Flow Networks: Analysis and optimization of repairable flow networks, networks with disturbed flows, static flow networks and reliability networks

266 Pages·2013·7.57 MB·English

by  Michael T. Todinov

Flow Networks
Thispageintentionallyleftblank
Flow Networks
Analysis and Optimization
of Repairable Flow Networks,
Networks with Disturbed Flows,
Static Flow Networks and
Reliability Networks
Michael T. Todinov
OxfordBrookesUniversity
Oxford,UK
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON(cid:129)NEWYORK(cid:129)OXFORD
PARIS(cid:129)SANDIEGO(cid:129)SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
Elsevier
32JamestownRoad,LondonNW17BY
225WymanStreet,Waltham,MA02451,USA
Firstedition2013
Copyright©2013ElsevierInc.Allrightsreserved
Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,
electronicormechanical,includingphotocopying,recording,oranyinformationstorageand
retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek
permission,furtherinformationaboutthePublisher’spermissionspoliciesandour
arrangementwithorganizationssuchastheCopyrightClearanceCenterandtheCopyright
LicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions
Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightby
thePublisher(otherthanasmaybenotedherein).
Notices
Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchand
experiencebroadenourunderstanding,changesinresearchmethods,professionalpractices,
ormedicaltreatmentmaybecomenecessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein
evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribed
herein.Inusingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyand
thesafetyofothers,includingpartiesforwhomtheyhaveaprofessionalresponsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,
assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterof
productsliability,negligenceorotherwise,orfromanyuseoroperationofanymethods,
products,instructions,orideascontainedinthematerialherein.
BritishLibraryCataloguing-in-PublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloging-in-PublicationData
AcatalogrecordforthisbookisavailablefromtheLibraryofCongress
ISBN:978-0-12-398396-1
ForinformationonallElsevierpublications
visitourwebsiteatstore.elsevier.com
ThisbookhasbeenmanufacturedusingPrintOnDemandtechnology.Eachcopyis
producedtoorderandislimitedtoblackink.Theonlineversionofthisbookwillshow
colorfigureswhereappropriate.
ToProlet,MarinaandMarin
Thispageintentionallyleftblank
Contents
Preface xiii
1 FlowNetworks(cid:1)ExistingAnalysisApproachesandLimitations 1
1.1 RepairableFlowNetworksandStaticFlowNetworks 1
1.2 RepairableFlowNetworksandStochasticFlowNetworks 6
1.3 NetworkswithDisturbedFlowsandStochasticFlowNetworks 9
1.4 PerformanceofRepairableFlowNetworks 11
2 FlowNetworksandPaths(cid:1)BasicConcepts,Conventions
andAlgorithms 13
2.1 BasicConceptsandConventions:DataStructuresforRepresenting
FlowNetworks 13
2.2 Pseudo-CodeConventionsUsedintheAlgorithms 14
2.3 EfficientRepresentationofFlowNetworkswith
ComplexTopology 17
2.3.1 RepresentingtheTopologyofaComplexFlowNetwork
byanAdjacencyMatrix 18
2.3.2 RepresentingtheTopologyofaComplexFlow
NetworkbyAdjacencyArrays 19
2.4 Paths:AlgorithmsRelatedtoPathsinFlowNetworks 20
2.4.1 DeterminingtheShortestPathfromtheSourcetotheSink 20
2.4.2 DeterminingAllPossibleSource-to-SinkMinimalPaths 23
2.5 DeterminingtheSmallest-CostPathsfromtheSource 25
2.6 TopologicalSortingofNetworksWithoutCycles 27
2.7 TransformingFlowNetworks 29
3 KeyConcepts,ResultsandAlgorithmsRelatedtoStatic
FlowNetworks 31
3.1 PathAugmentationinFlowNetworks 31
3.2 BoundingtheMaximumThroughputFlowbytheCapacity
ofs(cid:1)tCuts 33
3.3 ANecessaryandSufficientConditionforaMaximumThroughput
