of the total interval length. This is due to packet generated during the sleep period which have to be buffered until the active period. The 10% with adaptive listening scheme has a lower latency for the first two hops because of its shorter interval time. When the hop length is larger than 3, it has higher latency. Specifically, the latency has a jump each 2 hops. This is because by adaptive listening,apacketcanbeforwardedtwohopsinsteadofonehopinthe200msactiveperiod. Eachjump increasesthelatencyabout2swhichisexactlyascheduleinterval. Figure 3.20 shows the energy cost with different hop lengths. Similar to the simulation results, the energycostofallMACincreaselinearlywiththenumberofhops. However,theenergycostofthefull activeCSMA/CAincreasesmuchfasterthanothertwoMACprotocols. DMACconsumesslightlyless energycostthanSMAC(10%withadaptivelistening). We also test the rate adaption of these MAC protocols. We vary the traffic load by changing the sensor report interval on the source node from 12s to 2s. The hop length is fixed at 5 hops. Figure 21 showstheaveragedpacketlatencyunderdifferentsourcereportinterval. ClearlyfullactiveCSMA/CA hasthelowestlatency. DMAChasahigherlatencyduetotheinitiallatencyatthesource. SMAC(10% withadaptivelistening),however,hasevenhigherlatency,especiallywhentrafficloadisheavyatsmall sourcereportinterval. Thereasonisthatthosepacketssufferedfrombothsleepdelayandqueuingdelay. Whentrafficloadisveryhigh,contentionwouldsignificantlyincreasepacketlatencyasaretransmission 42 can only be done after one total schedule interval. The total synchronized active period of SMAC (10adaptivelistening)hasasmallerend-to-endcapacitythanDMAC. 3.5 Discussion ThischapterhasproposedDMAC,anenergyefficientandlowlatencyMACprotocolfortree-baseddata gathering in wireless sensor networks. The major traffic in wireless sensor netowrks are from sensor nodes to a sink which construct a data gathering tree. DMAC utilizes this data gathering tree structure specifictosensornetworkapplicationstoachievebothenergyefficiencyandlowpacketdeliverylatency. DMAC staggers the active/sleep schedule of the nodes in the data gathering tree according to its depth in the tree to allow continuous packet forwarding flow in which all nodes on the multihop path can be notifiedofthedatadeliveryinprogressanddutycycleadjustmentcommand. Datapredictionisemployedtosolvetheproblemwheneachsinglesourcehaslowtrafficratebutthe aggregatedrate atan intermediatenode islarger thanthe basicduty cyclecan handle. The interference between nodes with different parents could cause one traffic flow be interrupted because the nodes on the multihop path is not notified of the data transmission requirement. The use of an MTS packet is proposed to command nodes on the multihop path to remain active when a node fails to send a packet toitsparentduetointerference. Our simulation and experimental results have shown that DMAC achieves both energy savings and lowlatencywhenusedwithdatagatheringtreesinwirelesssensornetworks. 43 Chapter4 DESS:DelayEfficientSleepScheduling 4.1 Overview Inthepreviouschapter,weinvestigatedanapproachtodelay-efficientsleepscheduling,designedspecif- icallyforwirelesssensornetworkswherethecommunicationpatternisrestrictedtoanestablisheduni- directionaldatagatheringtree. Weshowedthatthesleeplatencycanbeessentiallyeliminatedbyhaving a periodic receive-transmit-sleep cycle with level-by-level offset schedules. In this chapter we seek to address a more general and harder version of this problem: how should the activity of sensor radio nodes be scheduled in arbitrary network communication topologies, in order to minimize the sleep la- tency while providing energy efficiency through periodic sleep? Thisisclearlyanissueoffundamental significance in the area of wireless sensor networks, and to our knowledge has never been investigated before. Unlike prior work in this area, which has focused primarily on designing new sensor network MACprotocolsinanintuitivemanner,weshalltakeanalgorithmicapproach. The rest of the chapter is organized as follows: We first discuss the problem scenario and the as- sumptions made in this study (in section 4.2). We define a graph-theoretic combinatorial optimization problemformulationfordelayefficientsleepscheduling(insection4.3)forthesinglewakeupschedule casewhereeachsensorchoosesexactlyoneofthekslotstowakeup. Weshow(insection 4.4)thatthis problemisinfactNP-hardingeneral. However,weareabletoderiveandanalyzeoptimalsolutionsfor somespecialcases,namelyaringtopologyandanytreetopology. Forarbitrarytopologies,wepropose severalheuristicsinsection4.5andevaluatethemusingsimulationsinsection4.6. 44 Figure4.1: Examplesofslotassignmentwithk = 3. Thedottedarrowsshowthedelayoneachlinkin thecorrespondingdirection. 4.2 ProblemScenarioandAssumptions In sensor networks with light traffic load, duty cycling (where sensors turn off their radios when not needed) is a very useful technique for reducing the energy consumption due to idle listening. We use k asaparameterthatcapturesthedutycyclingrequirementsofanapplication. Toachievetherequisite duty cycling, a sensor should be kept awake on an average for 1 k fraction of the time slots. We initially focus on the single wake up schedule case, where the schedule length is k slots and each sensor is assigned one of the k slots during which it activates its radio for reception (known as the active slot), while it can potentially transmit at any slot if it has a packet to be forwarded. If a node has to forward a packet to its neighbor, it can wake up at the active reception slot of that neighbor and transmit the packet. This conserves energy of both the transmitting and the receiving node. Figure 4.1 shows a couple of slot assignments on a network and the resulting delays on each link. Consider figure 4.1 (b). Assume that node A has a packet to send to node F. A would have received this packet in slot 0, but canonlytransmittoEatslot1. ThusthedelayfromAtoE is1(asAwaitsforthecompletereception of the packet at slot 0). Similarly E can only forward the packet to F in slot 2, thus incurring a delay of 1 fromE toF. In this case the end to end delivery latency is 2. Ideally, if every pair of nodes can have a path on which all nodes have sequentially increasing slots (modulok), the latency will only be the number of hops between them times a single slot length ( 1 k -th of the schedule length). However a schemesuchasthebasicS-MACschemewhichsynchronizesallnodestohavethesamecyclewillhave a latency as large as the number of hops times the duration of a full period. As mentioned in section 4.1, DMAC can achieve the ideal case for any source to sink communication path for a unidirectional datagatheringtree. However,thisstudyaddressestheissueofassigningslotstominimizethemaximum delaybetweennodesthatcancommunicateinanarbitrarypattern. Clearlyasseeninfigure4.1,different slotassignmentstothenodesinthenetworkcouldresultinsignificantlydifferentpathdelays. 45 Beforeformallydefiningtheproblem,wedescribeourassumptions: • Synchronization: Noneofthediscussionaboutsleepschedulingwouldberelevantiftherewere not some mechanism to provide time synchronization in the sensor network. However, tech- niques capable of providing micro-second level synchronization have been developed for sensor networks[27,39,40]. • Low Traffic: We have assumed that there is very low traffic within the sensor network. This is reasonable in low-data-rate sensor networks where phenomena of interest occur rarely. Energy- efficient low-duty cycles are only possible if this assumption is true. It also justifies the fact that this problem formulation does not take into account any queueing latency due to congestion, or significantinterference/collisions(thoughrandomaccessschemesmaybeimplementedtohandle occasionalcontentionduringtheactiveperiods,asinS-MAC).Sinceinterferenceisnotaprimary concern in light traffic, we have not incorporated any local vertex/edge coloring constraints into our problem formulation which would be necessary for graph-coloring based TDMA scheduled accessmechanismssuchas [6]. • Packet-Length Slot: A related assumption we make is that for such a low traffic scenario each reception slot is of a fixed length that is sufficient only for the transfer of a single packet. Thus a packet may travel at most one hop in a single slot. Longer fixed slot lengths would not be energy-efficientiftrafficislow. • Graph Abstraction: While several recent papers in sensor networks (e.g. [41, 43, 42]) have shown that wireless links can be quite unreliable and vary significantly in packet reception rates in each direction, we have used a binary-link-based graph-theoretic problem formulation in this work. Thisisjustifiedbecausethecommunicationgraphwearereferringtoisnotnecessarilythe full wireless network, but a logical topology which can be constructed, for instance, by filtering orblacklistingoutallunreliable/unidirectionallinks. Othershavesuggestedthatsuchblacklisting isnecessaryforreliablepacketdeliveryinanycase[43]. • Arbitrary Communication Pattern: In sensor networks where the traffic is restricted to data gathering from all nodes to a single sink, it is not necessary to minimize the delay diameter be- tween any two nodes in the graph. However, this unidirectional traffic pattern is a special case which has been addressed previously in the DMAC work [46]. In more sophisticated embed- ded wireless sensor networks, which may involve complex patterns of in-network processing, or 46 communication between sensors as well as actuators, other traffic patterns are possible. We for- mulate the problem for the more general case in section 4.3.1, which as we shall show is in fact computationallyharder. Althoughwedonottreatitindepthhere,analternativeformulationthat canprovidesomewayofweighingdifferentapplication-specifictrafficpatternsisalsodefinedin section4.3.2. • Fixed Number of Slots: In our formulation, we assume that the number of slots available to the network is fixed. This essentially defines the duration of the periodic sleep cycle, and the duty-cycle,whichareassumedtobedetermined aprioribyapplication-specificneedsforenergy efficiency as well as limitations on sleep/wakeup times of the radio hardware involved. As we shallsee,generallywithalargernumberofavailableslots,theenergyefficiencyishigherbutthe end-to-enddelayisalsolonger. • EnergyConservation: Sensornoderadiosincurdifferingenergycostsinidlelistening,receiving andtransmissionmodes. Transmissioncostsaregenerallyhigherthanidle/receptioncosts. Tech- nically,theminimumdelaypathobtainedmayinvolvelongerhops(moretransmissions)thanthe minimum hop-count path on the original graph. Thus delay minimization can result in a slight increaseintheenergycosts,howeverwebelievethisisasecondordereffectsincethebulkofthe energysavingsinthenetworkareprovidedbythesleepmodeoftheradio. Insection,4.3,weformallydefinetheproblemofassigningslotstonodestominimizethenetwork delay. 4.3 ProblemDefinition LetG = (V,E)beanarbitrarygraph. Letkbetheparameterthatdictatesthedutycyclingrequirements. Asmentionedinsection4.2,weinitiallyfocusonthesinglewakeupschedulecasewheretheschedule lengthisk slotsandeachsensorisassignedoneofthesek slots. Assigningaslots∈ [0···k−1]to a nodeischedulesitowakeup(activateitsradioforreceiving)onlyatslots. Whileicantransmitatany slot, it can only receive data at the beginning of slots. Letf : V → [0···k−1] be a slot assignment function that assigns a slot to every node in the graph. Clearly f determines the delay incurred in 47 transmittingdatafromonenodetotheother. Foragivenf,letd f (i,j)bethedelayintransmittingdata fromitoj where(i,j)∈E: d f (i,j) = k (iff(i) =f(j)) (f(j)−f(i)) mod k (otherwise) (4.1) Fromthedefinitionabove,italsofollowsthat: d f (i,j)+d f (j,i) = k (iff(i)6=f(j)) 2k (otherwise) (4.2) DelayonapathP underaslotassignmentf isdefinedas d f (P) = X (i,j)∈P d f (i,j) (4.3) As seen from the above discussion, duty cycling requirements will lead to increased delays in the network. Weconsiderthefollowingscenarios: 4.3.1 AlltoAllCommunication In this scenario, every pair of sensors is equally likely to communicate. Hence, it is desirable to as- sign slots to the nodes such that no two nodes incur arbitrarily long delays in communication. We characterizethisnetworkwidedelayusingthefollowingdefinition: Definition1: Delay diameter (D f ): For a given graphG = (V,E), number of slotsk and a slot assignment functionf : V → [0···k−1], the delay diameter is defined as max i,j∈V P f (i,j), where P f (i,j)isthedelayalongtheshortestdelaypathbetweennodesiandj underthegivenslotassignment functionf. In figure 4.1(a), the delay diameter is 5, while in (b) it is 8 (path D-F-E-C). Thus, in all to all commu- nication,ourdesigngoalisgivenasfollows: Definition2: DelayEfficientSleepScheduling(DESS):GivenagraphG = (V,E)andthenum- ber of slots k, find an assignment function f : V → [0···k− 1] that minimizes the delay diameter i.e. f = argmin f 0 {D f 0} (4.4) 48 4.3.2 WeightedCommunication In this scenario, the frequency of communication between a pair of sensors is not the same across all pairs. This may happen in the case of a hierarchical network structure (like clustering). Here, it would beofinteresttominimizetheaveragedelayinthenetwork,whichisdefinedasfollows: Definition3: AverageDelaydiameter(D avg f ): ForagivengraphG = (V,E),numberofslotsk, a slot assignment functionf : V → [0···k−1] and weightsw(i,j)≥ 0, the average delay diameter is defined as P i,j∈V w ij ∗P f (i,j), whereP f (i,j) is the delay along the shortest delay path between nodesiandj underthegivenslotassignmentfunctionf. Inweightedcommunication,ourdesigngoalisthefollowing: Definition4: Average Delay Efficient Sleep Scheduling (ADESS) Given a graph G = (V,E), the number of slots k, weights w(i,j)≥ 0, find an assignment function f : V → [0,···k− 1] that minimizestheaveragedelaydiameter i.e. f = argmin f 0 {D avg f 0 } (4.5) Intuitively, in both DESS and ADESS, the objective is to color a graph with the given k colors such that the desired global objective (minimizing the delay diameter in the former and the average delay diameter in the latter) is achieved. The reader may perceive a connection to the well-known NP-complete graph coloring problem [37], which deals with minimizing the number of colors needed to ensure that no two adjacent vertices are colored the same. However, a key difference between the graphcoloringproblemandDESS(orADESS)isthattheformerisessentiallyaboutalocalconstraint (adjacentverticesrequiringdistinctcolors),whilethelatterisinherentlymoreglobalinnature: adjacent vertices may share the same slot assignment but the maximum of the shortest delay paths between all pairsofnodesmustbereduced. WewillshowbelowthatbothDESSandADESSarealsoNP-Complete. 4.4 Analysis DESSandADESSareshowntobeNP-hardin[49]byNarayananSadagopan. Inthisthesis,weformally characterize the optimal solution for DESS in two specific topologies (tree and ring),. We then show howtheoptimalsolutionforaringmayformabasicbuildingblockforanoptimalassignmentforcyclic graphsusingthegridtopologyasanexample. 49 4.4.1 OptimalAssignmentonSpecificTopologies In this section, we formally characterize the optimal assignment function f (that minimizes the delay diameter D f ) for 2 specific topologies: tree and ring. Using results from simulated annealing on a grid, we also show how an optimal assignment for a ring might form a basic building block of a good assignmentoncyclicgraphs. 4.4.1.1 OptimalAssignmentonaTree Theorem1: Consider a treeT = (V,E). Let the number of slots bek. Let the diameter ofT (in hops)beh(fromnodeatob,say). Thenforeveryslotassignmentf :V → [0,···k−1],D f ≥ hk 2 . Proof: Considerapathbetweentwonodesptoq havingxhops. SinceT isatree,thisistheonly pathbetweenpandq. Consideranarbitraryslotassignmentfunctionf :V → [0,···k−1]. Now, d f (p→q) = x X j=1 d f (i j ,i j+1 ) d f (q→p) = x X j=1 (k−d f (i j ,i j+1 )) Thus, d f (p→q)+d f (q→p) = kx. max{d f (p→q),d f (q→p)} ≥ kx 2 (4.6) This is true for each pair of nodes including a and b. Thus, for every slot assignment function f, D f ≥ hk 2 ,wherehisthediameterofT. Based on theorem 1, the following assignment function f will minimize the delay diameter of the tree T = (V,E) whose hop diameter is h (from a to b): Just use 2 slot values, 0 andd k 2 e. Let d f (a) = 0. Adjacentverticesareassigneddifferentslots(similartoachessboardpattern). Inthiscase ∀i,j : (i,j)∈ E : max{d f (i,j) =d f (j,i)} =d k 2 e. Hence max{d f (a→b),d f (b→a)} =d hk 2 e, which tightly matches the lower bound on the delay diameter of T. Thus, an optimal slot assignment foratreebalancesthedelayineachdirectionalongapathasshowninfigure4.1(a). 