Efficient Multirate Teletraffic Loss Models Beyond Erlang
Description
Efficient Multirate Teletraffic Loss Models Beyond Erlang is an easy-to-read book filled with numerous efficient teletraffic loss models. Presented in three sections--Teletraffic Models of Random Input, Teletraffic Models of Quasi-Random Input, and Teletraffic Models of Batched Poisson Input--it covers everything that a professional experienced with optimization and dimensioning of telecom networks could ever need to know.
This unique book provides a detailed explanation on how efficient multirate teletraffic loss models are extracted and applied, and guides readers through almost all network technologies and services. Starting from the basics, it steadily increases in difficulty to keep the book self-contained and to provide a better understanding to those who might be new to the subject. It includes detailed explanations of the complex teletraffic models--many of which were developed by the authors. Tutorial examples, several backed by supplementary software, are accompanied by intermediate results and figures. Additionally, end-of-chapter applications describe the applicability of the models to modern network technologies, updating the incorporated teletraffic models of commercial packages/tools.
* Uses the classic EMLM (Erlang Multirate Loss Model) as its base to present a comprehensive range of teletraffic models through detailed explanation and numerical examples
* Filled with the authors' own original teletraffic models--making for a wholly unique learning experience
* Offers a clear, self-contained presentation with a beginning, middle, and end
* Starts with simple models, then moves to more complex models, before finishing with complicated ones
* Supplemented by an accompanying website with computer implementation of the most important models
Directed primarily at telecommunication engineers, Efficient Multirate Teletraffic Loss Models Beyond Erlang is also useful for telecom operators or managers on the higher and average levels, as well a Ph.D. students, researchers, and modelers.
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Persons
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.
Content
List of Figures xvii
List of Tables xxv
Preface xxix
Acronyms xxxiii
Symbols xxxvii
About the Companion Website xxxix
Introduction xli
I.1 Traffic-load Definition xlii
I.2 Traffic Congestion and GoS/QoS xliii
I.3 System Capacity xliv
I.4 Teletraffic Models xlv
I.5 Traffic-load Properties xlviii
I.6 Call Arrival Process l
I.6.1 Superposition and Decomposition of Poisson Processes lv
I.6.2 Poisson Arrivals See Time Averages lvi
I.7 Call Service Time lvii
I.7.1 Markov Property lvii
I.8 Service Systems lix
I.9 Little's Law lxi
I.10 Other Performance Metrics of Loss Systems lxii
I.11 General Examples lxiii
I.12 Service-classes - Bandwidth Sharing Policies lxiv
I.13 Classification of Teletraffic Loss Models lxx
I.14 Teletraffic Models and the Internet lxxi
References lxxiv
Part I Teletraffic Models of Random Input 1
1 The Erlang Multirate Loss Model 3
1.1 The Erlang Loss Model 3
1.1.1 The Service System 3
1.1.2 Global and Local Balance 5
1.1.3 Call Blocking Probability 8
1.1.4 Other Performance Metrics 11
1.2 The Erlang Multirate Loss Model 13
1.2.1 The Service System 13
1.2.2 The Analytical Model 15
1.3 The Erlang Multirate Loss Model under the BR policy 28
1.3.1 The Service System 28
1.3.2 The Analytical Model 30
1.4 The Erlang Multirate Loss Model under the Threshold Policy 38
1.4.1 The Service System 38
1.4.2 The Analytical Model 40
1.5 The Erlang Multirate Loss Model in a Fixed Routing Network 44
1.5.1 The Service System 44
1.5.2 The Analytical Model 45