FlowinaStaticNetwork:TheMax-FlowMin-CutTheorem 35
3.4 ClassicalAugmentationAlgorithmsforDeterminingthe
MaximumThroughputFlowinNetworks 37
3.5 GeneralPush-RelabelAlgorithmforMaximisingtheThroughput
FlowinaNetwork 42
viii Contents
3.6 Applications 47
3.7 SuccessiveShortest-PathAlgorithmforDeterminingthe
MaximumThroughputFlowataMinimumCost 54
3.7.1 SolvedExample 56
4 MaximisingtheThroughputFlowinSingle-and
Multi-CommodityNetworks:RemovingParasiticDirectedLoops
ofFlowinNetworksOptimisedbyClassicalAlgorithms 59
4.1 EliminatingParasitic DirectedLoopsofFlowinNetworks
OptimisedbyClassicalAlgorithms 59
4.2 ATwo-StageAugmentationAlgorithmforDetermining
theMaximumThroughputFlowinaNetwork 64
4.3 ANew,EfficientAlgorithmforMaximisingtheThroughput
FlowoftheUsefulCommodityinaMulti-CommodityFlowNetwork 67
4.4 NetworkFlowTransformationAlongCyclicPaths 71
5 NetworkswithDisturbedFlowsDualNetworkTheorems
forNetworkswithDisturbedFlows:ReoptimisingthePower
FlowsinActivePowerNetworksinRealTime 75
5.1 ReoptimisingtheFlowinNetworkswithDisturbedFlows
AfterEdgeFailuresandAfterChokingtheEdgeFlows 75
5.2 AFastAugmentationAlgorithmforReoptimisingthe
FlowinaRepairableNetworkAfteranEdgeFailure 76
5.3 AnAlgorithmforMaximisingtheThroughputFlowof
OilAfteraComponentFailureinMulti-Commodity
OilProductionNetworks 89
5.4 AHigh-SpeedControlofLargeandComplexActivePower
DistributionNetworks 92
5.4.1 OptimalControlofthePowerFlowsinPower
DistributionNetworkswithActiveControl,Aftera
ContingencyEvent 93
5.4.2 TransforminganActivePowerNetwork,withDistributed
SourcesofGenerationandLoads,intoaSingle-Source
Single-SinkNetwork 97
AppendixA 99
6 TheDualNetworkTheoremforStaticFlowNetworksand
ItsApplicationforMaximisingtheThroughputFlow 107
6.1 AnalysisoftheDrainingAlgorithmforMaximisingthe
ThroughputFlowinStaticNetworks 107
6.2 TheDualNetworkTheoremforStaticFlowNetworks 110
6.3 ImprovingtheAverageRunningTimeofMaximisingthe
ThroughputFlowintheDualNetwork 115
6.4 ApplicationoftheDualNetworkTheoremforDetermining
theMaximumThroughputFlowinaStaticFlowNetwork 117
Contents ix
6.4.1 SolvedExamples 119
6.5 AreaofApplicationoftheProposedThroughputFlow
MaximisationAlgorithm 122
6.5.1 ComparingthePerformanceoftheProposedAlgorithm
withthePerformanceofaConventionalAlgorithm 124
7 ReliabilityoftheThroughputFlow:AlgorithmsforDetermining
theThroughputFlowReliability 125
7.1 ProbabilitythatanEdgeWillBeinaWorkingStateonDemand 125
7.1.1 HazardRate:AGeneralTime-to-FailureModel 125
7.1.2 NegativeExponentialDistributionoftheTimeto
Failure:MeanTimetoFailure 127
7.1.3 OtherTime-to-FailureModels 129
7.2 ProbabilityofaSource-to-SinkFlowonDemand 131
7.2.1 AnalyticalMethods 131
7.2.1.1 AnalyticalExpressionsforSeriesandParallel
ArrangementoftheEdges 131
7.2.1.2 NetworkReductionMethod 133
7.2.1.3 DecompositionMethod 134
7.2.2 MonteCarloSimulationMethods 138
7.3 ProbabilityofaSource-to-SinkFlowonDemand,
ofSpecifiedMagnitude 139
8 ReliabilityNetworks 143
8.1 SeriesandParallelArrangementoftheComponents
inaReliabilityNetwork 143
8.2 BuildingReliabilityNetworks:DifferenceBetween
aPhysicalandLogicalArrangement 144
8.3 ComplexReliabilityNetworksWhichCannotBe
RepresentedAsaCombinationofSeries
andParallelArrangements 148
8.4 EvaluatingtheReliabilityofComplexSystems 157
9 ProductionAvailabilityofRepairableFlowNetworks 167
9.1 Discrete-EventSolverforDeterminingtheProduction
AvailabilityofRepairableFlowNetworks 167
9.2 AFastAlgorithmforDeterminingtheProduction
AvailabilityofRepairableFlowNetworks 173
9.3 ComparingthePerformanceofCompetingNetworkTopologies 177
10 LinkBetweenTopology,SizeandPerformanceofRepairable
FlowNetworks 179
10.1 ASoftwareToolforAnalysisandOptimisationof
RepairableFlowNetworks 179