50 4.4.1.2 OptimalAssignmentonaRing We first show the optimal assignment for the case where the number of nodesn on a ring is a multiple of the number of slotsk i.e. n = mk. We then present a lower bound for the case when the number of nodesisnotanexactmultiple. Theorem2: Considern =mknodes0,1,···mk−1arrangedonaringintheclockwisedirection. Theoptimalslotassignmentfunctionf isspecifiedasfollows: f(0) = 0.∀i : 1≤i≤mk−1 :f(i) = (f(i−1)+1) mod k. Proof: We will refer to such an f as the sequential slot assignment as it assigns a sequentially increasing slot (modulo k) to the nodes around the ring (see figure 4.7 (a)). We prove theorem 2 by contradiction. For k = 2, it is easy to show that assigning 2 adjacent nodes the same slot incurs a delayof 2inbothdirectionsonthatlink,whileasequentialassignmentwillyieldadelayof 1ineither direction. Hence, we focus on the case wherek≥ 3. For a sequential slot assignmentf, it is easy to showthatthedelaydiameter isgivenby: D f =m(k−1) (4.7) Assumethatthereexistsaslotassignmentfunctionf 0 ,suchthatD f 0 <D f . Intherestoftheproof,we willfocusonthedelayintheringduetof 0 . Consider a block of m links on the ring from node 0 to node m as shown in figure 4.2. Since we assumedthatD f 0 <m(k−1),theshortestdelaypathfromnode0tonodem(andviceversa)mustlie completely within the block. The alternative path hasm(k−1) links each incurring a delay of at least 1(Ifthisalternativepathistheshortestdelaypath,itcontradictsourassumptionthatD f 0 <m(k−1)). This is true for every block ofm links on the ring. Figure 4.3 shows the shortest delay path for nodes withineachofk suchblocks. ∀i : i ∈ [1,k],∀j : j ∈ [1,2], let d i1 be the delay in block i from node (i− 1)m to im, while d i2 be the delay in block i from node im to (i− 1)m as shown in the figure 4.3. We claim that d min = min i,j {d ij }< 2m. Thiscanagainbeprovedbycontradictionasfollows: Considerapathfromnode0tonode k−1 2 m. Therearetwopossibilitiesasshowninfigure4.3: 1. 0→m→ 2m···→ k−1 2 m. Thedelayalongthispathisatleast k−1 2 d min . 2. 0→mk−m···→ k−1 2 m. Thedelayalongthispathisatleast k+1 2 d min 51 Figure4.2: Shortestdelaypathforasingleblockofmlinks. Thus, ifd min ≥ 2m, it contradicts the assumption thatD f 0 < m(k−1). Moreover, since each block hasmlinks,eachincurringadelayofatleast1, m≤d min < 2m Letd min =m+x,wherex∈ [0,m). Considertheblockthathasthelowestdelayd min . Withoutloss of generality, label the starting and ending node in this block asmk−m and 0 as shown in the figure 4.4. Consider a path from node 0 to nodemk−m−x. There are two possibilities as shown in figure 4.4: 1. 0→mk−m→···→mk−m−x. Delayalongthispathisatleastmk−d min +x =m(k−1), whichcontradictsourassumptionaboutD f 0 <m(k−1). 2. 0→m→ 2m···→mk−m−x. Delayalongthispathisgivenby: D ≥ k−2 X i=1 d i +(m−x) ≥ (k−2)(m+x)+m−x ≥ m(k−1)+x(k−3) ≥ m(k−1)(for k≥ 3) (4.8) ThisagaincontradictsourassumptionthatD f 0 <m(k−1). Thus,fortheringwithn =mk nodes,thesequentialassignmentminimizesthedelaydiameter. Forthecasewhenn =mk+t,for0<t<k,theoptimalsolutionisslightlymoreinvolved. 52 Figure4.3: Shortestdelaypathfork blocksofmlinkseach. Figure4.4: Pathsfromnode0tonodemk−m−x Theorem3: For a ring withn nodes wheren = mk +t, for 0 < t < k, the following is a lower boundonthedelaydiameter: D f ≥ (m+1)k−b (m+1)k−y x c (4.9) wheren =mk+t = (m+1)x+y. Firstweprovetwolemmasthatwillbeusedinthetheoremproof. Lemma1: Considern =mk+t,0<t<k. C 1 = P i d f (i,i+1)+d f (n−1,0) =M·k,where i∈ [0,n−1],M≥m+1. Proof: Since, there aremk +t links and the delay on each link under any slot assignment is at least 1,M hastobeatleastm+1. Now, d f (i,j) = (S j −S i )modk = S j −S i ifS j −S i > 0 S j −S i +k ifS j −S i ≤ 0 53 So: C 1 = X i d f (i,i+1)+d f (n−1,0) = (S 1 −S 0 )modk+...+(S 0 −S n−1 )modk = M·k+(S 1 −S 0 +S 2 −S 1 +...+S 0 −S n−1 ) = M·k It is easy to know thatC 2 = P i d f (i,i−1)+d f (0,n−1) = M·k, wherei∈ [1,n],M≥ m+1. C 1 +C 2 = (mk+t)k. Withoutlossofgenerality,letC 1 ≤C 2 ,thenM≤ mk+t 2 . Lemma2: Foranoptimalslotassignment,M =m+1. Proof: Itcanbeshownthatthesequentialslotassignmentwhichassignsasequentiallyincreasing slot(byoneandmodulok)hasadelaydiameterof(m+1)(k−1). WewillshowthatforM >m+1,the delaydiameterwillalwaysbelargerthan(m+1)(k−1). AssumeM =m+2,henceC 1 = (m+2)k. Webreaktheringintoblocksofsizem+2: 0→ 1→ 2...m+1→m+2 1→ 2→ 3...m+2→m+3 . . . mk+t−1→ 0→ 1...m→m+1 Letd i bethesumoftheallthelinkdelaysoftheblockstartingatnodei. mk+t−1 X i=0 d i = (m+2)·C 1 = (m+2)(m+2)k Letd min betheminimumofalld i s,thus: (mk+t)d min ≤ (m+2)(m+2)k d min ≤ (m+2)(m+2)k mk+t d min ≤ m+2+ (2k−t)(m+2) mk+t 54 Consider the block that has the lowest delay d min . Without loss of generality, let d 0 = d min = m+2+xshowninfigure4.5,wherex =b (2k−t)(m+2) mk+t c. Considerthepathfromnodem+2tonode 0. Therearetwopossibilities: 1. m+2→m+3···→mk+t−1→ 0. Thedelayalongthispathis(m+2)k−d 0 . 2. m+2→m+1···→ 1→ 0. Thedelayalongthispathisalso(m+2)k−d 0 . Forbothcase,thedelayDisgivenby: D = (m+2)k−d 0 = (m+2)k−(m+2+x) = (m+1)(k−1)+k−1−x SinceM≤ mk+t 2 ,whenM =m+2: m+2 mk+t ≤ 1 2 Alsobecause0<t<k andk≥ 3: b 2k−t k−1 c≤ 2 So: b m+2 mk+t · 2k−t k−1 c ≤ 1 x =b 2k−t mk+t (m+2)c ≤ k−1 k−1−x ≥ 0 D ≥ (m+1)(k−1) ThuswehaveprovedthatwhenC 1 = (m+2)k,thedelaydiameterwillbeatleast(m+1)(k−1). Similarly, it can be proved that for any M ≥ (m + 2), the delay diameter will be no smaller than (m+1)(k−1). Henceforanoptimalslotassignment,C 1 = (m+1)k. 55 Figure4.5: Pathsfromnodem+2tonode0 Figure4.6: Shortestdelayforxblocksofm+1linkseach 56 Nowwewillcalculatethelowerboundonthedelaydiameteroftheringwhenn =mk+t. Similarly asthecasewhenn =mk,webreaktheringintoblocksofsizem+1showninfigure4.6. n = mk+t = (m+1)x+y (4.10) where0≤y <m+1 For any possible such block of m + 1 links, let d min be the minimum delay. The delay diameter of the ring is (m + 1)k−d min . If we get the maximum value of d min , we then achieve the smallest diameterD = (m+1)k−max(d min ). Since P d i = (m+1)k,wehave: x·d min +d y ≤ (m+1)k d min ≤ (m+1)k−d y x ≤ (m+1)k−y x max(d min ) = b (m+1)k−y x c Thus,thelowerboundonthedelaydiameterD f foranyslotassignmentfunctionf isgivenby: D f ≥ (m+1)k−b (m+1)k−y x c Aslotassignmentthatachievesthislowerboundisillustratedbythefigure4.7(b). Insection4.5,wedescribesomecentralizedanddistributedheuristicsforslotassignmentongeneral topologies. 4.5 HeuristicApproaches From the theoretical analysis, we know that DESS is NP-hard, hence it is unlikely that there exist polynomialtimealgorithmsforsolvingit. Weinsteadproposeseveralheuristicsolutionsinthissection andevaluatetheirperformancethroughsimulationsinsection4.6. 57 Figure 4.7: (a) The sequential slot assignmentf obtained for a ring withn = 8 nodes andk = 4 slots (n = mk). HereD f = 6. (b). A slot assignmentf obtained for a ring withn = 8 nodes withk = 6 using the optimal construction for (n = mk +t). Here D f = 9 which matches the lower bound in equation4.9. 4.5.1 CentralizedAlgorithm Initially,allnodesareassignedthesameslotandthedelaydiameterD ofthenetworkiscomputed. By eitherdeterministicorrandomorder,eachsensornodecalculatesthe delay diameter ofthenetworkfor all possible slot assignments for itself while keeping other nodes’ slots unchanged. If the minimum of the delay diameters of all possible slot assignments d min is smaller than the previous delay diameter (d min < d), the node changes its slot to the one that gives the minimum delay diameter and updates d← d min . If the delay diameter is unchanged, it chooses the new slot or keeps the current slot with equal probability. Otherwise it keeps its current slot unchanged. After all nodes finish this operation, the iteration can be repeated again. The number of iterations depends on limitations on the algorithm duration (which in turn depends upon the size of the network). The pseudo code for the centralized algorithmisshownbelow. AlgorithmCentralized 1. Assignslot0toallnodesinG 2. d =D(G) //delaydiameter of G 3. fori←1ton //numberofiterations 4. foreachnodesinthenetwork 5. fork 1 ←0tok−1 //totalslots 6. ok←slot(s) 7. slot(s)←k 1 8. md←D(G) 58 9. ifd min <d 10. thend←d min 11. minslot←k 1 12. ifd min ==d 13. thenminslot←k 1 with50%probability 14. minslot←ok with50%probability 15. slot(s)←minslot 4.5.2 LocalizedAlgorithms Thecentralizedalgorithmassumescompleteknowledgeofthenetworktopologyandslotassignment. In thissectionwe considersomelocalizedalgorithms in whichasensor nodeonlyknowsthe information storedatitsneighbors. Weproposetwodifferentlocalizedalgorithms. • Local-Neighbor: Anodeknowsonlytheslotassignmentsofitsneighbors. Itchoosesaslotwhich minimizesthemaximumofitsdelaystoandfromitsimmediateneighbors. Thiscanberepeated foracertainnumberofiterations. • Local-DV:ItsworkingissimilartoDistanceVectorroutingtechniques. Eachnodemaintainstwo Distance Vector tables: a forward tableFDV which stores its shortest delays to all other nodes and a backward table BDV which stores its shortest delays from all other nodes. These two tables can be calculated using the basic Bellman-Ford technique. A sensor node also knows the DVtablesofitsdirectneighbors. AsensornodecalculatestheDVtablesforallpossiblenewslot assignments for itself. Let the maximum value of entries in the sets of the two DV tables over all possible slot assignments bemaxd. The node will choose the slot which gives the minimum maxd. ThepseudocodesofLocal-NeighborandLocal-DVareshownbelow. AlgorithmLocal-Neighbor 1. EachnodesgettheslotsofitsdirectneighborN(s) 2. mind←MAX VALUE 3. fork 1 ←0tok−1 //totalslots 4. slot(s)←k 1 5. fd(s,t)←delayfromstotinN(s) 59 6. bd(s,t)←delayfromtinN(s)tos 7. maxd←max(fd,bd) 8. ifmaxd<mind 9. thenmind←maxd 10. minslot←k 1 11. slot(s)←minslot AlgorithmLocal-DV 1. EachnodescalculateDVtablesFDV,BDV 2. GettheFDV,BDV ofitsdirectneighborN(s) 3. mind←MAX VALUE 4. fork 1 ←0tok−1 //totalslots 5. slot(s)←k 6. updateFDV,BDV 7. maxd←max(FDV,BDV) 8. ifmaxd<mind 9. thenmind←maxd 10. minslot←k 1 11. slot(s)←minslot 4.5.3 Randomization The simplest slot assignment is to just randomly choose a slot for each node once. In a dense network whereanodehasalargenumberofneighbors(wheremultiplepathsareavailableforanypairofnodes), thereisahighprobabilitythatthisassignmentmayleadtoashortdelaypath. Wecallthisdecentralized random slot assignment as Random-Average. The performance of this method is evaluated by the expectedvalueofthedelaydiameter. Therandomizedslotassignmentcanalsobedoneinacentralized manner. We refer to this centralized version as the Random-Minimum strategy. After a certain number of iterations of choosing random slots for all the nodes, this strategy chooses the assignment that gives theminimumdelaydiameter andthendeploystheslotassignmentinthenetwork. Whilealltheaboveheuristicscanbeusedforanytopology,wenextproposeaspecializedheuristic forthegridthatexploitsthestructureofthetopology. 60 Figure 4.8: Concentric ring allocation for a grid of 4×4 nodes withk = 5. The dotted lines illustrate theconcentricringsateachlevel. 4.5.4 ConcentricRingfortheGridtopology Webelievethattheoptimalassignmentonaringcanserveasabasisforalowlatencyassignmentona gridthatcanbeviewedasasetofconcentricringswithinterconnectingbridges. Theoutermostringis givenasequentialassignmentgoingintheclock-wisedirectionstartingat0. Foreveryotherring,aslot assignmentischosenthatoffersthebestdelaydiameter forthatring. Anexampleofthisassignmentis showninfigure4.8 4.6 SimulationResults Inthissection,weevaluatetheperformanceoftheheuristicalgorithmsonthegridtopology(insection 4.6.1) and random topology (in section 4.6.2) through high level simulations. Since the current study focuses on comparing the delay diameter only across these heuristics, even the distributed algorithms are simulated in a centralized manner (without analyzing their overhead). We also assume that the numberofslotsk isdictatedbythedutycyclingrequirementsoftheapplication. 4.6.1 GridNetwork Firstweevaluatedthesixschemesonagridtopology: Centralized,Local-DV,Local-Neighbor,Random- Avg, Random-Min and Concentric Ring. To have a fair comparison, the centralized and the two local schemeshadthesamenumberofiterationI = 20whiletherandomalgorithmsranforI×k times. 61 Figure4.9: Thedelaydiameter oftheheuristicalgorithmsversusgridsizeforthenumberofslotsfixed atk = 15. ThegridisgivenasX×X. Figure 4.10: The delay diameter of the heuristic algorithms versus the number of slots (k) for a fixed gridsizeof9×9. 62 Figure 4.11: The delay diameter of the heuristic algorithms versus the number of slots (k) for nodes randomlydeployedina10×10area. Thetransmissionrangeis2. Figure 4.9 shows the results for different grid sizes while the number of slots k is fixed at 15. By exploiting the structure of the grid, concentric ring has the best performance compared to all other schemes. The centralized scheme is slightly worse than the concentric ring at small grid size but is about2timesworsethanconcentricringwhengridsizeislarge. Boththerandomizedschemesperform worse than the centralized algorithm with Random-Min doing better than Random-Avg. Moreover the twolocalizedalgorithmsalsoseemtoperformpoorlycomparedtothecentralizedone. Thisispossibly because of the fact that the delay diameter of a network being a global property, the local optimization schemesdonotconvergetotheglobaloptimum. Overall,wefindthatthecentralizedschemecanreduce the delay diameter of random schemes by about 50%, while the concentric ring can provide a further reductionofabout50%. Althoughk should be decided by the duty cycle requirement of applications, it is interesting to see its impact on the delay diameter. Figure 4.10 shows the results for different values ofk while the grid size is fixed at 9×9. Clearly, the delay diameter increases almost linearly with the number of slotsk. Concentric ring performs the best while local schemes perform the worst. We further evaluated these schemes on a larger grid with 20× 20 nodes and values ofk up to 20. We observed similar trends in performance. 4.6.2 RandomNetwork We also tested the five schemes (excluding the Concentric Ring heuristic) on a network with randomly deployedsensornodes. 63 Figure 4.12: The delay diameter of the heuristic algorithms versus the number of slots (k) for nodes randomlydeployedina3×33area. Thetransmissionrangeis2. Figure 4.13: The delay diameter of the heuristic algorithms versus the radio transmission range for nodesrandomlydeployedina10×10area. Numberofslotsisfixedatk = 10. 64 Figure 4.14: The delay diameter of the Random-Min algorithm versus radio transmission range for nodesrandomlydeployedina10×10areawithN = 50andN = 100. Thenumberofslotsk = 10. Firstwefixedtheradiotransmissionrangeat2. Figure4.11and4.12showtheresultwith100nodes uniformlydistributedina10×10squareanda3×33rectangle. Inbothcases,thecentralizedscheme performs best, followed by Random-Min. It is interesting to note that in the random network, Local- Neighbornowhasasmaller delay diameter thanRandom-Avg. Inthe 3×33area,theLocal-Neighbor performs quite well even on comparison with the Random-Min scheme. We believe this is not because Local-Neighbor perform better but because Random schemes perform worse in a random graph. In a grid, each internal node has 4 direct neighbors. In a random graph, however there is a probability that some nodes are bottlenecks (nodes through which several paths go through). An improper slot assignmentforsuchabridgenodemayhurtthedelaydiametersignificantly. Ina3×33longrectangle, theprobabilityofanodebeingabridgebecomeshigher,whichislikelythereasonthattheperformance of Local-Neighbor is closer to the Random-Min scheme. This intuition is also backed by figure 4.14 which shows the delay diameter obtained by the random schemes with 50 and 100 nodes. With 100 nodes, the density and the average degree of the network increases, the random schemes have better performance because of the increased number of paths between any pair of nodes (and hence fewer bottlenecks). Figure 4.13 shows the effect of the radio transmission range R on the delay diameter. As R in- creases,thedelaydiameterdecreases. ThisisbecauseanincreaseinRdecreasesthegraphdiameter(in hops). 