IOANNIS D. MOSCHOLIOS, PHD, is an Associate Professor in the Department of Informatics and Telecommunications, University of Peloponnese, Tripolis, Greece. His research interests include teletraffic engineering, simulation and performance analysis of communication networks, and queueing theory. MICHAEL D. LOGOTHETIS, PHD, is a Professor in the ECE Department of the University of Patras, Greece. His research interests include teletraffic theory/engineering, traffic/network control, and simulation and performance optimization of communications networks.

• List of Figures xviiList of Tables xxvPreface xxixAcronyms xxxiiiSymbols xxxviiAbout the Companion Website xxxixIntroduction xliI.1 Traffic-load Definition xliiI.2 Traffic Congestion and GoS/QoS xliiiI.3 System Capacity xlivI.4 Teletraffic Models xlvI.5 Traffic-load Properties xlviiiI.6 Call Arrival Process lI.6.1 Superposition and Decomposition of Poisson Processes lvI.6.2 Poisson Arrivals See Time Averages lviI.7 Call Service Time lviiI.7.1 Markov Property lviiI.8 Service Systems lixI.9 Little’s Law lxiI.10 Other Performance Metrics of Loss Systems lxiiI.11 General Examples lxiiiI.12 Service-classes – Bandwidth Sharing Policies lxivI.13 Classification of Teletraffic Loss Models lxxI.14 Teletraffic Models and the Internet lxxiReferences lxxivPart I Teletraffic Models of Random Input 11 The Erlang Multirate Loss Model 31.1 The Erlang Loss Model 31.1.1 The Service System 31.1.2 Global and Local Balance 51.1.3 Call Blocking Probability 81.1.4 Other Performance Metrics 111.2 The Erlang Multirate Loss Model 131.2.1 The Service System 131.2.2 The Analytical Model 151.3 The Erlang Multirate Loss Model under the BR policy 281.3.1 The Service System 281.3.2 The Analytical Model 301.4 The Erlang Multirate Loss Model under the Threshold Policy 381.4.1 The Service System 381.4.2 The Analytical Model 401.5 The Erlang Multirate Loss Model in a Fixed Routing Network 441.5.1 The Service System 441.5.2 The Analytical Model 451.5.3 CBP Calculation by the RLA Method 491.6 Applications 541.6.1 The Erlang-B Formula 541.6.2 The Erlang-C Formula 551.6.3 The Kaufman–Roberts Recursion 561.7 Further Reading 58References 602 Multirate Retry Threshold Loss Models 652.1 The Single-Retry Model 652.1.1 The Service System 652.1.2 The Analytical Model 692.2 The Single-Retry Model under the BR Policy 722.2.1 The Service System 722.2.2 The Analytical Model 752.3 The Multi-Retry Model 772.3.1 The Service System 772.3.2 The Analytical Model 832.4 The Multi-Retry Model under the BR Policy 862.4.1 The Service System 862.4.2 The Analytical Model 872.5 The Single-Threshold Model 922.5.1 The Service System 922.5.2 The Analytical Model 962.6 The Single-Threshold Model under the BR Policy 992.6.1 The Service System 992.6.2 The Analytical Model 1012.7 The Multi-Threshold Model 1072.7.1 The Service System 1072.7.2 The Analytical Model 1072.8 The Multi-Threshold Model under the BR Policy 1092.8.1 The Service System 1092.8.2 The Analytical Model 1092.9 The Connection Dependent Threshold Model 1122.9.1 The Service System 1122.9.2 The Analytical Model 1142.10 The Connection Dependent Threshold Model under the BR Policy 1192.10.1 The Service System 1192.10.2 The Analytical Model 1192.11 Applications 1212.12 Further Reading 129References 1303 Multirate Elastic Adaptive Loss Models 1333.1 The Elastic Erlang Multirate Loss Model 1333.1.1 The Service System 1333.1.2 The Analytical Model 1393.2 The Elastic Erlang Multirate Loss Model under the BR Policy 1463.2.1 The Service System 1463.2.2 The Analytical Model 1493.3 The Elastic Erlang Multirate Loss Model under the Threshold Policy 1523.3.1 The Service System 1523.3.2 The Analytical Model 1563.4 The Elastic Adaptive Erlang Multirate Loss Model 1633.4.1 The Service System 1633.4.2 The Analytical Model 1713.5 The Elastic Adaptive Erlang Multirate Loss Model under the BR Policy 1753.5.1 The Service System 1753.5.2 The Analytical Model 1773.6 The Elastic Adaptive Erlang Multirate Loss Model under the Threshold Policy 1793.6.1 The Service System 1793.6.2 The Analytical Model 1823.7 Applications 1853.8 Further Reading 190References 1914 Multirate Elastic Adaptive Retry Loss Models 1954.1 The Elastic Single-Retry Model 1954.1.1 The Service System 1954.1.2 The Analytical Model 2014.2 The Elastic Single-Retry Model under the BR Policy 2064.2.1 The Service System 2064.2.2 The Analytical Model 2104.3 The Elastic Multi-Retry Model 2124.3.1 The Service System 2124.3.2 The Analytical Model 2184.4 The Elastic Multi-Retry Model under the BR Policy 2204.4.1 The Service System 2204.4.2 The Analytical Model 2234.5 The Elastic Adaptive Single-Retry Model 2264.5.1 The Service System 2264.5.2 The Analytical Model 2334.6 The Elastic Adaptive Single-Retry Model under the BR Policy 2374.6.1 The Service