1.5.3 CBP Calculation by the RLA Method 49
1.6 Applications 54
1.6.1 The Erlang-B Formula 54
1.6.2 The Erlang-C Formula 55
1.6.3 The Kaufman-Roberts Recursion 56
1.7 Further Reading 58
References 60
2 Multirate Retry Threshold Loss Models 65
2.1 The Single-Retry Model 65
2.1.1 The Service System 65
2.1.2 The Analytical Model 69
2.2 The Single-Retry Model under the BR Policy 72
2.2.1 The Service System 72
2.2.2 The Analytical Model 75
2.3 The Multi-Retry Model 77
2.3.1 The Service System 77
2.3.2 The Analytical Model 83
2.4 The Multi-Retry Model under the BR Policy 86
2.4.1 The Service System 86
2.4.2 The Analytical Model 87
2.5 The Single-Threshold Model 92
2.5.1 The Service System 92
2.5.2 The Analytical Model 96
2.6 The Single-Threshold Model under the BR Policy 99
2.6.1 The Service System 99
2.6.2 The Analytical Model 101
2.7 The Multi-Threshold Model 107
2.7.1 The Service System 107
2.7.2 The Analytical Model 107
2.8 The Multi-Threshold Model under the BR Policy 109
2.8.1 The Service System 109
2.8.2 The Analytical Model 109
2.9 The Connection Dependent Threshold Model 112
2.9.1 The Service System 112
2.9.2 The Analytical Model 114
2.10 The Connection Dependent Threshold Model under the BR Policy 119
2.10.1 The Service System 119
2.10.2 The Analytical Model 119
2.11 Applications 121
2.12 Further Reading 129
References 130
3 Multirate Elastic Adaptive Loss Models 133
3.1 The Elastic Erlang Multirate Loss Model 133
3.1.1 The Service System 133
3.1.2 The Analytical Model 139
3.2 The Elastic Erlang Multirate Loss Model under the BR Policy 146
3.2.1 The Service System 146
3.2.2 The Analytical Model 149
3.3 The Elastic Erlang Multirate Loss Model under the Threshold Policy 152
3.3.1 The Service System 152
3.3.2 The Analytical Model 156
3.4 The Elastic Adaptive Erlang Multirate Loss Model 163
3.4.1 The Service System 163
3.4.2 The Analytical Model 171
3.5 The Elastic Adaptive Erlang Multirate Loss Model under the BR Policy 175
3.5.1 The Service System 175
3.5.2 The Analytical Model 177
3.6 The Elastic Adaptive Erlang Multirate Loss Model under the Threshold Policy 179
3.6.1 The Service System 179
3.6.2 The Analytical Model 182
3.7 Applications 185
3.8 Further Reading 190
References 191
4 Multirate Elastic Adaptive Retry Loss Models 195
4.1 The Elastic Single-Retry Model 195
4.1.1 The Service System 195
4.1.2 The Analytical Model 201
4.2 The Elastic Single-Retry Model under the BR Policy 206
4.2.1 The Service System 206
4.2.2 The Analytical Model 210
4.3 The Elastic Multi-Retry Model 212
4.3.1 The Service System 212
4.3.2 The Analytical Model 218
4.4 The Elastic Multi-Retry Model under the BR Policy 220
4.4.1 The Service System 220
4.4.2 The Analytical Model 223
4.5 The Elastic Adaptive Single-Retry Model 226
4.5.1 The Service System 226
4.5.2 The Analytical Model 233
4.6 The Elastic Adaptive Single-Retry Model under the BR Policy 237
4.6.1 The Service System 237
4.6.2 The Analytical Model 241
4.7 The Elastic Adaptive Multi-Retry Model 243
4.7.1 The Service System 243
4.7.2 The Analytical Model 248
4.8 The Elastic Adaptive Multi-Retry Model under the BR Policy 250
4.8.1 The Service System 250
4.8.2 The Analytical Model 254
4.9 Applications 258
4.10 Further Reading 258
References 260
5 ON-OFF Multirate Loss Models 263
5.1 The ON-OFF Multirate Loss Model 263
5.1.1 The Service System 263
5.1.2 The Analytical Model 265
5.2 The ON-OFF Multirate Loss Model under the BR Policy 275
5.2.1 The Service System 275
5.2.2 The Analytical Model 276
5.3 The ON-OFF Multirate Loss Model in a Fixed Routing Network 280
5.3.1 The Service System 280
5.3.2 The Analytical Model 280
5.4 Applications 285
5.5 Further Reading 288
References 289