65 Thus, for the single schedule case, where each node chooses exactly one of thek slots to wake up, we have presented several heuristics in section 4.5 and evaluated them through simulations in section 4.6. 4.7 Discussion In this chapter we have addressed the important problem of minimizing communication latency while providing energy-efficient periodic sleep cycles for nodes in wireless sensor networks. The objective is to minimize the latency given the duty cycling requirement that each sensor has to be awake for 1 k fractionoftimeslotsonanaverage. Forthesinglewakeupschedulecase,whereeachsensorcanwake up at exactly one of the k slots, we have provided graph-theoretic problem formulations for arbitrary all-to-all(DESS)aswellasweightedcommunicationpatterns(ADESS).Wealsoprovedthatboththese problemsareNP-hard. WethenfocusedontheDESSproblemandderivedandprovedoptimalsolutions for two special cases, viz. the tree and ring topologies. For arbitrary topologies, we proposed several heuristics and evaluated them through simulations. These simulations reveal several interesting obser- vations: thatpurelylocalizedheuristicstendtoperformworsethansimplerandomizedslotallocations, thatourcentralizedschemecanprovidedelayreductionsofaround50%overrandomizedschemesand thatspecializedheuristics(thatexploitthetopologicalstructure)liketheconcentricringforthegridcan provideadditionalgains. Further, we showed that by carefully choosing multiple wake up slots, one can obtain significant savings in the latency at the same duty cycling. Using this technique, we propose algorithms with provable guarantees on tree, grid and arbitrary graphs. These results obtained from an algorithmic perspective are novel and quite different from prior work in this area which has focused primarily on intuitiveMACprotocoldesigns(suchasS-MAC[60],T-MAC[26],andourownworkonD-MAC[46]). 66 Chapter5 MLSR:MinimumLatencyJointSchedulingandRouting 5.1 Overview In the last chapter (DESS), we investigated the problem of minimizing the worst case communication latency for arbitrary all possible source-destination pairs while each node has a fixed duty cycle. In manysensornetworkapplicationscenarios,typicalcommunicationpatternsarefromsensorssourcesto severallimitednumberofbasestations. Allsinksaresame,whichmeansapacketcanberoutedtoany oneofthesink. Alsoatanyspecifictime,notallsensornodeshavepacketstosenttothebasestations. So it is not necessary to minimize the worst case latency for arbitrary all-to-all communication pairs. Instead,weneedonlyoptimizefortheexistingflows. Anexampleisshowninfigure5.1 Thebestwaytosaveenergyistoputanodetosleep. However,anodethatisoffisunabletodeliver thesensordatatothebasestations. Thiscreatesafundamentaltrade-off. Astheflowsinsensornetwork arelikelytobepredictablelong-lived,wecouldscheduletheon-offactivityofthesensornodesthatcan wakeuptohelpdeliverthesensordatareportsintimeandgotosleeptosaveenergyotherwise. Puttingnodestosleepaffectsanotherimportantcommunicationlayer: thenetworklayer. Anodein sleep is no longer part of the network. Therefore, by the sleep scheduling, the topology of the network keeps changing at different times. A link between two neighboring nodes is available only if both of them are scheduled to be active at the same time slot. The paths selected by the routing algorithm also affects latency and power consumption. Different links could have different latency depending on the scheduled sending and receiving slots of the nodes. A shortest hop path may not be the path with shortestlatency. Thus, given certain source nodes and base stations in a sensor network, there are two key design considerations: one is the scheduling, the other is routing. Those two are closely coupled together and willaffecteachother. Forexample,infigure5.1,nodeJneedstoallocatetimeslotsfordatareportsfrom 67 Figure5.1: Adatagatheringapplicationinawirelesssensornetwork. GandI.HoweverifnodeIchangesitsnexthoptoothernodeoritdoesnotgenerateanymorereports, thennodeJonlyneedstoscheduleslotsforreportsfromG.Therearethreepossibleapproaches: 1. Schedulingfirst: Determinetheschedulesofthesensornodesfirst. Basedontheschedules,using aroutingalgorithmtofindanenergyefficientandlowlatencypath. 2. Routing first: Using a routing algorithm to find a path first. Given the path, find the schedules of thenodesonthepath. 3. Jointschedulingandrouting: findthescheduleandroutingsolutionjointly. Both scheduling first and routing first scheme have their disadvantages. Scheduling first schemes may causeroutingschemehardtofindshortpathswhileroutingfirstschemesmaycauselowlatencysched- ule impossible. In this chapter, we will discuss the joint scheduling and routing approach. Particularly, weareinterestedinfindingpathsandschedulesthatachievetheminimumaveragelatency. Weassume that energy efficiency will be provided automatically by the schedule, as nodes only wake up when neededandasleepduringothertimes. Thisisclearlyanissueoffundamentalsignificanceintheareaof wirelesssensornetworks,andtoourknowledgehasneverbeeninvestigatedbefore. 5.2 SchedulingandRoutinginWirelessSensorNetwork 5.2.1 ApplicationScenario Broadly speaking, there are two kinds of applications in sensor networks: event driven and continuous monitoring. In event driver sensor network, most of the time the sensor nodes are off until certain interestingeventhappens. Thenthenodesbegintosenddatatobasestation. Inacontinuousmonitoring 68 sensornetworks,sensornodessampleandtransmitdataatregularintervalsrequestedbythebasestation. In both kinds of applications, at any specific time, only certain nodes are source nodes that need to sampleenvironmentandreporttobasestation. Weneedtofindpathsandschedulesofthenodesonthe paths,inwhichtheaveragelatencyofalltheactiveflowsareminimized. Wefirstdescribethebasicapplicationassumptions. 1. Radio: Considerastaticwirelesssensornetwork,allnodesareequippedwithasingleradiowith omni-directionalantennas. Thetransmissionpoweranddataratearefixed. 2. Synchronization: None of the discussion about TDMA link scheduling would be relevant if therewerenotsomemechanismtoprovidetimesynchronizationinthesensornetwork. However, techniques capable of providing micro-second level synchronization have been developed for sensornetworks[27,39,40]. 3. TDMA time slots: Time is divided into equal sized slots that are long enough for one packet transmissionandgroupedintoframes. Thusapacketmaytravelatmostonehopinasingleslot. SomeworksonTDMAfocusonminimizingthelengthoftheframesubjecttotheconstraintthat every node or link is assigned at least one slot. In this work, however, the latency is not affected bytheframelengthbutthesleeplatencycausedbythescheduling. 4. Sources: Certain sourcenodes sample theenvironment periodically. The period canbe different for different source nodes. Each node generates certain number of packets of fixed length which needtobetransmittedinoneTDMAframe. 5. Sinks: There are several sink nodes in the network. A sensor report can be delivered and only needtobedeliveredtoanyonesink. 6. GraphAbstraction: SimilartotheassumptioninDESS,weassumethewirelessnetworkcanbe abstractedintoagraph. 7. EnergyConservation: SameasinDESS,weassumethemajorenergyconservationcomesfrom turningradiooff. 8. Interference: We will consider two different interference models: FDMA-based multiple chan- nelsandsinglechannel. 69 Figure5.2: Twoschedulingandroutingschemesinwirelesssensornetworks. 5.2.2 RoutingandScheduling In sensor networks with light traffic load, putting nodes to sleep (where sensors turn off their radios when not needed) is a very useful technique for reducing the energy consumption due to idle listening. WeuseK asaparameterthatindicatesthenumberofslotsinaTDMAframe. TheK isbigenoughthat allperiodicallyreportwillhaveatleastonereporteveryK slots. Ineachslot,theradioisinoneofthe three states: transmitting, receiving or free. Radio should be put to sleep in free state to save energy. If anodehastoforwardapackettoitsneighbor,itneedtofindaslotthatboththeneighboranditselfare free. Thentheslotinthesenderismarkedastransmittingandmarkedasreceivinginthereceiver. This conservestheenergyofboththetransmittingandthereceivingnode. Wedonotconsiderslotsreserved forroutingsetupandneighbordiscovering. LetG = (V,E)beanarbitrarygraph. LetP m bethepathforflowmfromasourcetoasink. Letf denotes the slot assignment. For a given nodei, letR i m andS i m denote the receiving and transmitting slotsofnodeiforflowm 1 . Clearly,R i m andS i m determinethedelayincurredintransmittingdatafrom onenodetotheother. Letd m (i,j)bethedelayintransmittingdatafromitoj where(i,j)∈E: d m (i,j) = S i m −R j m (ifS i m −R j m > 0) (S i m −R j m )+K(otherwise) (5.1) DelayonapathP m undertheslotassignmentisdefinedas d(P m ) = X (i,j)∈Pm d m (i,j) (5.2) 1 S i m = R i m 70 (a) Schedulingandroutingfor1stflow (b) Onepossibleschedulingandroutingfortwoflows (c) Abetterschedulingandroutingfortwoflows Figure5.3: Exampleofschedulingandroutingfortwoactiveflows. 71 As seen from the above discussion, the end-to-end delay for flow m depends on both the path and theslotassignment. ActiveFlowsCommunication: Forasensornetworkapplication,atanyspecifictime,notallnodes have sampling data to report to the base station: there are only a limited number of active flows in the network. Here,itwouldbeofinteresttominimizetheaveragedelayoftheactiveflowsinthenetwork, whichisdefinedasfollows: Definition5: Average Delay (D avg P,f ): For a given graph G = (V,E), number of slots k, a slot assignmentfunctionf andpathsP forM flows,the average delayisdefinedas P m∈M d(P m ),where d(P m ))isthedelayalongthepathP m underthegivenslotassignmentfunctionf. Inactiveflowscommunication,ourdesigngoalisthefollowing: Definition6: Minimum Latency joint Scheduling and Routing (MLSR) Given a graph G = (V,E), the number of slots k and M flows, find a path P m for each flow, and an slot assignment functionf thatminimizestheaveragedelay(D avg f )i.e. f = arg min P 0 ,f 0 {D avg P 0 ,f 0 } (5.3) Figure5.2showsanexampleofseparateroutingandschedulingsolution. Whenthereisanewflow request,theroutingalgorithmwillfindaroutefirst,thenonthegivenroute,ifascheduleisachievable, thefollowingdataforwardingwillusetherouteandschedulingtoforwarddatareport. Ifthescheduling processfails,thentheroutingalgorithmisaskedtofindanewroute. Figure 5.3 shows an example of scheduling and routing for two active flows. In figure 5.3(a), first there is only one active flow. If we run a shortest hop routing algorithm, it will find the path of A→ B→ C → D→ E→ Z. A schedule can be assigned on the nodes on the path. The delay is 8. If using the link delay as the weight of the link, however, shortest path routing algorithm now select A→ B→ C→ H→ I→ J→ Z which has a latency of only 6. Now assume there is another flow request from node F to node Z. Suppose the flow want to use routeF→ G→ I→ J→ Z. However at link (i,j), there is no slot that bothi andj are free, so the flow is forced to choose routeF→ G→ K→ L→ M→ N→ Z which has a delay of 8. So the total delay for the two active flows is 14 in figure5.3(b). However,asshowninfigure5.3(c),ifsourceAuserouteA→B→C→D→E→Z and source F use routeF→ G→ I→ J→ Z. A schedule can be achieved with total delay of only 12. Thisexampleshowsthatlatencyreductionbyjointschedulingandrouting. Intuitively,inMLSR,theobjectiveistocoloragraphwiththegivenK colorssuchthatthedesired global objective (minimizing the delay diameter in the former and the average delay diameter in the 72 Figure5.4: DelayGraph: Link Figure5.5: DelayGraph: Network latter)isachieved. Thereadermayperceiveaconnectiontothewell-knownNP-completegraphcoloring problem[37],whichdealswithminimizingthenumberofcolorsneededtoensurethatnotwoadjacent verticesarecoloredthesame. However,akeydifferencebetweenthegraphcoloringproblemandMLSR isthattheformerisessentiallyaboutalocalconstraint(adjacentverticesrequiringdistinctcolors),while the latter is inherently more global in nature: adjacent vertices may share the same slot assignment but themaximumoftheshortestdelaypathsbetweenallpairsofnodesmustbereduced. 73 5.3 MinimumLatencyJointSchedulingandRouting 5.3.1 DelayGraph SupposethereareM sourcenodesandN sinks. ThenumberofslotsperTDMAframeisK. Wecreate aDelayGraphasfollowing: 1. For each sensor nodeu, create 2K graph nodes. The firstK nodes represent the receiving slots of sensor node,R i u , which means nodeu receiving a packet at sloti from the previous hop. The second K nodes represent the transmitting slots of the sensor node, S i u , which means node u transmittingthepacketatslotitothenexthop. 2. Fromtheeachreceivingnodeofu,R i u ,addalinktoalltransmittingnodesofu,S j u exceptj =i. Thedelayofthelinkisdecidedbyequation5.1; 3. If two sensor nodes u and v can communicate with each other, create a graph link from each transmitting node of u, S i u to the corresponding receiving node of v, R i u , which means node u transmitsapackettov atsloti. Assigntheweightofthelink1. 4. Add a super sink graph nodePZ. Add a link from each receiving nodesR i Z(n) of sinkZ(n) to PZ. Assigntheweightofthelink1. 5. Add a graph node PA(m) for each source sensor node A(m), which is called pseudo source node. Add a graph link from PA(m) to each receiving node R i A(m) of A(m), with link delay weightof1. IfasourcehavemorethanonepackettosendperTDMAframe,treateachpacketas adifferentsource. 6. Add a super pseudo source graph nodePS. Add a directed link fromPS to eachPA(m) with linkdelayweightof1. Figure 5.4 shows how to split a node to 2K nodes in the delay graph and the connection between twonodes. Figure5.5showsanexampleofacompletedelaygraphwithtwosourceswhilesourceA(1) havetwopacketsperframe. 74 5.3.2 FDMAinterferencemodel In this section, we consider the joint scheduling and routing problem under the FDMA interference model. Each link can use a FDMA channel for communication. We assume that the number of chan- nels is large enough so that any two links within interference range are assigned two different FDMA channel. Inthismodel,theconstraintsontheradioarethat: 1. Withasingleomni-directionalantenna,nonodecantransmitorreceivedataatthesametime. 2. Anodecannottransmitdifferentpacketstodifferentreceiversatthesametime. 3. Anodecanonlyreceiveapacketfromasinglesenderatonetime. Wealsoassumenonodewillbroadcastasinglepackettomultiplereceivers. Thereforeeachsendercan onlyhaveonereceiver. FirstweconsidertheproblemoffindingM node-disjointpathsonthedelaygraph. Wecanmapthe M node-disjointpathsonthedelaygraphtotheminimumlatencyjointschedulingandroutingsolution forM sources. Proposition4: The minimum weightM node-disjointpaths in the delay graphcan bemapped to a minimumlatencyjointschedulingandroutingsolution. Proof: Firstweexplainhowtogetarouteandschedulefromthenode-disjointdisjointpath. Sup- poseoneoftheM node-disjointpathis P m . Assumethenodesthepathgoesthroughare:PS,PA(m),R i1 A(m) ,S j1 A(m) ,...,R iu u ,S ju u ,R iv v ,S jv v ,...,R i Z(n) Z(n) ,PZ. Itiseasytoknowthatj u ==i v . TheroutefortheflowmthenisA(m),...,u,v,...Z(n). Theschedule of nodeu on the route is to wake up to receive packet ati u and send it atj u . Atj u , nodev is wake up toreceivepacketandv willforwardittothenexthopattimej v . Then we need to prove that the schedule we get satisfy the three constraints of the radio. It is clear that no node can transmit and receive at the same time since there is no link in the delay graph from a node’s receiving node to its transmitting node that has the same slot. A node will not be scheduled to transmit different packets to different receivers at the same time, otherwise it will violate the node- disjoint rule. A node can also receive a packet from a single sender at the one time because of the node-disjointrule. Finally,thesumoftheweightsoftheM node-disjointpathscanbeinterpretedasthetotaldelayof M pathsdirectly. Thusthejointschedulingandroutingsolutionisoptimalintermsoflatency. References [81, 84] propose algorithms to findM node-disjoint paths with minimum total weights (here denotes delay) is minimized. We can apply the algorithms directly on the delay graph. We first 75 Figure5.6: Anexampleoffindingminimumlength2nodedisjointpaths. briefly describe the algorithm. Figure 5.6 shows an example. We can simply use any shortest path algorithm to find the first minimum weight node disjoint path froma toz, wherea is the super pseudo source node, andz is the pseudo sink node. We assumeP M is a given optimal set of M node-disjoint paths in delay graph DG. Now we need to find optimal (M + 1)th node-disjoint paths P M+1 , as follows: 1. Reverse the direction of each edge onP M , and make its length negative. These edges are called negativearcs. Otheredgesarecalledpositivearcs. 