Efficient Multirate Teletraffic Loss Models B (Wiley - IEEE)

556 Pages·2019·25.587 MB·English

by  Ioannis D. Moscholios, Michael D. Logothetis

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EfficientMultirateTeletrafficLossModelsBeyondErlang
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Efficient Multirate Teletraffic Loss Models
Beyond Erlang
IoannisD.Moscholios
UniversityofPeloponnese,Greece
MichaelD.Logothetis
UniversityofPatras,Greece
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Thiseditionfirstpublished2019
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LibraryofCongressCataloging-in-PublicationData
Names:Moscholios,IoannisD(AssociateProfessorattheUniversityofPeloponnese),author.|
Logothetis,MichaelD(ProfessorattheUniversityofPatras),author.
Title:EfficientmultirateteletrafficlossmodelsbeyondErlang/Ioannis
D.Moscholios,UniversityofPeloponnese,MichaelD.Logothetis,UniversityofPatras.
Description:Firstedition.|Hoboken,NJ:JohnWiley&Sons,Inc.,2019.|
Includesbibliographicalreferencesandindex.|
Identifiers:LCCN2018052862(print)|LCCN2018056391(ebook)|ISBN
9781119426905(AdobePDF)|ISBN9781119426912(ePub)|ISBN9781119426882
(hardcover)
Subjects:LCSH:Telecommunication–Traffic–Mathematicalmodels.|Queuing
theory.
Classification:LCCTK5102.985(ebook)|LCCTK5102.985.L642019(print)|
DDC621.38201/51982–dc23
LCrecordavailableathttps://lccn.loc.gov/2018052862
CoverDesign:Wiley
CoverImage:©WenjieDong/iStock.com
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
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Toourfamilies
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vii
Contents
ListofFigures xvii
ListofTables xxv
Preface xxix
Acronyms xxxiii
Symbols xxxvii
AbouttheCompanionWebsite xxxix
Introduction xli
I.1 Traffic-loadDefinition xlii
I.2 TrafficCongestionandGoS/QoS xliii
I.3 SystemCapacity xliv
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I.4 TeletrafficModels xlv
I.5 Traffic-loadProperties xlviii
I.6 CallArrivalProcess l
I.6.1 SuperpositionandDecompositionofPoissonProcesses lv
I.6.2 PoissonArrivalsSeeTimeAverages lvi
I.7 CallServiceTime lvii
I.7.1 MarkovProperty lvii
I.8 ServiceSystems lix
I.9 Little’sLaw lxi
I.10 OtherPerformanceMetricsofLossSystems lxii
I.11 GeneralExamples lxiii
I.12 Service-classes–BandwidthSharingPolicies lxiv
I.13 ClassificationofTeletrafficLossModels lxx
I.14 TeletrafficModelsandtheInternet lxxi
References lxxiv
PartI TeletrafficModelsofRandomInput 1
1 TheErlangMultirateLossModel 3
1.1 TheErlangLossModel 3
1.1.1 TheServiceSystem 3
1.1.2 GlobalandLocalBalance 5
1.1.3 CallBlockingProbability 8
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viii Contents
1.1.4 OtherPerformanceMetrics 11
1.2 TheErlangMultirateLossModel 13
1.2.1 TheServiceSystem 13
1.2.2 TheAnalyticalModel 15
1.2.2.1 SteadyStateProbabilities 15
1.2.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 21
1.3 TheErlangMultirateLossModelundertheBRpolicy 28
1.3.1 TheServiceSystem 28
1.3.2 TheAnalyticalModel 30
1.3.2.1 AccurateCBPCalculation 31
1.3.2.2 ApproximateCBPCalculationbasedontheRobertsMethod 32
1.3.2.3 CBPCalculationRecursivelybasedontheStasiak–GlabowskiMethod 34
1.4 TheErlangMultirateLossModelundertheThresholdPolicy 38
1.4.1 TheServiceSystem 38
1.4.2 TheAnalyticalModel 40
1.4.2.1 SteadyStateProbabilities 40
1.4.2.2 CBP,UtilizationandMeanNumberofIn-serviceCalls 42
