Optimization of Computer Networks: Modeling and Algorithms: A Hands-On Approach

420 Pages·2016·3.18 MB·English

by  Pablo Pav?n Mari?o

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OPTIMIZATION
OF COMPUTER
NETWORKS –
MODELING AND
ALGORITHMS
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OPTIMIZATION
OF COMPUTER
NETWORKS –
MODELING AND
ALGORITHMS
A HANDS-ON APPROACH
PabloPavónMariño
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Thiseditionfirstpublished2016
©2016,JohnWiley&Sons,Ltd
Registeredoffice
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LibraryofCongressCataloging-in-PublicationData
Names:Marino,PabloPavon,author.
Title:Optimizationofcomputernetworks:modelingandalgorithms:a
hands-onapproach/PabloPavonMarino.
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Description:Chichester,WestSussex,UnitedKingdom:JohnWiley&Sons,
Inc.,[2016]|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2015044522(print)|LCCN2016000694(ebook)|ISBN
9781119013358(cloth)|ISBN9781119013334(ePub)|ISBN9781119013341
(AdobePDF)
Subjects:LCSH:Networkperformance(Telecommunication)–Mathematicalmodels.
|Computernetworks–Mathematicalmodels.|Computeralgorithms.
Classification:LCCTK5102.83.M372016(print)|LCCTK5102.83(ebook)|DDC
004.601–dc23
LCrecordavailableathttp://lccn.loc.gov/2015044522
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
Setin10/12pt,TimesLTStdbySPiGlobal,Chennai,India.
1 2016
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To my sons, Pablo and Guille, and to my wife Victoria,
the smiles of my life.
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Contents
AbouttheAuthor xv
Preface xvii
Acknowledgments xxi
1 Introduction 1
1.1 WhatisaCommunicationNetwork? 1
1.2 CapturingtheRandomUserBehavior 4
1.3 QueueingTheoryandOptimizationTheory 5
(cid:2) 1.4 TheRationaleandOrganizationofthisBook 6 (cid:2)
1.4.1 PartI:Modeling 6
1.4.2 PartII:Algorithms 7
1.4.3 BasicOptimizationRequisites:AppendicesI,II,andIII 10
1.4.4 Net2PlanTool:AppendixIV 11
PartI MODELING
2 DefinitionsandNotation 15
2.1 NotationforSets,VectorsandMatrices 15
2.1.1 NormBasics 15
2.1.2 SetBasics 16
2.2 NetworkTopology 17
2.3 InstalledCapacities 19
2.4 TrafficDemands 19
2.4.1 Unicast,Anycast,andMulticastDemands 20
2.4.2 ElasticversusInelasticDemands 21
2.5 TrafficRouting 21
References 22
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viii Contents
3 PerformanceMetricsinNetworks 23
3.1 Introduction 23
3.2 Delay 23
3.2.1 LinkDelay 23
3.2.2 End-to-EndDelay 27
3.2.3 AverageNetworkDelay 27
3.2.4 ConvexityProperties 27
3.3 BlockingProbability 28
3.3.1 LinkBlockingProbability 28
3.3.2 DemandandNetworkBlockingProbability 30
3.3.3 OtherBlockingEstimations 31
3.3.4 ConvexityProperties 34
3.4 AverageNumberofHops 34
3.5 NetworkCongestion 36
3.6 NetworkCost 36
3.7 NetworkResilienceMetrics 37
3.7.1 SharedRiskGroups 40
3.7.2 SimplifiedAvailabilityCalculations 41
3.7.3 GeneralModel 41
3.8 NetworkUtilityandFairnessinResourceAllocation 44
3.8.1 FairnessinResourceAllocation 44
3.8.2 FairnessandUtilityFunctions 45
3.8.3 ConvexityProperties 47
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3.9 NotesandSources 47
3.10 Exercises 49
References 51
4 RoutingProblems 53
4.1 Introduction 53
4.2 Flow-PathFormulation 54
4.2.1 OptimalityAnalysis 55
4.2.2 CandidatePathListPre-Computation 58
4.2.3 RankingofPathsElaboration 58