Part II Teletraffic Models of Quasi-Random Input 291
6 The Engset Multirate Loss Model 293
6.1 The Engset Loss Model 293
6.1.1 The Service System 293
6.1.2 The Analytical Model 293
6.2 The Engset Multirate Loss Model 298
6.2.1 The Service System 298
6.2.2 The Analytical Model 300
6.3 The Engset Multirate Loss Model under the BR Policy 308
6.3.1 The Service System 308
6.3.2 The Analytical Model 310
6.4 The Engset Multirate Loss Model under the TH Policy 312
6.4.1 The Service System 312
6.4.2 The Analytical Model 312
6.5 Applications 318
6.6 Further Reading 324
References 327
7 Finite Multirate Retry Threshold Loss Models 331
7.1 The Finite Single-Retry Model 331
7.1.1 The Service System 331
7.1.2 The Analytical Model 333
7.2 The Finite Single-Retry Model under the BR Policy 338
7.2.1 The Service System 338
7.2.2 The Analytical Model 340
7.3 The Finite Multi-Retry Model 342
7.3.1 The Service System 342
7.3.2 The Analytical Model 344
7.4 The Finite Multi-Retry Model under the BR Policy 348
7.4.1 The Service System 348
7.4.2 The Analytical Model 349
7.5 The Finite Single-Threshold Model 353
7.5.1 The Service System 353
7.5.2 The Analytical Model 355
7.6 The Finite Single-Threshold Model under the BR Policy 360
7.6.1 The Service System 360
7.6.2 The Analytical Model 362
7.7 The Finite Multi-Threshold Model 363
7.7.1 The Service System 363
7.7.2 The Analytical Model 364
7.8 The Finite Multi-Threshold Model under the BR Policy 366
7.8.1 The Service System 366
7.8.2 The Analytical Model 366
7.9 The Finite Connection Dependent Threshold Model 367
7.9.1 The Service System 367
7.9.2 The Analytical Model 368
7.10 The Finite Connection Dependent Threshold Model under the BR Policy 373
7.10.1 The Service System 373
7.10.2 The Analytical Model 373
7.11 Applications 374
7.12 Further Reading 374
References 375
8 Finite Multirate Elastic Adaptive Loss Models 377
8.1 The Elastic Engset Multirate Loss Model 377
8.1.1 The Service System 377
8.1.2 The Analytical Model 380
8.2 The Elastic Engset Multirate Loss Model under the BR Policy 383
8.2.1 The Service System 383
8.2.2 The Analytical Model 385
8.3 The Elastic Adaptive Engset Multirate Loss Model 387
8.3.1 The Service System 387
8.3.2 The Analytical Model 389
8.4 The Elastic Adaptive Engset Multirate Loss Model under the BR Policy 392
8.4.1 The Service System 392
8.4.2 The Analytical Model 394
8.5 Applications 402
8.6 Further Reading 405
References 405
9 Finite ON-OFF Multirate Loss Models 407
9.1 The Finite ON-OFF Multirate Loss Model 407
9.1.1 The Service System 407
9.1.2 The AnalyticalModel 408
9.2 Generalization of the f-ON-OFF Model to include Service-classes with a Mixture of a Finite and an Infinite Number of Sources 415
9.3 Applications 416
9.4 Further Reading 422
References 423
Part III Teletraffic Models of Batched Poisson Input 425
10 The Erlang Multirate Loss ModelWith Batched Poisson Arrivals 427
10.1 The Erlang Multirate Loss Model with Batched Poisson Arrivals 427
10.1.1 The Service System 427
10.1.2 The AnalyticalModel 428
10.2 The Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR Policy 435
10.2.1 The Service System 435
10.2.2 The AnalyticalModel 435
10.3 The Erlang Multirate Loss Model with Batched Poisson Arrivals under the Threshold Policy 441
10.3.1 The Service System 441
10.3.2 The Analytical Model 441
10.4 Applications 445
10.5 Further Reading 451
References 451
11 Batched Poisson Multirate Elastic Adaptive Loss Models 455
11.1 The Elastic Erlang Multirate Loss Model with Batched Poisson Arrivals 455
11.1.1 The Service System 455
11.1.2 The Analytical Model 456
11.2 The Elastic Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR Policy 461