1.5 TheErlangMultirateLossModelinaFixed
RoutingNetwork 44
1.5.1 TheServiceSystem 44
1.5.2 TheAnalyticalModel 45
1.5.2.1 SteadyStateProbabilities 46
(cid:2) 1.5.2.2 CBP,Utilization,andMeanNumberofIn-serviceCallsintheSystem 46 (cid:2)
1.5.3 CBPCalculationbytheRLAMethod 49
1.5.3.1 AFixedRoutingNetworkSupportingaSingleService-class 49
1.5.3.2 AFixedRoutingNetworkSupportingMultipleService-classes 51
1.6 Applications 54
1.6.1 TheErlang-BFormula 54
1.6.2 TheErlang-CFormula 55
1.6.3 TheKaufman–RobertsRecursion 56
1.7 FurtherReading 58
References 60
2 MultirateRetryThresholdLossModels 65
2.1 TheSingle-RetryModel 65
2.1.1 TheServiceSystem 65
2.1.2 TheAnalyticalModel 69
2.1.2.1 SteadyStateProbabilities 69
2.1.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 70
2.2 TheSingle-RetryModelundertheBRPolicy 72
2.2.1 TheServiceSystem 72
2.2.2 TheAnalyticalModel 75
2.2.2.1 SteadyStateProbabilities 75
2.2.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 75
2.3 TheMulti-RetryModel 77
2.3.1 TheServiceSystem 77
2.3.2 TheAnalyticalModel 83
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Contents ix
2.3.2.1 SteadyStateProbabilities 83
2.3.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 83
2.4 TheMulti-RetryModelundertheBRPolicy 86
2.4.1 TheServiceSystem 86
2.4.2 TheAnalyticalModel 87
2.4.2.1 SteadyStateProbabilities 87
2.4.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 88
2.5 TheSingle-ThresholdModel 92
2.5.1 TheServiceSystem 92
2.5.2 TheAnalyticalModel 96
2.5.2.1 SteadyStateProbabilities 96
2.5.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 97
2.6 TheSingle-ThresholdModelundertheBRPolicy 99
2.6.1 TheServiceSystem 99
2.6.2 TheAnalyticalModel 101
2.6.2.1 SteadyStateProbabilities 101
2.6.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 101
2.7 TheMulti-ThresholdModel 107
2.7.1 TheServiceSystem 107
2.7.2 TheAnalyticalModel 107
2.7.2.1 SteadyStateProbabilities 107
2.7.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 108
(cid:2) 2.8 TheMulti-ThresholdModelundertheBRPolicy 109 (cid:2)
2.8.1 TheServiceSystem 109
2.8.2 TheAnalyticalModel 109
2.8.2.1 SteadyStateProbabilities 109
2.8.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 109
2.9 TheConnectionDependentThresholdModel 112
2.9.1 TheServiceSystem 112
2.9.2 TheAnalyticalModel 114
2.9.2.1 SteadyStateProbabilities 114
2.9.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 116
2.10 TheConnectionDependentThresholdModelundertheBRPolicy 119
2.10.1 TheServiceSystem 119
2.10.2 TheAnalyticalModel 119
2.10.2.1 LinkOccupancyDistribution 119
2.10.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 120
2.11 Applications 121
2.12 FurtherReading 129
References 130
3 MultirateElasticAdaptiveLossModels 133
3.1 TheElasticErlangMultirateLossModel 133
3.1.1 TheServiceSystem 133
3.1.2 TheAnalyticalModel 139
3.1.2.1 SteadyStateProbabilities 139
3.1.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 141
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3.1.2.3 RelationshipbetweentheE-EMLMandtheBalancedFairShareModel 143
3.2 TheElasticErlangMultirateLossModelundertheBRPolicy 146
3.2.1 TheServiceSystem 146
3.2.2 TheAnalyticalModel 149
3.2.2.1 LinkOccupancyDistribution 149
3.2.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 149
3.3 TheElasticErlangMultirateLossModelundertheThresholdPolicy 152