System 2374.6.2 The Analytical Model 2414.7 The Elastic Adaptive Multi-Retry Model 2434.7.1 The Service System 2434.7.2 The Analytical Model 2484.8 The Elastic Adaptive Multi-Retry Model under the BR Policy 2504.8.1 The Service System 2504.8.2 The Analytical Model 2544.9 Applications 2584.10 Further Reading 258References 2605 ON–OFF Multirate Loss Models 2635.1 The ON–OFF Multirate Loss Model 2635.1.1 The Service System 2635.1.2 The Analytical Model 2655.2 The ON–OFF Multirate Loss Model under the BR Policy 2755.2.1 The Service System 2755.2.2 The Analytical Model 2765.3 The ON–OFF Multirate Loss Model in a Fixed Routing Network 2805.3.1 The Service System 2805.3.2 The Analytical Model 2805.4 Applications 2855.5 Further Reading 288References 289Part II Teletraffic Models of Quasi-Random Input 2916 The Engset Multirate Loss Model 2936.1 The Engset Loss Model 2936.1.1 The Service System 2936.1.2 The Analytical Model 2936.2 The Engset Multirate Loss Model 2986.2.1 The Service System 2986.2.2 The Analytical Model 3006.3 The Engset Multirate Loss Model under the BR Policy 3086.3.1 The Service System 3086.3.2 The Analytical Model 3106.4 The Engset Multirate Loss Model under the TH Policy 3126.4.1 The Service System 3126.4.2 The Analytical Model 3126.5 Applications 3186.6 Further Reading 324References 3277 Finite Multirate Retry Threshold Loss Models 3317.1 The Finite Single-Retry Model 3317.1.1 The Service System 3317.1.2 The Analytical Model 3337.2 The Finite Single-Retry Model under the BR Policy 3387.2.1 The Service System 3387.2.2 The Analytical Model 3407.3 The Finite Multi-Retry Model 3427.3.1 The Service System 3427.3.2 The Analytical Model 3447.4 The Finite Multi-Retry Model under the BR Policy 3487.4.1 The Service System 3487.4.2 The Analytical Model 3497.5 The Finite Single-Threshold Model 3537.5.1 The Service System 3537.5.2 The Analytical Model 3557.6 The Finite Single-Threshold Model under the BR Policy 3607.6.1 The Service System 3607.6.2 The Analytical Model 3627.7 The Finite Multi-Threshold Model 3637.7.1 The Service System 3637.7.2 The Analytical Model 3647.8 The Finite Multi-Threshold Model under the BR Policy 3667.8.1 The Service System 3667.8.2 The Analytical Model 3667.9 The Finite Connection Dependent Threshold Model 3677.9.1 The Service System 3677.9.2 The Analytical Model 3687.10 The Finite Connection Dependent Threshold Model under the BR Policy 3737.10.1 The Service System 3737.10.2 The Analytical Model 3737.11 Applications 3747.12 Further Reading 374References 3758 Finite Multirate Elastic Adaptive Loss Models 3778.1 The Elastic Engset Multirate Loss Model 3778.1.1 The Service System 3778.1.2 The Analytical Model 3808.2 The Elastic Engset Multirate Loss Model under the BR Policy 3838.2.1 The Service System 3838.2.2 The Analytical Model 3858.3 The Elastic Adaptive Engset Multirate Loss Model 3878.3.1 The Service System 3878.3.2 The Analytical Model 3898.4 The Elastic Adaptive Engset Multirate Loss Model under the BR Policy 3928.4.1 The Service System 3928.4.2 The Analytical Model 3948.5 Applications 4028.6 Further Reading 405References 4059 Finite ON–OFF Multirate Loss Models 4079.1 The Finite ON–OFF Multirate Loss Model 4079.1.1 The Service System 4079.1.2 The AnalyticalModel 4089.2 Generalization of the f-ON–OFF Model to include Service-classes with a Mixture of a Finite and an Infinite Number of Sources 4159.3 Applications 4169.4 Further Reading 422References 423Part III Teletraffic Models of Batched Poisson Input 42510 The Erlang Multirate Loss ModelWith Batched Poisson Arrivals 42710.1 The Erlang Multirate Loss Model with Batched Poisson Arrivals 42710.1.1 The Service System 42710.1.2 The AnalyticalModel 42810.2 The Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR Policy 43510.2.1 The Service System 43510.2.2 The AnalyticalModel 43510.3 The Erlang Multirate Loss Model with Batched Poisson Arrivals under the Threshold Policy 44110.3.1 The Service System 44110.3.2 The Analytical Model 44110.4 Applications 44510.5 Further Reading 451References 45111 Batched Poisson Multirate Elastic Adaptive Loss Models 45511.1 The Elastic Erlang Multirate Loss Model with Batched Poisson Arrivals 45511.1.1 The Service System 45511.1.2 The Analytical Model 45611.2 The Elastic Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR Policy 46111.2.1 The Service System 46111.2.2 The Analytical Model 46311.3 The Elastic Adaptive Erlang Multirate Loss Model with Batched Poisson Arrivals 46611.3.1 The Service System 46611.3.2 The Analytical Model 46711.4 The Elastic Adaptive Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR Policy 47511.4.1 The Service System 47511.4.2 The Analytical Model 47711.5 Applications 48211.6 Further Reading 483References 485Appendix A Interdependency of the Teletraffic Models 487Index 491