2. Split each vertex v on P M into two nodes v 1 and v 2 , joined by an arc of length zero, directed towardsa. Assignoutputlinksonv 2 andinputlinksonv 1 . 3. Findashortestpathfromatoz onthistransformeddelaygraph. Wecallthispathaninterlacing S,whichmaycontainbothpositivearcsandnegativearcs. 4. letP M +S represent the graph obtained by adding toP M the positive arcs ofS, and removing fromP M thenegativearcsofS. ThisiscalledAugmentation,whichresultsintheoptimalP M+1 paths,theminimumweightM +1node-disjointpaths. Wepresentalemmathatwillbeusedinthefollowingproofs. Lemma3: The output of the augmentation of P M +S is a set of minimum weight M + 1 nod- disjointpaths: P M+1 =P M +S. Weomitproofshere. Interestedreaderscouldsee[81,84]fordetails. Theauthors[81,84]onlyproposedalgorithmtocomputeP M+1 fromP M . Thiscanbeextendedto computeM−1node-disjointpathsfrom M node-disjointpathasfollows: 1. Reverse the direction of each edge onP M , and make its length negative. These edges are called negativearcs. Otheredgesarecalledpositivearcs. 2. Split each vertex v on P M into two nodes v 1 and v 2 , joined by an arc of length zero, directed towardsa. Assignoutputlinksonv 2 andinputlinksonv 1 . 76 Figure5.7: Anexamplenetworkwithoriginalarc-length 3. Findashortestpathfromz toz onthistransformeddelaygraph. Wecallthispathaninterlacing rS,whichmaycontainbothpositivearcsandnegativearcs. 4. letP M +rS represent the graph obtained by adding toP M the positive arcs ofS, and removing fromP M thenegativearcsofS. ThisiscalledAugmentation,whichresultsintheoptimalP M−1 paths,theminimumweightM−1node-disjointpaths. Lemma4: Theoutput ofthe augmentation ofP M +rS isa setof minimum weightM−1 node- disjointpaths: P M−1 =P M +rS. Proof: Suppose we computeP M fromP M−1 by augmentation of an interlacingS. Suppose the original graph is G. According to [81], in an equivalent graph G 0 of G, P M−1 contains all negative links ofG 0 and all links onS have 0 length. In the link reversed graph ofG 0 ,G 0 M , the exact reverse of S,rS havethesmallestweightof0. ByaugmentationofP M andrS, we will getP M−1 . Itispossible there are other reverse interlacing with length 0, but the result P M−1 has the same total length. Thus theaugmentationofP M +rS isasetofminimumweightM−1node-disjointpaths. 5.3.3 MLSRunderTrafficchange The algorithm in reference [81] is aimed to find M node-disjoint path from the beginning. In a real sensor network application, however, flows can appear or disappear dynamically and randomly. The overhead to re-run the whole algorithm whenever there is a change of existing flows is high and also 77 Figure5.8: Anexamplenetworkafternode-splittingandlinkreverse. hard to implement. We propose an extension of the algorithm that is able to work on the newly added floworremovedflow. 5.3.3.1 AddingaFlow GivenaDelayGraphandM existingflows,supposewealreadyhaveminimumlatencyM node-disjoint paths. For each source added, we add a pseudo source node in the Delay Graph and connect the super pseudosourcenodetoit. ThenwetrytoconstructaninterlacingonthenewDelayGraphandinterpreted it to construct M + 1 node-disjoint paths. The paths found maybe different from the paths found by rerunthewholealgorithmontheDelayGraphfrombeginning,butthelatenciesaresame. In general, the new source could be a new source node or an additional report slot request from an existing source node. Without loss of generality, suppose there is a new source node A that needs to reporttosinks. AddFlowAlgorithm: 1. Add a pseudo source nodePA for source nodeA. Create links fromPA to each receiving node orpacketgeneratednodeofA,R i A withlinkdelay1. Alsocreatealinkfromsuperpseudosource nodePS toPA. 2. Assign the link (PS,PA) a very large weight which assure that any path use this link will have longerdelaythanthepathwithoutusingit. 3. FindaminimumlengthinterlacingS,fromPS toPZ. 78 4. ByP M +S,wegetP M+1 minimumlatencypaths. Proposition5: AddFlowalgorithmreservesoptimality. Proof: We will prove it by induction. Suppose we have M optimal paths P M . Now a new source nodeS i start to generate packets. We add a pseudo source nodePS i and the necessary links as describedinthealgorithm. WecallthisdelaygraphG. Thenweassignaverylargeweightβ tothelink of (PS,PS i ). We call the new graphG 0 . Asβ is large enough that the path using this link always has lengthlargerthananyotherpath. ThusP M remainsoptimalinG 0 . Therefore,wecanstillusealgorithm in[81]togetP M+1 inG 0 fromP M . NowwewanttoprovethatP M+1 isalsooptimalinG. First the links fromPS to all other pseudo source nodesPS i must be inP M+1 as those nodes are the only M + 1 out neighbors of PS. Second, let us consider only the paths from all PS i to pseudo sink nodePZ. These paths are optimal inG 0 and remain optimal inG. Therefore theM +1 optimal pathsinG 0 arestilloptimalinG. Thiscompletestheproof. 5.3.3.2 RemovingaFlow Removing a flow from the M flows is different. We will construct a shortest length interlacing that originatedfromthepseudosinknodetothesuperpseudosourcenode. Weremovealllinksfromsuper pseudosourcenodetothepseudosourcenodes,excepttheonethatwewanttoremove. Afterinterpret the interlacing with the existingk node-disjoint paths, only K−1 paths remains, which is a minimum latencyk−1 node-disjoint paths. Suppose we need to remove the flow originated from source node i; itspseudosourcenodeindelaygraphiss i . RemoveFlowAlgorithm: 1. Assign the link from PS to other pseudo source nodes except PS i a very large weight β such thatanypathusing(PS,PS i )issmallerthanthepaths. 2. Reverse the direction of each edge onP M , and make its length negative. These edges are called negativearcs. Otheredgesarecalledpositivearcs. 3. Split each vertex v on P M into two nodes v 1 and v 2 , joined by an arc of length zero, directed towardsPS. Assignoutputlinksonv 2 andinputlinksonv 1 . 4. FindashortestpathfromPZ toPS onthistransformeddelaygraph,whichisareverseinterlac- ingrS. 79 5. letP M +rS representthegraphobtainedbyaddingtoP M thepositivearcsofrS,andremoving fromP M thenegativearcsofrS. ThisiscalledAugmentation,whichresultsintheoptimalP M−1 paths,theminimumweightM−1node-disjointpaths. Proposition6: The output of the augmentation of P M +rS is a set of minimum weight M− 1 nod-disjointpaths. Proof: Similarly we can prove the algorithm by induction. It is clear that the output of the augmentation is a set ofM−1 node-disjoint path. So we only need to prove that it has the minimum weight. letW P M be the sum of the weights of all the links onP M andW S be the sum of the weights of all the links on S. The negative arcs on S will be removed from P M +S, with negative length. The same arc (with reverse direction) is on P M with positive length. The sum of these two links is zero. Positive arcs on S will be added from P M +S, which is not in P M . Thus it is easy to get that W P M +S = W P M +W S . SinceS is the shortest path fromPS toPZ on the transformed delay graph, W P M +S hastheminimumweight. ThustheaugmentationofP M +S isasetofminimumweightM+1 node-disjointpaths. It isalso clear that rS must usethe link (PS i ,PS), thus theflow willbe removed fromthepaths. 5.3.4 MLSRunderTopologychange Thebasicalgorithmintheprevioussectionassumesthatthenetworktopologyisstaticwhilethek dis- joint paths are discovered. In this section, we generalize this approach to a network that is undergoing constant topological changes. For instance, a mobile node can simply walk away from the communi- cation network or a link is under strong interference in a harsh environment. We model such changes by link failures. Note that node failures can be modeled as a special case of a certain set of link fail- ures. That is, if nodev were to fail, this event can be modeled as the failure of all links adjacent tov. Besides link failures, new sensor nodes may be put into the field when there are not enough old nodes available for the application. Or an environmental noise disappeared so a link between two nodes is nowavailable. Wemodelsuchchangesbylinkjoins. When link failures or link joins happen, the topology of the network changed. If a failed link is currentlyused bythe oneof thek minimumlatency disjointpaths, theflow usingthis path isunable to transmit the report. If a new link joins, the existingk disjoint paths may no longer have the minimum latency. Underbothsituations,anewsetofkminimumlatencydisjointpathsneedtobecomputed. One way is to recompute thek disjoint paths from beginning on the new topology. However, the overhead 80 ishighiftopologychangeshappenfrequently. Sameastheflowchanges,weproposealgorithmswhich can adjust the existing k disjoint paths incrementally with only two computation of the shortest path algorithm. When a link e = (u,v) currently used by one of the P M path failed, a new set of P M is needed. Assumeeisusedbysources i andthepathispi. Theideaistofirstremovetheflow1togetminimum latencyM−1 node disjoint pathP M−1 without using the failed link, then construct a new set ofP M paths. Thestepsofthealgorithmarefollowing: LinkFailureAlgorithm: 1. Reverse the direction of each edge onP M , and make its length negative. These edges are called negative arcs. Other edges are called positive arcs. Failed link e = (u,v) now becomes e 0 = (v,u). 2. Split each vertex v on P M into two nodes v 1 and v 2 , joined by an arc of length zero, directed towardsPS. Assignoutputlinksonv 2 andinputlinksonv 1 . 3. Find a shortest path fromPZ tov on this transformed delay graph. This is a reverse interlacing rS 1 . 4. Find a shortest path fromu toPS on this transformed delay graph. This is a reverse interlacing rS 2 . 5. letP M +rS 1 +rS 2 +(v,u) represent the graph obtained by adding toP M the positive arcs of rS, and removing fromP M the negative arcs ofrS. This is called Augmentation, which results intheoptimalP M−1 paths,theminimumweightM−1node-disjointpathswithlink e = (u,v) removed. 6. Using algorithm described in section ”adding a flow” to construct a new set of P M minimum latencynode-disjointpath. ForLinkJoinAlgorithm,supposethenewlyjointlinkise = (u,v). LinkJoinAlgorithm: 1. Reverse the direction of each edge onP M , and make its length negative. These edges are called negativearcs. Otheredgesarecalledpositivearcs. Thenewlyaddedlinkis(u,v). 2. Split each vertex v on P M into two nodes v 1 and v 2 , joined by an arc of length zero, directed towardsPS. Assignoutputlinksonv 2 andinputlinksonv 1 . 81 3. Find a shortest path fromPZ tou on this transformed delay graph. This is a reverse interlacing rS 1 . 4. Find a shortest path fromv toPS on this transformed delay graph. This is a reverse interlacing rS 2 . 5. Let P M +S 1 +S 2 + (u,v) represent the graph obtained by adding to P M the positive arcs of S, and removing fromP M the negative arcs ofS. This is called Augmentation, which results in the optimal P 0 M−1 paths with (u,v), the minimum weight M + 1 node-disjoint paths with link e = (u,v)added. 6. ComputeP 00 M−1 byRemovFlowalgorithmwithoutlink(u,v). 7. UsethesmallerofP 00 M−1 orP 0 M−1 asP M−1 tocomputeP M . 5.3.5 Otherissues 5.3.5.1 Energyefficiency 1. Energy efficiency: The energy savings are achieved by the schedule of the nodes; that is, nodes areon onlywhennecessaryto deliver thepacketand asleep otherwise. However, sinceour algo- rithm aims to minimize the latency, the route may take longer hops than a minimum hop routing algorithm. However, the energy saving by the schedule is more significant than the possible energycostbyextranumberofhops. 2. Loadbalancing: Althoughouralgorithmdoesnottakeloadbalancingintodirectconsideration, the algorithm will naturally achieve load balancing since a heavy loaded node is more likely to havehighdeliverylatency,andishenceavoidedbythealgorithm. 5.3.5.2 Distributedsolution Thealgorithmcanbeeasilyimplementedinadistributedmanner. Theonlyoperationneededintheal- gorithmistofindtheshortestpathbetweensourceandsink,withpossiblenegativeweights(nonegative cycles). DistributedversionsofBellman-Fordalgorithmcanbeemployeddirectly[89]. Bellman-Ford algorithm has been used widely in Internet, known as the Distance Vector routing algorithm specified in [86]. In the decentralized implementation in Internet, each node periodically broadcasts its routing tables, which contains the cost from itself to all other nodes, to all its neighbors. A router updates its own routing table according to the routing tables of its neighbors. The algorithm 82 willconvergetotheoptimalsolutionaftercertainnumberofiterations. Eachnodethenknowsthenext hoptoforwardapacketbyitsroutingtable. AODV[88],AdhocOndemandDistanceVector,isanon- demand routing protocol for wireless multi-hop networks, that is able to find the shortest path between two nodes based on Bellman-Ford algorithm. Thus in this work, we assume that distributed version of shortest path algorithm is available. Since we assume that traffic flows are long lived, the overhead of distributedBellman-Fordalgorithmcanbeignored. 5.3.6 Heuristicsolutions Wewillcomparetheperformanceofouralgorithmswiththefollowingtwosimpleheuristicsolutions. 1. Naive Dijkstra algorithm: This algorithm is a very basic algorithm that finds the link disjoint paths. It entails running Dijkstra’s shortest path algorithm k times on the Delay Graph G, where aftereachrun,linksbelongstothelastpathfoundareremoved,ensuringlink-disjointnessamong thek paths. A new Dijkstra’s shortest path is found each time a new flow is added. When a flow ends, links belonging to the path of the flow is recovered. When a link is broken, if it is used by one of the path, the path will be removed and then a new path is computed for that source. Nothingisdoneifanewlinkisadded. WewillreferthisalgorithmasNaiveD. 2. CentralizedDijkstraalgorithm: Thisalgorithmisdifferentfromthepreviousalgorithminthat thealgorithmisrunontheDelayGraphGthattakealltheexistingflowsintoconsideration. Each time a new flow is injected or an existing flow is removed, the delay graph G is reconstructed, then the Dijkstra algorithm is runk times to findk node-disjoint path, with links belongs to the previouspathfoundremoved. WewillreferthisalgorithmasCentraD. 5.4 MLSRunderInterference In last section, we assume that links in interference range can use different channels. In this section, we assume that all nodes share the same wireless channel, thus interference need to be taken care of. Weassumeadiskinterferencemode,inwhichasendernodewillinterferewithanothercommunication linkifandonlyifitisamongcertaindistancefromthereceiverofthatlink. ClearlythisproblemisNP-hard(sincetheTDMAschedulingproblemisNP-hard),soweproposed aheuristicapproach. Wedefinepathstobeinterference-freeiftherearenointerferenceamongthelinks onthepaths. Firstweshownhowtofindthefirstinterferencepathforaflow: 83 1. FindtheshortestdelaypathfortheflowonthedelayGraphDG. 2. Ifthereisnointerferenceamonglinksonthepath,thenfinished. Otherwise,removethelinkthat causes the most interferences. Check if there is still interference. Keep deleting links that cause themostinterferenceuntilthereisnointerferenceinthepath. Gobacktostep1. NowsupposewehaveM node-disjointinterference-freepaths,weneedtofind M+1node-disjoint interferencefreepaths. 1. RemovelinksinDGthatinterferewiththelinksontheM node-disjointpaths. 2. On the remainingDG, find a minimum latency interlacingS using algorithm described in [81]. IfthereisnointerferenceamonglinksinS,gotostep4. Otherwisegotostep3. 