3.3.1 TheServiceSystem 152
3.3.2 TheAnalyticalModel 156
3.3.2.1 SteadyStateProbabilities 156
3.3.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 157
3.4 TheElasticAdaptiveErlangMultirateLossModel 163
3.4.1 TheServiceSystem 163
3.4.2 TheAnalyticalModel 171
3.4.2.1 SteadyStateProbabilities 171
3.4.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 172
3.5 TheElasticAdaptiveErlangMultirateLossModelundertheBRPolicy 175
3.5.1 TheServiceSystem 175
3.5.2 TheAnalyticalModel 177
3.5.2.1 LinkOccupancyDistribution 177
3.5.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 178
3.6 TheElasticAdaptiveErlangMultirateLossModelundertheThreshold
(cid:2) Policy 179 (cid:2)
3.6.1 TheServiceSystem 179
3.6.2 TheAnalyticalModel 182
3.6.2.1 SteadyStateProbabilities 182
3.6.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 183
3.7 Applications 185
3.8 FurtherReading 190
References 191
4 MultirateElasticAdaptiveRetryLossModels 195
4.1 TheElasticSingle-RetryModel 195
4.1.1 TheServiceSystem 195
4.1.2 TheAnalyticalModel 201
4.1.2.1 SteadyStateProbabilities 201
4.1.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 204
4.2 TheElasticSingle-RetryModelundertheBRPolicy 206
4.2.1 TheServiceSystem 206
4.2.2 TheAnalyticalModel 210
4.2.2.1 LinkOccupancyDistribution 210
4.2.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 211
4.3 TheElasticMulti-RetryModel 212
4.3.1 TheServiceSystem 212
4.3.2 TheAnalyticalModel 218
4.3.2.1 SteadyStateProbabilities 218
4.3.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 218
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Contents xi
4.4 TheElasticMulti-RetryModelundertheBRPolicy 220
4.4.1 TheServiceSystem 220
4.4.2 TheAnalyticalModel 223
4.4.2.1 SteadyStateProbabilities 223
4.4.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 224
4.5 TheElasticAdaptiveSingle-RetryModel 226
4.5.1 TheServiceSystem 226
4.5.2 TheAnalyticalModel 233
4.5.2.1 SteadyStateProbabilities 233
4.5.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 236
4.6 TheElasticAdaptiveSingle-RetryModel
undertheBRPolicy 237
4.6.1 TheServiceSystem 237
4.6.2 TheAnalyticalModel 241
4.6.2.1 LinkOccupancyDistribution 241
4.6.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 241
4.7 TheElasticAdaptiveMulti-RetryModel 243
4.7.1 TheServiceSystem 243
4.7.2 TheAnalyticalModel 248
4.7.2.1 SteadyStateProbabilities 248
4.7.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 249
4.8 TheElasticAdaptiveMulti-RetryModelundertheBRPolicy 250
(cid:2) 4.8.1 TheServiceSystem 250 (cid:2)
4.8.2 TheAnalyticalModel 254
4.8.2.1 SteadyStateProbabilities 254
4.8.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 255
4.9 Applications 258
4.10 FurtherReading 258
References 260
5 On–OffMultirateLossModels 263
5.1 TheON–OFFMultirateLossModel 263
5.1.1 TheServiceSystem 263
5.1.2 TheAnalyticalModel 265
5.1.2.1 SteadyStateProbabilities 265
5.1.2.2 CBPandUtilization 269
5.1.2.3 BBP 270
5.2 TheON–OFFMultirateLossModelundertheBRPolicy 275
5.2.1 TheServiceSystem 275
5.2.2 TheAnalyticalModel 276
5.2.2.1 SteadyStateProbabilities 276
5.2.2.2 CBP,Utilization,andMeanNumberofIn-serviceCalls 276
5.2.2.3 BBP 276
5.3 TheON–OFFMultirateLossModelinaFixedRoutingNetwork 280
5.3.1 TheServiceSystem 280
5.3.2 TheAnalyticalModel 280
5.3.2.1 SteadyStateProbabilities 280
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