11.2.1 The Service System 461
11.2.2 The Analytical Model 463
11.3 The Elastic Adaptive Erlang Multirate Loss Model with Batched Poisson Arrivals 466
11.3.1 The Service System 466
11.3.2 The Analytical Model 467
11.4 The Elastic Adaptive Erlang Multirate Loss Model with Batched Poisson Arrivals under the BR Policy 475
11.4.1 The Service System 475
11.4.2 The Analytical Model 477
11.5 Applications 482
11.6 Further Reading 483
References 485
Appendix A Interdependency of the Teletraffic Models 487
Index 491
List of Figures
Figure I.1 Traffic-load in a link of three trunks (Example I.1)
Figure I.2 Qualitative relationships between traffic-load, system capacity and GoS
Figure I.3 Call generation process
Figure I.4 Poisson distribution with rate calls/hour
Figure I.5 Superposition and decomposition of Poisson processes
Figure I.6 Exponential distribution
Figure I.7 Markov/memoryless property
Figure I.8 Representation of service systems
Figure I.9 Service systems of full and restricted availability (Example I.19)
Figure I.10 An access network as a queuing system (Example I.21)
Figure I.11 The CS policy (Example I.26)
Figure I.12 A CS policy with ordering constraint (Example I.27)
Figure I.13 The TH policy (Example I.28)
Figure I.14 Comparison of the BR policy with the CS policy (Example I.29)
Figure I.15 System states in the CS and the BR policies (Example I.29)
Figure I.16 Visualization of (a) random/quasi-random and (b) batch Poisson arrivals
Figure I.17 Visualization of (a) fixed and (b) elastic bandwidth requirements
Figure I.18 Visualization of (a) stream, (b) elastic, and (c) ON-OFF traffic
Figure I.19 (a) Resource separation ( QoS-aware flows) and (b) resource sharing (two QoS classes)
Figure 1.1 State transition diagram for the Erlang loss model (///0)
Figure 1.2 /// FIFO - state transition diagram for (Example 1.2)
Figure 1.3 Quantitative relationships between traffic-load, system capacity, and CBP
Figure 1.4 Trunk efficiency for various values of GoS and
Figure 1.5 A service system of b.u. and two service-classes under the CS policy (Example 1.6)
Figure 1.6 The state space (CS policy) and the state transition diagram (Example 1.6)
Figure 1.7 State transition diagram of the EMLM
Figure 1.8 GB in the system of Example 1.6 (Example 1.7)
Figure 1.9 Sets and for the EMLM of two service-classes, under the CS policy
Figure 1.10 The Kaufman-Roberts recursion as a birth-death process
Figure 1.11 Visualization of CBP calculation
Figure 1.12 CBP oscillations in the EMLM (CS policy) (Example 1.14)
Figure 1.13 An example of the EMLM under the BR policy
Figure 1.14 The state space of the EMLM under the BR policy (Example 1.15)
Figure 1.15 The one-dimensional Markov chain of the EMLM/BR (Roberts' assumption, Example 1.18)
Figure 1.20 The state space of system under the TH policy (Example 1.23)
Figure 1.21 Comparison of the EMLM, the EMLM/BR, and the EMLM/TH (Example 1.23)
Figure 1.22 The state space of the three link network (Example 1.24)
Figure 1.23 Two service-classes accommodated in a fixed routing network of two links (Example 1.25)
Figure 1.24 Application of the RLA method in a telephone network of three links (Example 1.26)
Figure 1.25 A ring network supporting service-classes under the BR policy (Example 1.28)
Figure 2.1 Service system of the SRM
Figure 2.2 The CAC mechanism for a new call in the SRM
Figure 2.3 The state space (CS policy) and the state transition diagram (Example 2.1)
Figure 2.4 The state space (BR policy) and the state transition diagram (Example 2.3)
Figure 2.5 CBP in the SRM and EMLM, for various values of (Example 2.5)
Figure 2.6 Link utilization in the SRM and EMLM (Example 2.5)