3. Removethelinkthatcausesthemostinterferences,whichwillbeamongthenewlinksintroduced by S. Check if there is still interference. Keep removing links on the paths that cause the most interference until there is no interference in the paths (the links in the original M node-disjoint interferencefreepathswon’tberemoved). Gobacktostep2. 4. GettheM +1node-disjointinterferencefreepathbyinterpret P M +S. Recoverthepreviously removedlinksthatinterferewithlinksthatwasinM node-disjointpathsbutnotin M +1node- disjointpaths. RemovelinksthatinterferewiththenewlyaddedlinksontheM +1node-disjoint interferencefreepaths. 5.5 NumericalResults In this section, we evaluate the performance of the MLSR algorithm and heuristic algorithms through highlevelsimulations. Sincethecurrentstudyfocusesoncomparingthetotallatencyonlyacrossthese heuristics,eventhedistributedalgorithmsaresimulatedinacentralizedmanner(withoutanalyzingtheir overhead). A sensor network is generated by randomly scattering 200 nodes on a 200x100 rectangle. There are four sinks in the corners of the area. The radio range is set to be 10 meters. We use the topology generation tool provided by [68] to get the packet reception ratio (PRR) of links between two nodes. LinkswithPRRlargerthan0.9areaddedintotheabstractcommunicationgraph. 84 5.5.1 FDMAchannelModel First we evaluate the algorithm under the FDMA model which means there is no interference between two links. Figure 5.9 shows the average delay under different frame length for MLSR, NaiveD and CentraDalgorithms. Foreachframelengthk,thenumberofflowsare4K whichisthelargestpossible number of flows that can be supported by the 4 sinks. The results are averaged over 10 different seeds. Clearly MLSR has the smallest average latency while NaiveD has the largest latency. Compared to NaiveD algorithm,thedelayofMLSRisreducedtoaround15%. AsK increases,theaveragelatency decreases. This is because as number of flows increases, more flows are closed to the sink, thus the latencyisreduced. Figure 5.11 shows theNaiveD algorithm under different flow join order. In this scenario,K = 5, thenumberofflowsFN = 20. TheflowsarefixedbuttheorderofbeingprocessedbytheNaiveD is different. Clearlytheorderwillaffecttheperformanceofthealgorithm. However,CentraD algorithm islikelytoachievelowerlatencywhileMLSRachievestheminimumlatencyregardlessoftheorder. Figure 5.12 shows the performance of MLSR and NaiveD under traffic changes: flows comes in order and then later leaves. The CentraD algorithm is not simulated here as it can not handle traffic change adaptively. For the first 27 flows, theNaiveD algorithm achieves the same latency as MLSR. This shows that when the number of flows is small, there is no need to do the complicated MLSR algorithm. However when the number of flows is larger than 27, the MLSR has smaller latency. Later whenflowsfinishedtheirdatatransmissioninthesameorderastheyjoins(thefirstjoinedflowfirstleft), theMLSRalwaysachievestheminimumlatencyforcurrentactiveflows. Thenaivealgorithm,however, performspoorlyevenwhentherearelessthen27activeflows,ithashigherlatencythanMLSR. Figure 5.13 and 5.14 show the performance of MLSR and NaiveD under topology change with k = 10. We keep removing links and computes the latency after each link failure until we can not find 30 or 40 node-disjoint paths. As link failure happens, the latency increases. The MLSR achieves smalleraveragelatencyundervarioustopologychangesthanNaiveD. 5.5.2 SingleChannelInterference In this section, we investigate the performance of the heuristic MLSR algorithm under single channel interference model through simulations. The interference range is set to 20 meters. Figure 5.15 shows the number of average delay of flow under differentK andFN. AsK increases, the number of flows can be supported also increase. For eachK, there is a big jump of latency at certain point. Since each 85 Figure5.9: Averagedelayunderdifferentframelength Figure5.10: Averageloadperactivenodeunderdifferentframelength 86 Figure5.11: TotalDelayofNaiveD heuristicunderdifferentflowjoinorder Figure5.12: TotaldelayofNaiveD heuristicandMLSRforflowjoinsandleaves 87 Figure5.13: TotaldelayofNaiveD heuristicandMLSRundertopologychange Figure5.14: TotaldelayofNaiveD heuristicandMLSRundertopologychange 88 Figure5.15: AverageDelayunderdifferentframelengthandnumberofflows sourcehasapackettosenteveryK slots,thismeansthetrafficloadistooheavyforcurrentnetworkto support. 5.6 Discussion Inthischapterweaddressedtheimportantproblemofminimizingcommunicationlatencywhileprovid- ingenergy-efficiencyfornodesinwirelesssensornetworks. DifferentfromDESSwhoseobjectiveisto minimizetheworstcaselatencygiventhedutycyclingrequirementthateachsensorhastobeawakefor 1 k fraction of time slots on an average, MLSR is interested in the average latency for the current active flows. A node is allowed to wake up multiple slots to receive/transmit and asleep otherwise. We for- mulatedajointschedulingandroutingproblemwithobjectivetofindthescheduleandrouteforcurrent active flows with minimum average latency. By constructing a delay graph, the problem can be solved optimally by M node-disjoint paths algorithm under FDMA channel model. We further extended the algorithmtohandledynamictrafficchangesandtopologychangesinwirelesssensornetworks. Wealso proposed a heuristic solution for the minimum latency joint scheduling and routing problem under sin- glechannelinterference. Numericalresultsshowthelatencycanreduced15%understationaryscenario and50%underdynamictrafficortopologychanges. 89 Chapter6 EEJSPC:EnergyEfficientJointSchedulingandPowerControl 6.1 Overview In previous chapters, we assumed radio models with fixed transmission power. However, many radios now can support multiple level of transmission power which provide another knobs for system design. Inthischapter,wewillstudytheproblemofenergyefficientjointschedulingandpowercontrol. TDMAscheduledmediumaccessisgenerallymoreenergyefficientthanrandomaccess,andispar- ticularly suitable for implementation with low overhead when traffic is predictable or slowly changing. Several studies have investigated TDMA scheduling techniques for ad hoc and sensor networks [6, 7, 8, 12, 9, 10, 13]. In these studies, typically a simple model for interference is used where a receiving nodeseesinterferencefromanothertransmitterifandonlyifitiswithinsomenominalrangeR I . This model, while useful in providing a simple graph-coloring approach to TDMA scheduling, can be quite misleading in practice. In reality, simultaneous wireless transmissions within the nominal range do not necessarily collide if the signal to interference plus noise ratios (SINR) at the corresponding receivers are sufficiently high; and, at the other extreme, aggregate interference from multiple transmitters that arewellbeyondthenominalrangecanbehighenoughtocausecollisions. Another concern with many studies of TDMA in wireless ad hoc and sensor networks is that they ignore the possibility of variable transmission power. In practical systems this can be an important tunableparameterforreliableandenergy-efficientcommunication,becausehighertransmitpowerscan increasetheSINRatthereceivertoenablesuccessfulreceptiononalink,andlowertransmissionpower canmitigateinterferencetoothersimultaneouslyutilizedlinks. We treat in this work TDMA link scheduling using a realistic SINR-based interference model, ex- plicitly taking transmission power control into account. This approach to joint scheduling and power controlwasfirsttakenbyElBattandEphremides[15,16],followedbyothersincluding[17,18,19,20, 90 67]. Given a set of one-hop links and number of packets that need to be transmitted within a certain number of slots, the scheduling problem is to decide in each time slot which source-destination pairs communicate while power control problem is to decide the transmission power of source nodes in a givenslot. In these prior works, the primary objective of the link scheduling algorithm is to maximize the numberofsimultaneoustransmissionswhichmaximizethethroughput. Whilethepowercontrolphase minimizes transmission powers on the scheduled links, link scheduling can not guarantee power effi- ciency,becausemaximizingtheconcurrenttransmissionsincreasesinter-senderinterferenceandhence the total required transmission power. Potentially significant energy savings are possible through al- ternate link schedules. Even further energy savings may be achievable by trading off throughput and latency. In this chapter, we study the energy efficient joint scheduling and power control problem. Our contributions in this work are four-fold. First, we formulate joint scheduling and power control as a noveloptimizationproblemthatprovidestunabletradeoffsbetweenthroughput,energyandlatency. We show that the prior formulations in [15, 17] can in fact be treated as special cases of our formulation. Second, while the optimization problem that we formulate is NP-hard, we present both exponential and polynomial complexity greedy based heuristic algorithms. Third, we show the performance of these algorithms through simulation results and demonstrate the energy-latency-throughput tradeoffs that can be achieved with joint link scheduling and power control. Interestingly, we find that, at least for moderate loads, major energy savings can be obtained without significantly sacrificing throughput. Finally,westudythetheenergyefficientjointschedulingandpowercontrolproblemwiththeobjective ofminimizingminimizethetotalenergycostsubjecttoallpacketsofthelinksaretransmittedwithina latencybound. The rest of the chapter is organized as follows. In section 6.2, we define the energy efficient joint scheduling and power control problem. We study the tunable joint link scheduling and power control probleminsection6.3. Insection6.4,weinvestigatetheproblemofjointschedulingandpowercontrol with transmission request constraint. We evaluate the performance by simulations in section 6.5. We thensummarizeanddiscusstheworkin6.6. 91 6.2 Energy,LatencyandThroughputTradeoffsinJSPC 6.2.1 ApplicationScenario Wefirstdescribethebasicapplicationscenarioandassumptions. 1. Consider a static wireless sensor network, all nodes are equipped with same radio with omni- directional antennas and share the same channel. The transmission power of the radio can be adjusted continuously 1 , with constraints on the minimum and maximum transmission power levels. Theradiodatarateisfixed. 2. Consider a general application in wireless sensor network, each sensor node samples the envi- ronment periodically. A node either reports to sink or communicate with neighbors when an interesting event is detected. Sensing data need to be processed or reported before a latency deadline,suchasinfiredetectionorrealtimetargettrackingapplications. 3. Thedeadlinecanbeper-hopdeadlineorend-to-enddeadline. Incaseofend-to-enddeadline,we dividetheend-to-enddeadlinebythenumberofhopssowehaveaper-hopdeadlineforeachlink onthepath. Thisisreasonablesinceend-to-enddeadlineshouldbeproportionaltothenumberof hopsonthepath. 4. Time is divided into equal sized slots that are long enough for one packet transmission and groupedintoframes. SomeworksonTDMAfocusonminimizingthelengthoftheframesubject to the constraint that every node or link is assigned at least one slot. In this work, however, the framelengthischosenaccordingontheper-hoplatencydeadline. 5. Each node generates random number of packets of fixed length which need to be transmitted in one TDMA frame. This is called a transmission request. Packets not transmitted within the currenttimeframearedropped. 6. For end-to-end data packet (e.g, from a sensor to the sink), every TDMA frame, it will be for- wardedonehoptoaneighboringnode. InthenextTDMAframe,thepacketwillthenbecounted asthetransmissionrequestoftheneighnodeuntilitreachesthesink. 1 Inpractice,theremayonlybeseveraldiscretetransmissionpowerlevels. Thisassumption,howevercansimplifytheanalysis anddoesnotaffectthecorrectnessofthealgorithm. 92 6.2.2 InterferenceModel The interference model that we consider is a SINR-based TDMA system. Let G = (V,E) be the wireless sensor network, with V representing the set of nodes in the network and E, the set of com- munication links. Given a link (i,j)∈ E, i is the sending node andj is the receiving node. A link is called active in a slot if nodei transmits data packet to nodej in that slot. We refer all active links in a single time slot as a transmission scenario, or transmission set. The signal to interference and noise ratio(SINR)forlink(i,j)isdefinedas: SINR ij = α ij P i N j + P k6=i α kj P k (6.1) where α ij is the propagation attenuation of the signal from node i to node j, which is proportional to 1 d n ij , where n is the path loss factor. We assume α ij s changes slowly so that we can regard α ij as constantforthedurationofatimeframeinthefollowingdiscussion. N j istheenvironmentnoisepower atreceiverj. P i andP k arethetransmissionpowersofsendingnodeiandk separately. A data transmission on a link (i,j) can be successfully received at the receiver only if the corre- spondingSINRonthatlinkisequalorgreaterthanagiventhresholdγ: SINR ij ≥γ (6.2) 6.2.3 PowerControl If there is only one active link (i,j), nodei only needs to transmit at a power level just high enough to satisfySINR ij ≥ γ. However, if there are multiple active links in the same time slot, because of the interfere among each other each node has to transmit at higher power in order to meet theSINR≥ γ requirements, which increases the interference in return. The power control problem is to compute a set of transmission power for all links in a transmission scenario by solving the following optimization problem: minimize P ij P ij subjectto SINR ij ≥γ P min ≤P ij ≤P max ,∀ij links (6.3) 93 Some distributed power control algorithms have been proposed for cellular network [14] and wire- lessadhocnetworks[15],whichwewillusedirectly. We call a transmission scenario/set feasible if a set of transmission powers are available such that the SINR requirements of all receivers in the transmission scenario are satisfied. A set is called a maximal transmission set if adding any additional active link will result in an infeasible transmission set. All subsets of a maximal transmission set are also feasible transmission sets. We refer the sum of thetransmissionpowerofallactivelinksinatransmissionscenarioasitsenergycost. We make two important observations about the total transmission power of a feasible transmission scenario. 1. Two feasible transmission scenarios with same number of concurrent transmissions could have significantly different costs because of the different interference among the the links, depending onthelocationandwirelesschannelofthelinks. 2. Afeasibleset’scostisalwayslargerorequaltosumofthecostsofitssubsets. The first observation needs no further clarification. We use a single example to explain the second observation. Consider a set S and its subset S−l (remove link l from S) and l. Suppose the costs are C S−l and C l . Now add l to subset S−l. l’s transmission power will interference with links in S−l andviceversa. Thereforebothlinkl andlinksinS−l havetoincreasetheirtransmissionpower respectively. Clearly,C S > C S−l +C l . The subsets in the right hands do not need to be exclusive to eachother,astheredundantlinkswillonlyincreasethetransmissioncost. If S j = S k S jk then C j ≥ P k C jk (6.4) 6.2.4 StateoftheArtofJointSchedulingandPowerControl In previous works on joint scheduling and power control [15, 16, 17, 67], the scheduling policy is to pack the maximum number of links that can be active simultaneously in each time slot. The objective is to maximize the spatial reuse of system resources and the throughput. Although the power control phase minimizes the transmission powers on the scheduled links, this scheduling policy does not take energyintoconsiderationandthusmaynotbeenergyefficient. 