4.2.4 CandidatePathListAugmentation(CPLA) 59
4.3 Flow-LinkFormulation 61
4.3.1 FlowConservationConstraints 62
4.3.2 ObtainingtheRoutingfromx Variables 63
de
4.3.3 OptimalityAnalysis 64
4.4 Destination-LinkFormulation 65
4.4.1 ObtainingtheRoutingTablesfromx Variables 67
te
4.4.2 SomePropertiesoftheRoutingTableRepresentation 67
4.4.3 ComparingFlow-BasedandDestination-BasedRouting 71
4.5 ConvexityPropertiesofPerformanceMetrics 71
4.6 ProblemVariants 72
4.6.1 AnycastRouting 72
4.6.2 MulticastRouting 74
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Contents ix
4.6.3 Non-BifurcatedRouting 75
4.6.4 IntegralRouting 77
4.6.5 Destination-BasedShortestPathRouting 77
4.6.6 SRG-Disjoint1+1DedicatedProtectionRouting 79
4.6.7 SharedRestorationRouting 80
4.6.8 Multi-HourRouting 81
4.7 NotesandSources 83
4.8 Exercises 83
References 86
5 CapacityAssignmentProblems 88
5.1 Introduction 88
5.2 Long-TermCapacityPlanningProblemVariants 89
5.2.1 CapacityPlanningforConcaveCosts 89
5.2.2 CapacityPlanningwithModularCapacities 94
5.2.3 Multi-PeriodCapacityPlanning 97
5.3 FastCapacityAllocationProblemVariants:WirelessNetworks 98
5.3.1 TheWirelessChannel 99
5.3.2 WirelessNetworks 100
5.3.3 ModelingWirelessNetworks 101
5.4 MACDesigninHard-InterferenceScenarios 104
5.4.1 OptimizationinRandomAccessNetworks 105
5.4.2 OptimizationinCarrier-SenseNetworks 109
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5.5 TransmissionPowerOptimizationinSoftInterferenceScenarios 113
5.6 NotesandSources 116
5.7 Exercises 117
References 118
6 CongestionControlProblems 120
6.1 Introduction 120
6.2 NUMModel 121
6.2.1 UtilityFunctionsforElasticandInelasticTraffic 121
6.2.2 FairCongestionControl 122
6.2.3 OptimalityConditions 123
6.3 CaseStudy:TCP 124
6.3.1 Window-BasedFlowControl 125
6.3.2 TCPReno 126
6.3.3 TCPVegas 131
6.4 ActiveQueueManagement(AQM) 134
6.4.1 ASimplifiedModeloftheTCP-AQMInterplay 135
6.5 NotesandSources 136
6.6 Exercises 137
References 139
7 TopologyDesignProblems 141
7.1 Introduction 141
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7.2 NodeLocationProblems 142
7.2.1 ProblemVariants 143
7.2.2 Results 144
7.3 FullTopologyDesignProblems 146
7.3.1 ProblemVariants 148
7.3.2 Results 150
7.4 MultilayerNetworkDesign 152
7.5 NotesandSources 154
7.6 Exercises 154
References 157
PartII ALGORITHMS
8 GradientAlgorithmsinNetworkDesign 161
8.1 Introduction 161
8.2 ConvergenceRates 163
8.3 ProjectedGradientMethods 164
8.3.1 BasicGradientProjectionAlgorithm 165
8.3.2 ScaledProjectedGradientMethod 165
8.3.3 SingularandIll-ConditionedProblems 168
8.4 AsynchronousandDistributedAlgorithmImplementations 169
8.5 Non-SmoothFunctions 172
(cid:2) 8.6 StochasticGradientMethods 174 (cid:2)
8.7 StoppingCriteria 176
8.8 AlgorithmDesignHints 177
8.8.1 DimensioningtheStepSize 177
8.8.2 DiscreteStepLength 178
8.8.3 Heavy-BallMethods 179
8.9 NotesandSources 181
8.10 Exercises 181
References 182
9 PrimalGradientAlgorithms 184
9.1 Introduction 184
9.2 PenaltyMethods 185
9.2.1 InteriorPenaltyMethods 185
9.2.2 ExteriorPenaltyMethods 186
9.3 AdaptiveBifurcatedRouting 188
9.3.1 RemovingEqualityConstraints 189
9.3.2 OptimalityandStability 190
9.3.3 ImplementationExample 192
9.4 CongestionControlusingBarrierFunctions 197
9.4.1 ImplementationExample 198
9.4.2 ExteriorPenalty 200
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