Figure 2.7 CBP in the SRM/BR and the EMLM/BR for various values of (Example 2.5)
Figure 2.8 The state space (CS policy) and the state transition diagram (Example 2.6)
Figure 2.9 The state space (BR policy) and the state transition diagram (Example 2.8)
Figure 2.11 CBP of service-class 4 in the MRM, SRM, and EMLM for various values of (Example 2.10)
Figure 2.12 Equalized CBP in the MRM/BR and EMLM/BR for various values of (Example 2.10)
Figure 2.13 The state space (CS policy) and the state transition diagram (Example 2.11)
Figure 2.14 The state space (BR policy) and the state transition diagram (Example 2.13)
Figure 2.16 CBP in the STM/BR and SRM/BR versus and two values of (Example 2.15)
Figure 2.17 The MTM principle of operation
Figure 2.20 The CDTM principle of operation
Figure 2.21 The service system (Example 2.17)
Figure 2.22 Graphical representation of the LB equations 2.63 (left) and 2.64 (right)
Figure 2.23 Migration and upward migration spaces (Example 2.18)
Figure 2.24 Thresholds and bandwidth requirements of service-classes 3 and 4 (Example 2.20)
Figure 2.25 Recurrent determination of the resource share (Example 2.21)
Figure 2.26 Excerpt of the state transition diagram (Example 2.22)
Figure 2.27 Migration and upward migration space (Example 2.22)
Figure 3.1 The state space and the state transition diagram (Example 3.1)
Figure 3.2 State transition diagram of four adjacent states (Example 3.2)
Figure 3.3 The state space and the modified state transition diagram (Example 3.3)
Figure 3.4 State transition diagram of the E-EMLM
Figure 3.5 CBP of both service-classes in the E-EMLM (Example 3.5)
Figure 3.6 Link utilization in the E-EMLM (Example 3.5)
Figure 3.7 The state space and the state transition diagram (Example 3.6)
Figure 3.8 The state space and the modified state transition diagram (Example 3.6)
Figure 3.9 CBP of service-class 1 (EMLM, E-EMLM) (Example 3.8)
Figure 3.10 CBP of service-class 2 (EMLM, E-EMLM) (Example 3.8)
Figure 3.11 Equalized CBP (EMLM/BR, E-EMLM/BR) (Example 3.8)
Figure 3.12 Link utilization for all models (Example 3.8)
Figure 3.13 The state space and the state transition diagram (Example 3.9)
Figure 3.14 The state space and the modified state transition diagram (Example 3.9)
Figure 3.15 The loss system of Example 3.9 as an access tree network (Example 3.11)
Figure 3.16 CBP of service-class 1, when (Example 3.12)
Figure 3.17 CBP of service-class 2, when (Example 3.12)
Figure 3.18 CBP of service-class 3, when (Example 3.12)
Figure 3.19 Link utilization (Example 3.12)
Figure 3.20 CBP of the first service-class, when and (Example 3.12)
Figure 3.21 CBP of the second service-class, when and (Example 3.12)
Figure 3.22 CBP of the third service-class, when and (Example 3.12)
Figure 3.23 The state space and the state transition diagram (Example 3.13)
Figure 3.24 CBP of both service-classes in the EA-EMLM (Example 3.16)
Figure 3.25 Link utilization in the EA-EMLM (Example 3.16)
Figure 3.26 The state space and the state transition diagram (Example 3.17)
Figure 3.27 Equalized CBP of the EA-EMLM/BR and CBP per service-class of the EA-EMLM (Example 3.19)
Figure 3.28 The state space and the state transition diagram (Example 3.20)
Figure 3.29 CBP of service-class 1, when and 5 (Example 3.22)
Figure 3.30 CBP of service-class 2, when , and (Example 3.22)
Figure 3.31 CBP of service-class 3, when , and (Example 3.22)
Figure 3.32 SDN/NFV based next-generation network architecture
Figure 3.33 Layering concept in SDN
Figure 4.1 The state space and the state transition diagram (Example 4.1)
Figure 4.2 The state space and the modified state transition diagram (Example 4.2)
Figure 4.3 The state space and the state transition diagram (Example 4.4)