94 Figure 6.1: Illustration of energy efficient scheduling. ~ b is the number packets need to be transmitted for each link. S are all possible feasible transmission scenarios. C are the total transmission power of thetransmissionscenarios. Figure 6.1 shows an example of energy efficient joint scheduling and power control 2 . Given ~ b, the numberofpacketsneedtobetransmittedandallfeasibletransmissionscenariosandtheirrelatedcosts, therearethreepossibleschedulesthatsatisfythe ~ bconstraint: 1. Option 1: Choose S 1 , S 3 and S 7 . The transmission request is finished in three slots. The total energycostis7.56. 2. Option 2: Choose S 2 , S 3 and S 6 . The transmission request is also finished in three slots. The totalenergycostisreducedto6.2. 3. Option3: ChooseS 2 ,S 5 ,S 6 andS 7 . Thetransmissionrequestnowisfinishedinfourslots. The totalenergycostisfurtherreducedto4.42. Thisexampleshowsthattheschedulingpolicythatmaximizesthenumberofconcurrenttrans- missionsisnotenergyefficientandsuggeststwowaystoachieveenergyefficientschedule: 1. Choose energy efficient combination of feasible transmission sets. In the example, compare op- tion 2 to option 1, the combination of S 2 +S 6 is more energy efficient than S 1 +S 7 . This is because the interference between link 1 and 4 is higher than the interference between link 1 and 5. 2. Tradeofflatencyforenergyefficiency. Intheexample,compareoption3tooption2,S 3 isdivided intoS 5 +S 7 . Instead of being scheduled simultaneously in one slot, link 2 and 5 are scheduled separatelyintwoslots. Becauseoftheeliminationofinterference,thetotalenergycostisfurther reduced. Tobetterunderstandthetwoapproachestosaveenergy,figure6.2(a)and6.2(b)showtwodifferent schedules. Each column is a slot and each colored box represents an active link during that slot. The 2 ThedataiscollectedbysimulationsdescribedinsectionV 95 (a) β = 0 (b) β =10 Figure6.2: Anexampleoftwodifferentschedulesunderβ = 0andβ = 10. coloroftheboxesinacolumnindicatesthetheenergycostofthetransmissionsetinthatslot. Redcolor means high energy cost while green color means low energy cost. The meaning ofβ will be explained later. Whenβ = 0,thetransmissionrequestisfinishedinlessthan50slotsandmanytransmissionsets have high energy cost. While in the schedule chosen byβ = 10, the transmission request is finished in morethan70slots. Evenfortwosetshavingthesamenumberofactivelinks,theenergycostoftheset chosenbyβ = 10hasmuchlowerenergycostcomparedtothesetchosenbyβ = 0. Inthefollowingsections,wewillinvestigatetwodifferentproblemsofenergyefficientjointschedul- ingandpowercontrol. 6.3 TJSPC:TunableJointSchedulingandPowerControl 6.3.1 MathematicalFormulation Inthissection,wewillformulatethetunablejointschedulingandpowercontrolproblemandshowthat prior works [15, 17] can be treated as special cases of our formulation. First we describe the notation used. Assume that a TDMA time frame containsT slots. HereT models the per-hop delay tolerance of the application. The duration of a slot is normalized to 1. Letb(e) denote the number of packets need to be sent on linke = (i,j)∈ E in a time frame. Denote ~ b as a vector of size|E| with each element correspondingtoalink. We denoteS as the collection of all feasible transmission sets and|S|. Each feasible transmission setS k is a vector of sizeE, withS k (e) equal to 1 ife is active in the setS k . For each feasible setS k , there is an energy costC k = P S k (e)=1 (P e ) which is the sum of the energy cost all active links in that 96 Table6.1: SummaryoftheNotations e = (i,j) Alinkwithithesenderandj thereceiver T NumberofslotsinaTDMAframe ~ b Transmission request: Number of packets needtobesentforeachlink S Thecollectionofallfeasibletransmissionset, S k beingoneoftheset S k (e) 1iflinkeisactiveintransmissionsetS k M |S|,numberoffeasibletransmissionset C k EnergycostoftransmissionsetS k ~ x Theschedulingsolution: x k isthenumberof timesS k ischosen β Parameter to tune between throughput and energy set in a single slot. Here, P e is the transmission power of link e from i to j. We ignore the reception power as it is almost constant regardless of the transmission power. Let~ x denote the solution, withx k beingthenumberoftimesthatsetS k ischosen. Themaximumnumberofsetsallowedtobechosenis T. The three important metrics of a sensor network system can be easily represented using the above parameters. • Energy: ThetotalcommunicationenergycostinT slots: P k x k C k . • Throughput: We use the number of packets transmitted in T slots to represent the throughput. The number of slots that a link e is scheduled to be active is P k x k S k (e). However if a link is assignedaslotbutthereisnomorepackettotransmit,itisawasteofresourceandshouldnotbe counted. So the actual number of packet a linke transmits ismin( P k x k S k (e), ~ b(e)) The total numberofpacketstransmittedbyalllinksisthen: P e∈E min( P k x k S k (e), ~ b(e)). • Latency: T istheworstper-hoplatencyofapacketifitistransmitted. Asmaller T meansthata packetneedtobetransmittedinashortertimeframe,andhenceasmallerper-hopdelay. It is clear that it is not possible to optimize these three metrics simultaneously. Depending on the application requirements, different tradeoff strategies may be used. Some applications may need all transmission requests be satisfied before the deadline, while others may tolerate a certain number of packet drops. We will study the energy cost minimizing problem subject to transmission request guar- anteeinsectionIV.Inthissectionwefirstformaproblemthatallowstheapplicationstochoosedifferent tradeoffsamongenergy,latencyandthroughput. 97 ProblemTJSPC: maxgain = α X e∈E min( X k x k S k (e), ~ b(e)) −β X k x k C k s.t. X k x k ≤ T (6.5) By tuningα,β andT, we can achieve different tradeoffs between throughput and energy given the latency constraint. Specially, ifα is 0, the problem is reduced to minimizing energy consumption with noconstraintonthroughput. Thenthepolicyoftheschedulingalgorithmistoalwayssearchthesetwith minimum energy cost. If β is 0, the problem is reduced to maximizing throughput with no constraint onenergyconsumption. Thentheobjectiveoftheschedulingalgorithmistomaximizethethroughput, same as previous scheduling algorithms[15, 17]. Without loss of generality, we will assume α = 1 in the following discussion. As β increases, to maximize the gain it is better to choose transmission scenario with less energy cost. So the application can increase β when it is more interested in saving energyanddecreaseβ whenthethroughputisamoreimportantmetric. ThechoiceofT wouldbebased onapplication-specificworsthop-to-hoplatencyrequirements. Asβ increases, the solution tends to choose transmission sets with smaller energy cost. However, to prevent a transmission set from being chosen because of its low energy cost even if it does not contribute any throughput, there should be an upper bound forβ. LetC min = min k C k andC max = max k,|S k |=1 C k . It is easy to see that to guarantee that a transmission set that can at least contribute 1 tothethroughputispreferabletothesetwithminimumcost,wehave: −C min < 1−βC max ⇒β < 1 C max −C min (6.6) ThisproblemisNP-hardasitcanbereducedfromtheMaximumCoverageproblem[23]. However based on the fast greedy heuristic algorithm with constant factor approximation in [23], we propose greedybasedheuristicalgorithmsandevaluatetheperformancebysimulations. 98 6.3.2 HeuristicApproaches 6.3.2.1 ExponentialComplexityGreedyApproximation In this section, we present a greedy algorithm that has a constant factor approximation to the optimum solution. Given the collection of all feasible transmission setsS, the greedy algorithm selectsT trans- missionsetsbyiterativelychoosingthesetthatmaximizethetotalgain(definedinproblemTJSPC)of thealreadychosensetsplusthecurrentchosenset. WedenotethisalgorithmasGreedy. Thegreedyheuristiccanbeprovedtobea(1− 1 e )-approximationalgorithm. Proposition7: wt(~ x)≥ [1−(1− 1 k ) k ]wt(OPT)> (1− 1 e )wt(OPT) Thisfollowsfromthelemma3.13in[23]. Forcompleteness,weshowtheproofhere. Proof: Suppose~ x i isthegreedysolutioninthefirstislots,let G i = X k x i k S k and wt(G i ) = X e min( X k x i k S k , ~ b(e))−β X k x i k c k Supposeini+1slot,transmissionsetS j ischosen,Thenx i+1 j =x i j +1andG i+1 =G i ∪S j ,wehave: wt(G i+1 ) = X e min( X k x i+1 k S k , ~ b(e))−β X k x i+1 k c k Now,thegainofthefirstselected(i−1)setsiswt(G i−1 ). Thedifferencebetweenwt(G i−1 )tothe gain of the optimal solution iswt(OPT)−wt(G i−1 ). Then at leastwt(OPT)−wt(G i−1 ) worth of gainnotcoveredbythefirst(i−1)setsarecoveredbytheT setsofOPT. Bythepigeonholeprinciple, oneoftheT setsintheoptimalsolutionmustcoveratleast wt(OPT)−wt(Gi−1) T worthofgain. SinceS j isasetthatachievesmaximumadditionalgain,itmustalsocoveratleast wt(OPT)−wt(Gi−1) T . Thatis: wt(G i )−wt(G i−1 )≥ wt(OPT)−wt(G i−1 ) T 99 Nowletussupposefori = 1,wt(G 1 )≥ wt(opt) T ,then, wt(G i+1 ) = wt(G i )+(wt(G i+1 )−wt(G i )) ≥ wt(G i )+ wt(OPT)−wt(G i ) T = (1− 1 T )wt(G i )+ wt(OPT) T ≥ (1− 1 T )(1−(1− 1 T ) i )wt(OPT)+ wt(OPT) T = (1−(1− 1 T ) i+1 )wt(OPT) > (1− 1 e )wt(OPT) When β is 0, to maximize the gain, the greedy algorithm will choose a feasible transmission set which can maximize the throughput, which leads to the solution to choose the set with maximum con- currenttransmission. Thisisexactlytheschedulingalgorithmin[15,17]. The complexity of the greedy algorithm is upper-bounded by O(T|S|). A loose upper bound on |S| is 2 E , which means that the complexity of the algorithm is exponential to the number of links. With the feasibility constraint,|S| can be greatly reduced. Cluster hierarchical structures which have been proposed widely for wireless sensor networks (e.g. in [21, 22]) can further reduce|S|. Since cluster size are chosen to accommodate event monitor range, it is expected that at any time if an event happens, most of the time only one cluster may need to be active. Each cluster only schedules its own data transmission while treating interference from other clusters as ambient noise. Interference from clustersfarawayisnegligible. Becauseonlylinkswithinoneclusterneedtobeconsidered,thenumber of feasible transmission sets is reduced considerably. We can further limit the maximum number of concurrent transmission links to a small number k, since in practice as it is difficult to sustain a large number of simultaneously active links in a given region. In this case, the number of feasible sets is upperboundedby2 k+1 . Even|S| can be reduced, the greedy algorithm needs to compute all possible transmission sets S and their energy cost in advance and has an exponential complexity ofO(T|S|) whenever the wireless channel condition changes, which makes it infeasible for practical use. However, it could be used as a framework or offline algorithm to give good insight on the performance of the network. In the next section,basedonthegreedyapproximationalgorithm,weproposeagreedybasedheuristicwhichdoes notneedtopre-computeallfeasibletransmissionsetswithpolynomialcomplexity. 100 6.3.2.2 PolynomialGreedyHeuristic Assumethatthelinkgainα ij changesslowlycomparedtotimeframeT,thenodesneedonlytocollect such information until a significant change ofα ij happens. The parameters can also be updated incre- mentally. Therefore, we assumeα ij is available in each node. Secondly, at the beginning of each time frame, source nodes will generate a control packet that contains the number of packets intended to its receivers. Thereforeallsourcenodesareawareof ~ b. Weassumethecontrolpacketissmallercompared to the data packet and the overhead is small. We will not discuss the details of the control message exchangeprotocolhere. Given a transmission scenario, a source node first check whether it is feasible. If it is infeasible, a linkwithminimumSNRorMaximumInterferencetoMinimumSignalRatio(MIMSR)[17]isdeferred. Then the new transmission scenario is checked again. Previous scheduling algorithms will stop once an feasible transmission set is found. The proposed algorithm, however, continues to search for a transmission set that can maximize the gain. Suppose the first admissible set is S k , it will continue to drop the link with maximum MIMSR until there is only one active link. Suppose the following transmission sets the node gets are S k1 ,S k2 ,...,S kn . It is clear all these transmission sets are still feasible and S k ⊃ S k1 ...⊃ S kn . For each feasible set S ki , the node computes the related gains by α P e∈E min( P k x k S k (e), ~ b(e))−β P k x k C k . Then the transmission set with the maximum gain is chosen and ~ b is updated. The whole process is repeated again until either ~ b = 0 orT sets are chosen. WedenotesthealgorithmasDiGreedy. AlgorithmDiGreedy 1. Collect ~ b. 2. fori←1toT 3. m←numberofunzeroelementin ~ b 4. S(e)←1ifb(e)≥ 1 5. forj←mto1 6. RunpowercontrolalgorithmforS 7. gain←α P e∈E min( P k x k S k (e), ~ b(e)) 8. −β P k x k C k ifS isfeasible 9. deferthelinkk withMIMSR 10. S(k)←0 11. SelectthefeasibletransmissionsetS withmaximumgain 12. ~ b←( ~ b−S) 101 Figure6.3: Thefourcharacteristicregionsinthenumberofusedslot,energyvs. β. 13. if ~ b == ~ 0 14. break; TheproposedDiGreedyalgorithmhasacomplexityofO(T|E|)whichispolynomialtothenumber of links. However, unlike the greedy algorithm which always choose the transmission scenario that maximizesα P e∈E min( P k x k S k (e), ~ b(e))−β P k x k C k fromallpossibletransmissionsets,theDi- GreedyalgorithmonlychooseonefromthetransmissionsetsthatareobtainedbydeferringtheMIMSR link one by one. Therefore, it does not necessarily guarantee a (1− 1 e )-approximation to the optimal solution. However it is practically implementable and we will show by simulations that it achieves comparableperformancetothegreedyalgorithm. 6.4 JSPC-TR:JSPCwithTransmissionRequestConstraint 6.4.1 ProblemFormulation InTJSPC,weinvestigatethetradeoffsbetweenthroughputandenergyefficiency. However,someappli- cations may require all the transmission requests be satisfied. So in this section, we study the problem of joint scheduling and power control with transmission request constraint (JSPC-TR): given a trans- mission request, minimize the energy cost subject to the constraint that all transmission requests are satisfiedwithinthelatencybound: 102 ProblemJSPC-TR: min P k x k C k s.t. P k x k S k (e)≥b(e),∀e P k x k ≤T (6.7) ThisisstillaNP-hardproblemasitcanalsobereducedfromthemaximumcoverageproblem. Even the scheduling policy which always schedules maximum number of concurrent transmissions in each slot can not guarantee all transmission requests be satisfied. However, here we assume that the traffic load of the transmission requests are relatively low compared to the capacity of the network so that at least the scheduling policy that maximizes the concurrent transmissions can schedule all transmission requestsinT slots. WeleveragetheheuristicsolutionofproblemTJSPCtosolveJSPC-TR.Firstconsiderthefollowing problem: maxgain = P e∈E min( P k x k S k (e), ~ b(e)) −β P k x k C k P e∈E min( P k x k S k (e), ~ b(e)) s.t. P k x k S k (e)≥b(e),∀e (6.8) In contrast to TJSPC, there are two differences. First since the transmission requests have to be satisfied, to minimize the energy cost, we need to choose more energy efficient sets. So we change the energy metric to energy efficiency metric which is the average cost of sending one packet. Second, there is no constraint on the total number of slots but the transmission request. This problem can be solved using the same greedy algorithm for TJSPC. Suppose for each β, the solution is ~ x β . Define E(β) = P k x β k C k . Thenweneedtofindanoptimumβ thathastheminimumenergycost: E 0 : min β E(β) s.t. P k x β k ≤T (6.9) Suppose β ∗ is the optimum β, then ~ x β ∗ is the heuristic solution to JSPC-TR. In next section, we discussthealgorithmtofindtheoptimumβ ∗ . 103 6.4.2 β ∗ -searchAlgorithm Generally, asβ increases, equation 6.8 tends to find solutions that are more energy efficient thusE(β) decreases. Theoretically,E(β) is not a monotonically decreasing function. However, in all the simula- tions, we see a clearly decreasing trend. Therefore, heuristically, we will assumeE(β) is a decreasing function. ConsideratypicalcurveinFigure6.3 3 whichshowstheenergyandnumberofslotsusedtotransmit atransmissionrequest. LetT = 100,sotransmissionrequestshouldbefinishedin100slots. Asshown in the energy curve, the energy cost reduces as β increases, however at the same time, the number of usedslotsalsoincrease. TheoptimumoperationpointispointAinwhichexactly100slotsareusedand theenergycostisminimized. Forpracticalpurpose,wedefineatolerancezoneofwidth,asshownin Figure 6.3. Here, is a protocol parameter that determine the converge rate of the protocol which we willshowlater. Wedenoteuasthenumberofusedslots. Thenumberofpacketsneedtobetransmitted inatransmissionrequest ~ bisN = P k ~ b(k). Fromfigure6.3,weidentifyfourcharacteristicoperationregions(boundedbydottedline): • small- β: u < T−. In this sate, transmission requests are satisfied within T slots. The energy cost is high. It is clear that in order to reduce the energy cost, we need to increaseβ. However, this reduction must be performed carefully so that the transmission request is always satisfied. Intuitively, we need to achieve a balance between saving energy and satisfying transmission re- quest. Byinvokingthefactthattherelationshipofuvs. β,foru<N,isnearlinear,thisprompts theuseofthefollowingincreasestrategy: β i+1 = β i 2 (1+ u i T ) We will show later that such an update policy can reduce the energy cost while guaranteeing the transmissionrequestsatisfaction. • opt- β: T−≤ u≤ T. In this state, the network is operating within tolerance of the optimal point, where transmission request is satisfied and energy cost is a slightly higher. Hence theβ is leftunchangedforthenextframe: β i+1 =β i 3 ThefigureisobtainedbysimulationsdiscussedinsectionV. 104 • large- β: T < u < N. In this state, the network is operating in a region that not all transmission requests can be satisfied within T slots. It is clearthat we need todecreaseβ aggressively. Since therelationshipofuvs. β isnearlinear,weuseadecreasestrategyasfollows: β i+1 =β i T u i δ 1 We will show later by choosingδ 1 < 1, we can guarantee that policy will converge to the opt- β region. • xlarge- β: u≥ N. In this sate, in all time slots, only one link is active. This consumes the least energy, howevertransmissionrequestcannotbesatisfiedwithinTslotswhenT <N. Itis clear we need to decreaseβ aggressively. However in this region,u andβ is no longer linear and we havenoideahowlargeβ isnow. Inordertoconvergetoopt- β regionandguaranteetransmission request,β needtobedecreasedmoreaggressivelythanintheregionoflarge- β: β i+1 =β i T u i δ 2 withδ 2 ≤δ 1 . Wewillshowinnextsubsectionthatstartingfromanyregion,theaboveβ ∗ -searchalgorithmconverges toopt- β region. The entire JSPC-TR protocol is summarized in figure 6.4. The basic process is following: at a TDMA time frame, under the current β and transmission request, the scheduler decides the state of the network then adjustsβ according to theβ ∗ -search algorithm. The updated β is then used for next TDMAframe. Hereweassumethetrafficrequestschangeslowlycomparedtotheconvergerateofthe β ∗ -searchalgorithm. 6.4.3 Analysis First we present some analysis of theβ ∗ -searching algorithm. Under the assumption of linear relation- ship of u vs. β in small- β region/state, we are able to prove that network will converge to the opt- β state. Another assumption is that the traffic load in TDMA frame does not change abruptly. The proof issimilartotheoneusedin[69]. Proposition8: Startingfromsmall- β,withlinearrelationshipbetweenuandβ,thestatewillremain small- β untilitconvergestoopt- β ind u0−1 eiterations. 105 N = P e ~ b(e) SolveJSPC-TRusingequation6.8with β ifu<T−/*Stateissmall- β*/ β = β 2 (1+ u T ) elseifT−≤u≤T /*Stateisopt- β*/ β =β elseifT <u<N /*Stateislarge- β*/ β =β T u δ 1 elseifT≥N /*Stateisxlarge- β*/ β =β T u δ 2 end Figure6.4: JSPC-TRprotocoland β ∗ -searchalgorithm. Proof: Supposethelinearbehaviorforu<T−isu =aβ andu i <T−. Sotheβ isincreased by: β i+1 = β i 2 (1+ T u i ) Thus, u i+1 = u i 2 (1+ T u i ) = u i +T 2 Sinceβ i+1 > β i , the next state can either be small- β, opt- β, large- β or xlarge- β. Suppose the next stateisneithersmall- β noropt- beta,thenu i+1 >T. Then, u i+1 = u i +T 2 >T Hence,u i >T. Howeverthiscontradictswithu i <T−sincethestartingstateissmall- β. Thus,the statecanonlybesmall- β beforeitreachesopt- β. Nowweprovethattheconvergetakesd u0−1 eiterations. Letj bethefirstonewhenthenetworkis inopt- β state. u j = u j−1 +T 2 >T− u j−1 = u j−2 +T 2 >T−2 . . . u 1 = u 0 +T 2 >T−2 j−1 Thus, it takesj > log 2 ( u0−1 2 ) iterates beforeu j > T−. In the whole process, the transmission requestisalwaysguaranteed. 106 Figure6.5: EnergycostreducesaslatencyconstraintincreasesasafunctionofT withvaryingβ. Proposition9: Startingfromlarge- β orxlarge- β,thestatewillconvergetoopt- β. Proof: Supposethelinearbehaviorforu<T−isu =aβ. Forlarge- betastate,u>T. Soβ is decreasedby: β i+1 =β i T u i δ 1 =β 0 T i Q i k=0 u k δ i 1 Sinceδ 1 < 1 andu k > T,β will keep decreasing until it change to either opt- β region or small- β regionwhichwillconvergetoopt- β byLemma8. Similarly,startingfromxlarge- β,thenetworkcanalsoconvergetoopt- β. 6.5 SimulationResults Wesimulatetheperformanceofthealgorithmsforastationarynetworkconsistingofagridof49nodes. The distance between adjacent nodes is set to 20 meter. The radio parameters are set according to the CC1000 radio used in Mote MICA2 [70, 3]. The minimum transmission power isP min =−20dBm and the maximum transmission power is P max = 5dBm. According to [68], The path loss factor in a typical outdoor environment is 4 and the noise floor is around−105dBm. The SNR threshold γ for successfully packet reception is set to be 10dB. We choose 42 links and pre-computed all feasible transmissionsetsandtheirenergycosts. Themaximumnumberofactivelinksinatransmissionscenario is5. 6.5.1 SimulationResultsforTJSPC Besides the Greedy and DiGreedy algorithms, we also simulate the scheduling algorithm (referred as MIMSR) proposed in [17]. We simulate 20 time frames which consist ofT slots. Each node randomly 107 generates 1 to 6 packets to be transmitted in each time frame. All results are averaged over 10 seeds. Fromthesimulations,welearnedthreekeylessons,describedbelow. Lesson 1: By relaxing the latency bound, we can get significant energy savings 4 . In the simulation, we fix the traffic load while increasing the latency boundT. Figure 6.5 shows the impact ofT on the energy cost performance of the algorithms. The packet reception ratio (which is directly proportional to the throughput) remains above 95% for allT andβ. Largerβ can be used for higher latency bound because preference can be given to feasible transmission set with smaller energy cost. AsT increases, the energy cost of Greedy and DiGreedy decreases significantly. Compared to MIMSR which remains around435regardlessofβ,thesavingscanbeashighas50%. Figure6.6(d)showsthattotalnumberofusedslotsforthealgorithmswiththesametrafficloadand fixedT = 100. AsMIMSRalwaysschedulesthemaximalfeasibleset,ituseslessslotsintransmitting the traffic. However, by increasingβ, Greedy and DiGreedy would give higher and higher preference onlowenergycosttransmissionsets,thusincreasethenumberofslotsused. Themoreslotsusedmeans morepacketswillbetransmittedattheendofatimeframe,thusahigheraveragelatency,butstillwithin thelatencybound. Go back to figure 6.2(a) and 6.2(b) which show the schedules computed by β = 0 and β = 10 separately. Clearlyβ = 10isabletochoosemoreenergyefficienttransmissionsets. Lesson2: Byvaryingβ,thealgorithmisabletosavesignificantenergywithouthurtingthroughput. Figure 6.6(a) and 6.6(b) shows the number of packets delivered and the total energy cost in 20 frames which consists of 100 slots respectively. When β ≤ 10, Greedy and DiGreedy can deliver almost same number of packets. The energy cost decreases asβ increases even though the number of packets deliveredisthesame. Theenergysavingscanbeasmuchas50%. Thisshowsthealgorithms’abilityto chooseabettercombinationoftransmissionscenarios. Whenβ > 10, thenumberofpacketsdelivered by Greedy and DiGreedy begins to decrease. When β > 15, the algorithms will always choose the transmission scenario with only one link active that is most energy efficient. Thus the total number of packetscanbedeliveredin2000slotsremains2000. Figure6.6(c)showstheenergyefficiencyinterms of the number of packets delivered in units of energy. Clearly asβ increases, the energy efficiency of thescheduledsetincreases. Lesson 3: DiGreedy algorithm has comparable performance to the Greedy approximation algo- rithm. For all the simulations, Greedy and DiGreedy can save more energy than MIMSR while main- taining relatively same throughput or at a little sacrifice of the throughput. As we can see from all 4 Theunitofenergyis12.7τ mJ,whereτ isthetransmissiontimeofonepacket 108 (a) PacketTransmittedin2000slots. (b) Energycost. (c) Energy efficiency in terms of number of packets trans- mittedperunitofenergy. (d) Totalusedslotsfordeliveredpacket. Figure6.6: PerformanceofMIMSR,GreedyandDiGreedyasafunctionofβ withT = 100. figures,DiGreedy,asaheuristicsolutionwithnoapproximationguarantee,hasalmostthesameperfor- manceastheGreedywhichis(1− 1 e approximatetotheoptimizationsolution. 6.5.2 SimulationResultsforJSPC-TR We simulated the β ∗ -searching algorithm under various traffic load requests to find the β ∗ . Then we compared the performance of two different schedules computed by β = 0 and β ∗ . All results are averagedover10seeds. Inthesimulation,δ 1 =δ 2 = 0.8and = 10. Figure6.7(a)and6.7(b)showthenumberofslotsandenergyusedtofinishthetransmissionrequest under different traffic load separately. Under all traffic load request, our algorithm is able to operate in opt- β region and thus consume much less energy while all transmission requests are satisfied within T = 100 slots. The number of slots used by β ∗ are always between 90 and 100, except for very low trafficloadwhenthenumberofpacketsislessthan100. 109 (a) Numberofslotsused (b) Energycost Figure6.7: Performanceundervarioustrafficrequestload. 6.6 Discussion InEEJSPC,westudiedthefundamentalenergyefficiencyproblemofjointTDMAlinkschedulingand powercontrolinwirelesssensornetworks. Wefoundthatdifferenttransmissionscenariocanhavesig- nificantly different total transmission powers. By carefully choosing different combinations of feasible transmissionscenariosinmultipleslots,thetotalenergycostscanbereduced. Thisimprovesenergyef- ficiencycomparedtopreviouslyproposedjointschedulingandpowercontrolalgorithms,whichalways trytoschedulemaximumconcurrenttransmissions. Weformulatedajointlinkschedulingandpowercontrolproblemthataimstomaximizeafunction ofthroughputandenergycostsubjecttolatencyconstraint(TJPSPC).Thisformulationallowsatunable performance tradeoffs between throughput, latency and total energy cost. We showed this NP-hard problem formulation can be solved using a greedy algorithm which is an (1− 1 e )-approximation to the optimal solution with exponential approximation. We then presented DiGreedy, a heuristic greedy algorithm with polynomial complexity. Simulation results show that DiGreedy algorithm has similar performancetothegreedyalgorithm, andcanachievesignificantenergysavingsatnoorlittlesacrifice ofthethroughput. Wealsoinvestigatedthejointschedulingandpowercontrolproblemwithconstraint on the number of packets to be sent on each link. We leverage the heuristics for TJSPC to solve this problembyusingtheoptimumβwhichachievesenergyefficiencywhileguaranteeingthesatisfactionof transmissionrequests. Simulationresultsshow50%energysavingscanbeachievedwithoutsacrificing throughput. 110 6.7 Appendix Proposition10: wt(~ x)≥ [1−(1− 1 k k ]wt(OPT)> (1− 1 e )wt(OPT) Proof: Suppose~ x i isthegreedysolutioninthefirstislots,let G i = X k x i k S k and wt(G i ) = X e min( X k x i k S k , ~ b(e))−β X k x i k c k Supposeini+1slot,transmissionsetS j ischosen,Thenx i+1 j =x i j +1andG i+1 =G i ∪S j ,wehave: wt(G i+1 ) = X e min( X k x i+1 k S k , ~ b(e))−β X k x i+1 k c k Now,thegainofthefirstselected(i−1)setsiswt(G i−1 ). Thedifferencebetweenwt(G i−1 )tothe gain of the optimal solution iswt(OPT)−wt(G i−1 ). Then at leastwt(OPT)−wt(G i−1 ) worth of gainnotcoveredbythefirst(i−1)setsarecoveredbytheT setsofOPT. Bythepigeonholeprinciple, oneoftheT setsintheoptimalsolutionmustcoveratleast wt(OPT)−wt(Gi−1) T worthofgain. SinceS j isasetthatachievesmaximumadditionalgain,itmustalsocoveratleast wt(OPT)−wt(Gi−1) T . Thatis: wt(G i )−wt(G i−1 )≥ wt(OPT)−wt(G i−1 ) T Nowletussupposefori = 1,wt(G 1 )≥ wt(opt) T ,then, wt(G i+1 ) = wt(G i )+(wt(G i+1 )−wt(G i )) ≥ wt(G i )+ wt(OPT)−wt(G i ) T = (1− 1 T )wt(G i )+ wt(OPT) T ≥ (1− 1 T )(1−(1− 1 T ) i )wt(OPT)+ wt(OPT) T = (1−(1− 1 T ) i+1 )wt(OPT) > (1− 1 e )wt(OPT) 111 Chapter7 Conclusions 7.1 Summary In this thesis, we discussed the energy latency tradeoffs for medium access and sleep scheduling in wireless sensor networks and presented MAC protocol and scheduling algorithms for four specific ap- plication scenarios, which could achieve the balance between energy and latency under the different applicationrequirements. Wesummarizeourcontributionsinthischapter. PrevioussensornetworkMACprotocolssaveenergybysacrificingthelatencyperformance,which motivated us to design energy efficient yet also low latency MAC for wireless sensor networks. With differentapplicationscenarios,wehavestudiedfourproblemsandshownthatenergyefficientMACpro- tocolscanbedesignedforwirelesssensornetworkswithoutnecessarilysacrificingapplication-specific latencyperformance. For contention-based MAC, we first show that previously proposed MAC protocols for sensor net- works that utilize activation/sleep duty cycles suffer from a data forwarding interruption problem. In theseschemes, notallnodesonamultihoppathtothesinkcanbenotifiedofdatadeliveryinprogress, therefore intermediate nodes may go to sleep and can not help forward the packets, resulting in signif- icant sleep delay. By giving the active/sleep schedule of a node an offset that depends upon its depth onthetree,DMACallowscontinuouspacketforwardingbecauseallnodesonthemultihoppathcanbe notified of the data delivery in progress in a pipeline way. DMAC also adjusts node duty cycles adap- tively according to the traffic load in the network by varying the number of active slots in an schedule interval. Wefurtherproposeadatapredictionmechanismandtheuseofmoretosend(MTS)packetsin ordertoalleviateproblemspertainingtochannelcontentionandcollisions. Oursimulationresultsshow that by exploiting the application-specific structure of data gathering trees in sensor networks, DMAC providessignificantenergysavingsandlatencyreductionwhileensuringhighdatareliability. 112 Thesecondstudy,DESS,aimstominimizetheworstcommunicationlatencygiventhateachsensor has a duty cycling requirement of being awake for only 1 k time slots on an average. As a first step we consider the single wake-up schedule case, where each sensor can choose exactly one of the k slots to wake up. We formulate a novel graph-theoretical abstraction of this problem in the general setting of a low-traffic wireless sensor network with arbitrary communication flows and prove that minimizing the end-to-end communication delays is in general NP-hard. However, we are able to derive and analyze optimal solutions for two special cases: tree topologies and ring topologies. Several heuristics for arbitrarytopologiesareproposedandevaluatedbysimulations. Oursimulationssuggestthatdistributed heuristicsmayperformpoorlybecauseoftheglobalnatureoftheconstraintsinvolved. The third study, MLSR, considers the problem of minimizing the average communication latency for only the active flows to the base station in the network. Since the typical flows in wireless sensor networkarepredictableandlong-lived,itispossibletodesignroutingpathsoftheflowsandtheon/off schedulesofthenodesonthepathstominimizetheaveragelatencyforalltheactiveflows. Clearlythe scheduling and routing are closely coupled together, thus we formulated a joint scheduling and routing problem with objective to find the minimum latency joint schedule and route for current active flows. By constructing a novel delay graph, the problem can be solved optimally by M node-disjoint paths algorithm under FDMA channel model. We further extended the algorithm to handle dynamic traffic changes and topology changes in wireless sensor networks. We also proposed a heuristic solution for theminimumlatencyjointschedulingandroutingproblemundersinglechannelinterference. In fourth study, we investigate the fundamental issue of TDMA link scheduling with transmission powercontrolusingarealisticSINR-basedinterferencemodel. Weformulateitasanoveloptimization problem (TJSPC) that provides tunable tradeoffs between energy , throughput, and latency, through a single parameter β. We present a centralized greedy algorithm for this problem that has a provable (1− 1 e )-approximationguarantee,alongwithagooddistributedheuristic. Weevaluatetheperformance of these algorithms through simulations. Our results show that for moderate traffic loads, with appro- priate tuning of parameter β, major energy savings can be obtained without significantly sacrificing throughput. We further proposed the minimum energy joint scheduling and power control problem (EEJSPC) under throughput and latency constraints. We designed distributed iterative approach which leveragestheheurisitcsforTJSPCandconvergestotheoptimalβ inO( 1 epsilon )steps. All four case studies show that under specific application scenarios, it is possible to design both energy efficient and low latency medium access and sleep scheduling suitable for the specific sensor networkapplication. 113 7.2 FutureDirections Thereareseveralresearchdirectionsfortheworkpresentedinthisthesis. Herewebrieflydiscussthree possible extensions: the integration of information processing in general sleep scheduling techniques, different latency metrics in DESS and MLSR, the adaptive transmission rate and end-to-end latency probleminEEJSPC. 1. A specific feature of wireless sensor network is its data-centric paradigm [32, 92, 95, 96], as opposite to the address-centric or node-centric paradigm. Physical samples collected by sensors nearby are often strongly correlated. In-network processing, such as compression and signal processingisusefultoeliminateredundantdata,thussavestheinformationtobesenttothesink. A data centric routing scheme could affect the efficiency of data aggregation achieved in the network. Forexample,theauthorsin[85]analyzedtheperformanceofroutingwithcompression inwirelesssensornetworks. Asleepschedulingschemechangesthenetworktopologyfromtime to time, leading to re-construction of the routing paths. Yet it is not clear how to integrate the data centric routing schemes with sleep scheduling algorithms to choose the right node to sleep, the right time to sleep and the right path for data compression to satisfy the energy and latency requirementsoftheapplication. 2. InDESS,theobjectivefunctionistominimizetheworstcaselatencywhileinMLSRtheobjective is to minimize the average latency. There are other latency performance metrics. One example is that the flows in the network have different latency deadline requirements when the physical events the network detected require different respond speeds. Even for flows with same latency deadline,theflowwithsourceclosertothesinkcantoleratehighersleeplatencyperhop. Thusa differentsleepschedulingproblemwouldbetofindschedulesfornodesinthenetworktosatisfy eachflow’slatencydeadlinewithminimumenergy. 3. IntheworkofEEJSPC,weassumedafixeddatarateandSINRthresholdofwirelessradio. Many modern wireless radios [3], however, are capable of supporting multiple data rates. There are manyresearchworks[91,94,97,101,102]onenergyefficientschedulingofdynamicmodulation. Normallylowdataratemodulationislessefficientinutilizingchannelbandwidthbutmorerobust tonoiseandinterference,thuscanworkunderlowSINRenvironment. Highdataratemodulation, however,ismorebandwidthefficientyetlessrobusttochannelerror,thusrequireshighSINRand hightransmissionpower. WeneedtoextendthemodelinEEJSPCtotakethemultipledatarates andSINRthresholdsintoconsideration. 114 Another possible extension of EEJSPC is to consider the end-to-end delay of flows. In EEJSPC, weassumedaperhoplatencyboundwhichcanbecalculatedbasedonend-to-endlatencyandthe routing paths. A better scheme is to directly consider the end-to-end latency of the traffic flows. Packets can have different per hop latency bounds. Also the same packet can have different hop latency bounds at different hops. This, along with the multiple data rates and SINR thresholds, createsalargerdesignspacetoexplorebetterenergylatencytradeoffs. 115 AppendixA WakeupRadio A.1 Overview Wireless sensor networks have limited energy resource and need to save energy as much as possible. As idle listening in radios has been identified as a major source of energy wastage, energy efficient communicationprotocolsturnofftheradiotosaveenergywhenanodeisnotinsending/receivingstates ordoesnotdetectanyevent. However,thiscreatesproblemswithcommunication. Oftenitisnecessary for nodes that are not directly involved with sensing an event to be involved in communication later, such as a multihop relay node. Thus some wakeup schemes are needed in the network to wake up a sleepingnodewhenthenodeisneededforcommunication. Therearetwotypesofwakeupprotocols: activewakeupprotocolandondemandwakeupprotocol. In active wakeup protocols, nodes follow a pre-determined periodical wakeup/sleep schedule so that whennodesentersleepmode,theyscheduleatimertowakeupatapre-determinedtime,whichcanbe synchronous[60]orasynchronous[62]. Inondemandwakeupprotocol,asleepingnodecanbewoken atanytimeviaanout-of-bandchannel,suchaswake-on-wireless[51],STEM[54]andPicaRadio[75]. Therearealsohybridschemessuchasthosepresentedin[63]and[53]. Both active and on demand wakeup schemes have great potential in energy saving for sensor net- workswhencommunicationshappeninfrequently. However,thewakeupschemeshavethedisadvantage of increased latency. In active protocols, the periodical wakeup/sleep schedule in active wakeup pro- tocols cause sleep latency that is proportional to the number of hops with a slope of the duration of the pre-determined schedule iteration. Our works on DMAC [46] and DESS [48] identified this prob- lem and reduced the sleep latency to achieve low latency while keeping the same energy efficiency of the periodical wakeup/sleep schedule. The on-demand approaches, at the cost of additional hardware, 116 TableA.1: ThemeasuredaveragepowerconsumptionoftheMiniBrick Mode Sleep Receive Transmit Current(mA) 0.6 2.2 2.4 Power(mW) 2.0 7 8 potentiallycouldhavesmallerlatency. However,duetocurrentradiotechnologylimitations,eithernon- negligibleenergycostorlatencystillexistsintheon-demandwakeupprotocols. Inthischapter,wewill discuss the energy-latency tradeoffs for on-demand wakeup protocols. We argue that our low-latency andenergy-efficientsleepschedulingalgorithmscanbeemployedontopoftheon-demandprotocolsto achievebetterenergy-latencytradeoffs. On-demand wakeup schemes need an additional wakeup radio besides the data radio. Figure A.1 shows the communication abilities and energy cost of the radios. Current data radios have better com- munication abilities such as high data rate and long distance, but also with high idle listening power consumption. Thewakeupradioshavelimitedcommunicationabilities,suchasdetectingbusytone[53] orfrequencyidentification[58]. Thewakeupradiousesmuchlesspowercomparedtothedataradiovia eitheralowdutycycle[53,54]orhardwaredesign[56]. A.2 PreliminaryWakeupRadio The simplest way to implement a wakeup radio is to have the wakeup radio active all the time [51]. When a node need to communicate with a neighbor node, it sends a wakeup signal which may be a shortimpulseorashortmessage. However,duetocurrentradioabilities,theidlelisteningofthewakeup radiostillhasnon-negligibleenergycost. Forapplicationsthatneedtooperateformonthsorevenyears, the energy cost from the wakeup radio can not ignored. The authors in [51] built a prototype wakeup radio which is called MiniBrick. Table A.1 shows the power consumption of MinBrick. Compared to the power consumption of Lucent Orinoco card shown in table A.2, the power consumption is very low. However, compared to the radio in MICA2 mote shown in table A.3, the power consumption of MiniBrickcannotbeignored. IfMiniBrickisusedasawakeupradioinMica2, itcannotbeactive all thetimeotherwiseenergywillbedrainedoutquickly. Aslongasthepowerconsumptionofthewakeup radio is not negligible, it is still necessary to preserve energy of the wakeup radio. The best way again istoturnthewakeupradiooff. Thusactiveschedulingalgorithmscanstillbeemployedinthiscategory ofwakeupradio. 117 TableA.2: TheaveragepowerconsumptionoftheLucentOrinocoWLANcard Mode Sleep Receive Transmit Current(mA) 10 180 280 Power(mW) 50 900 1400 TableA.3: TheaveragepowerconsumptionofCC1000inMica2 Mode Sleep Receive Transmit Current(mA) 0.6 7.4 5.6 Power(mW) 1.8 22.2 16.8 A.3 PeriodicalActive/SleepWakeupRadio Some works [52, 53, 54] assume the wakeup radio achieves ultra low power by turning off wakeup radio periodically according to a pre-defined sleep schedule, same as the sleep schedule on the data radio. When a node has a message to its destination, it sends a wakeup signal on the wakeup radio thatislongenoughforthereceiver’swakeupradiotodetectthewakeupsignalduringitsactiveperiod, shown in Figure A.2. Some other works [64, 65, 66] proposed Preamble Sampling or Low Power Listening scheme, in which the receiver periodically wake up to sample the channel. If a node wish to transmit, it sends a preamble that is long enough so that the receiver can detect the preamble. Then the receiverwillbefullactivetoreceivethepacketfollowingthepreamble. Thewakeupsignalcanbesent overahighlevelinterfaceanddirectlyinthephysicallayerwhichismoreenergyefficient. Depending on the communication ability of the wakeup radio, there are broadcast wakeup or di- rected wakeup signals. If the destination ID can be encoded into the wakeup signal and the wakeup radioisabletodecodeit,thenonlytheintendedreceiverneedtobewakenup. Ifthewakeupsignalcan onlydetectabusytonebytheenergythreshold, thentheentireneighborhoodthesenderwillbewaken up. Inbroadcastwakeupschemes,becausethewakeupradioonlyneedstodetectawakeupsignal(e.g. busy tone) by an energy threshold, it does not need sophisticated circuit to decode a message thus the detection time of the wakeup radio can be designed to be very short (e.g. 1ms). Thus a short schedule iteration can be employed to reduce latency. However a broadcast wakeup signal will wake up entire neighborhood,inwhichmanynodesdoesnotneedtobewakenup. Althoughafilterpacketcanbesent latertoputnon-receivernodesbacktosleep,theswitchon/offoverheadcouldbehigh(e.g. inCC1000, the delay is about 4ms and power consumption is about 20mW). In a dense sensor network, this could incur significant energy wastage when only a small part of the nodes need to be active. In directed wakeupschemes,asthewakeupradioisdesignedtowakeuponlytheintendedreceiver,theactivetime 118 FigureA.1: Energyandcommunicationabilitiesofradios FigureA.2: Wakeupprocessintheperiodicalactive/sleepwakeupchannel of the wakeup radio has to be significantly long to receive a message, so is the total schedule iteration. Thusagainbecauseoftheperiodicalsleepscheduleofthewakeupradio,therewillbesleeplatencyon thewakeupchannel. STEM [54, 55] investigated both the directed wakeup scheme STEM-B and broadcast wakeup scheme STEM-T. While STEM-B is more energy efficient than STEM-T, it has significant longer la- tencyonthewakeupchannelthanSTEM-B.Authorsin[52]proposedaschemetoschedulethewakeup radio ahead of data radio in a similar way to DMAC to reduce the wakeup latency by pipeline the wakeupsignal. [52]usedabroadcastwakeupschemebutsentafilterpacketafterentireneighbornodes arewakenup. Thenduringthedatatransmissionfromthesendertothereceiveronthedatachannel,the receiver will send busy tone to wake up its own neighborhood on the wakeup channel. Then when the receiverreceivedthepacket,itcanimmediatelysendafilterpackettoitsneighborhoodanddatapacket toitsintendednexthopwithoutsleeplatency. Thus,webelievethesleepschedulealgorithmwestudied ondataradiocanalsobeemployedonthewakeupchanneltoachievebetterenergylatencytradeoffs. A.4 UltraLowPowerWakeupRadio Therearealsoworksondesignradiohardwarewithultralowpowerconsumptionthatthewakeupradio can be kept active all the time, such as PicoRadio [56, 75] and RTID [57]. RTID designed a radio- triggered hardware that is able to extracting energy from the radio signal to provide wake-up signals to the network node. However their wakeup radio acts as a mechanism to wakeup the CPU of the node, 119 TableA.4: Thewakeupradiotechnology WakeupRadios Preliminary Intermediate Premium Future Power Con- sumption Non-negligible Non-negligible Ultralow Ultralow ActiveSchedule Alwayson Periodical on/off Alwayson Alwayson Addressibility Directed Broadcast or Directed Broadcast Directed Strongpoint No sleep la- tency Low energy consumption of wakeupradio No sleep la- tency and low energycost No sleep la- tency and low energycost Weakness High energy cost Latency caused by periodical schedule Overhead of waking up all neighbors Contention in dataradio RoleofDESS DESS can schedule wakeup radio sleep without hurtinglatency DESS can reduce sleep latency on wakeupradio The schedule of DESS can avoid wak- ing up entire neighborhoods DESScanbein- corporated into TDMA to re- duce end-to-end sleeplatency notanintendedreceiverofamessage. AndtheeventonRTIDcanonlybesomeradiomessagesinstead of environment stimulant. The PicoRadio is not addressible, so it can be only designed as a broadcast mechanismwhichisnotsuitableforadensewirelesssensornetwork. Currently,thePicoRadioisstilla prototypeandhasnotbeenfullyimplemented. Even if we assume an ultra low power wakeup radio that can be kept active all the time and is ad- dressibleexists,thereisapotentialproblemofcontentionundermediumorhightrafficload. Firstthere are contentions on the wakeup channel. Because the wakeup signals contain the ID of the intended receivers, they must be correctly received by the receivers without collision. If in a single broadcast domain, multiple senders need to wakeup their receivers, the contentions on the wakeup channel could cause significant collisions of the wakeup signals because of the limited MAC ability of the wakeup radio. Eitherunrelatednodeshavetobewakenuportheintendedreceiverwillmissthepacketdepend- ingonthehandlingofacorruptedwakeupsignal. Forexample,STEM-B[54,55]isadirectedwakeup scheme. Whenthereiscollisioninthewakeupsignals, a nodedetectedacollisionpacketwillwakeup forasufficientperiodandgobacktosleepifitisnottheintendedreceiver. We further assume that the wakeup radio can employ CDMA schemes, so there is no contention in the wakeup channel. However, there are contention on the high rate data radio. Suppose multiple intended receivers are waken up and their senders will transmit the data messages to them. Under synchronized traffic load [61] which is caused by the same event, all the nodes are waken up at the sametimeandthuswillcontendforthedatachannelwhichcouldcausesignificantcollisionandenergy 120 cost. The TDMA-like contention free MAC can potentially eliminate the contention. However, since allnodesareassignedactiveslotstocommunicate,anodewouldhavetowaitforitsintendedreceiver’s active slot to transmit the data, which will cause the sleep latency. Previous TMAC protocols only focused on minimizing the length of a time frame in which each node is assigned at least one active slot. This can minimize the hop-by-hop latency, however, does not consider the increased end-to-end latencycausedbysleepscheduling. TheworkofDESScanbecombinedintothedesignofTDMAslot assignmenttoreducethesleeplatency,whilemaintainingcontentionfree. Oneofourfutureworkisto incorporatesomemechanismsintothesleepschedulingalgorithmtoreducethepossiblecontentionsof thesynchronizedtrafficload. Astheradiotechnologyevolves,whentheradioisabletosend/receivelongframeathighdatarate with negligible idle listening power, such as the future radio indicated in Figure A.1, then there is no need to turn off radio to save communication. The radio can be used for data transmission and be kept activeallthetime. 121 References [1] D. Estrin , J. Heidemann , R. Govindan and S. 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Gang, Lu
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Energy latency tradeoffs for medium access and sleep scheduling in wireless sensor networks
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