Efficient Multirate Teletraffic Loss Models Beyond Erlang E-Book

Ioannis D. Moscholios

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 743

Veröffentlichungsjahr: 2019

Beschreibung

A comprehensive study in efficient multi-rate teletraffic loss models used for designing, performance analysis, and optimization of systems and networks 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.

Leseprobe

Efficient Multirate Teletraffic Loss Models Beyond Erlang

Ioannis D. Moscholios

University of Peloponnese, Greece

Michael D. Logothetis

University of Patras, Greece

Copyright

This edition first published 2019

© 2019 John Wiley & Sons Ltd

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Ioannis D. Moscholios and Michael D. Logothetis to be identified as the authors of this work has been asserted in accordance with law.

Registered Offices

John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

Editorial Office

The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data

Names: Moscholios, Ioannis D (Associate Professor at the University of Peloponnese), author. |

       Logothetis, Michael D (Professor at the University of Patras), author.

Title: Efficient multirate teletraffic loss models beyond Erlang / Ioannis

       D. Moscholios, University of Peloponnese, Michael D. Logothetis, University of Patras.

Description: First edition. | Hoboken, NJ : John Wiley & Sons, Inc., 2019. |

       Includes bibliographical references and index. |

Identifiers: LCCN 2018052862 (print) | LCCN 2018056391 (ebook) | ISBN

       9781119426905 (Adobe PDF) | ISBN 9781119426912 (ePub) | ISBN 9781119426882

       (hardcover)

Subjects: LCSH: Telecommunication--Traffic--Mathematical models. | Queuing

       theory.

Classification: LCC TK5102.985 (ebook) | LCC TK5102.985 .L64 2019 (print) |

       DDC 621.38201/51982--dc23

LC record available at https://lccn.loc.gov/2018052862

Cover Design: Wiley

Cover Image: © Wenjie Dong/iStock.com

Dedication

To our families

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 1.16 Calls of service‐classes contribute in by transferring the population of service‐class to state

Figure 1.17 The one‐dimensional Markov chain of the EMLM/BR under the Stasiak–Glabowski assumption (Example 1.19)

Figure 1.18 A multirate access tree network that accommodates service‐classes of Poisson input (Example 1.22)

Figure 1.19 A single link that accommodates service‐classes of Poisson input described by the EMLM/TH (Example 1.22)

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 2.10 CBP of the first three service‐classes in the MRM, SRM, and EMLM for various values of (Example 2.10) 

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 2.15 Left: CBP of service‐classes 1, 2 in the STM and SRM versus various values of . Right: The corresponding graphs for service‐classes 3, 4 (Example 2.15)

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 2.18 Left: CBP of service‐classes 1, 2, and 3 versus the sets of thresholds. Right: Conditional CBP of service‐class 4 versus the sets of thresholds (MTM) (Example 2.16)

Figure 2.19 Equalized CBP of all service‐classes versus the sets of thresholds (MTM/BR) (Example 2.16)

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 3.34 SDN/NFV based RAN

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)

Figure 4.4 The state space and the modified state transition diagram (Example 4.4)

Figure 4.5 CBP of service‐class 1 (MRM, E‐MRM) (Example 4.12)

Figure 4.6 CBP of service‐class 2 (MRM, E‐MRM) (Example 4.12)

Figure 4.7 CBP of service‐class 3 (MRM, E‐MRM) (Example 4.12)

Figure 4.8 Equalized CBP (MRM/BR, E‐MRM/BR) (Example 4.12)

Figure 4.9 The state space and the state transition diagram (Example 4.13)

Figure 4.10 The state space and the state transition diagram (Example 4.16)

Figure 4.11 CBP of service‐class 1 (MRM, MRM/BR, EA‐MRM, EA‐MRM/BR) (Example 4.24)

Figure 4.12 CBP of service‐class 2 (MRM, MRM/BR, EA‐MRM, EA‐MRM/BR) (Example 4.24)

Figure 4.13 CBP of service‐class 3 (MRM, MRM/BR, EA‐MRM, EA‐MRM/BR) (Example 4.24)

Figure 4.14 Link utilization (MRM/BR, EA‐MRM/BR) (Example 4.24)

Figure 5.1 The service model of ON–OFF calls

Figure 5.2 The mechanisms of call and burst blocking in the ON–OFF model

Figure 5.3 The state transition diagram of the ON–OFF model

Figure 5.4 Basic assumption (approximation) for the determination of BBP

Figure 5.5 Analytical CBP when b.u. (Example 5.6)

Figure 5.6 Analytical CBP when b.u. (Example 5.6)

Figure 5.7 The fixed routing network with two links and three service‐classes (Example 5.7) 

Figure 5.8 Analytical CBP for the three service‐classes (Example 5.7)

Figure 5.9 Total utilization for the first link (Example 5.7.)

Figure 5.10 Total utilization for the second link (Example 5.7)

Figure 5.11 BBP for all service‐classes when and (Example 5.7)

Figure 5.12 A WDM‐TDMA PON servicing ON–OFF traffic

Figure 6.1 State transition diagram for the Engset loss model

Figure 6.2 The state space and the state transition diagram (Example 6.4) 

Figure 6.3 State transition diagram of the EnMLM

Figure 6.4 TC probabilities (Example 6.9)

Figure 6.5 TC probabilities of service‐class 1 (Example 6.12)

Figure 6.6 TC probabilities of service‐class 2 (Example 6.12)

Figure 6.7 TC probabilities of service‐class 3 (Example 6.12)

Figure 6.8 Link utilization (Example 6.12) 

Figure 6.9 TC probabilities of service‐class 1 for various numbers of sources (Example 6.12)

Figure 6.10 TC probabilities of service‐class 2 for various numbers of sources (Example 6.12)

Figure 6.11 TC probabilities of service‐class 3 for various numbers of sources (Example 6.12)

Figure 6.12 The S1 interface and the X2 interface between source and target eNBs

Figure 7.1 The state space and the state transition diagram (Example 7.1)

Figure 7.2 The state space and the state transition diagram (Example 7.4)

Figure 7.3 The state space and the state transition diagram (Example 7.6)

Figure 7.4 The state space and the state transition diagram (Example 7.8)

Figure 7.5 The state space and the state transition diagram (Example 7.11)

Figure 7.6 The state space and the state transition diagram (Example 7.14)

Figure 8.1 The state space and the state transition diagram (Example 8.1)

Figure 8.2 The state space and the state transition diagram (Example 8.2)

Figure 8.3 The state space and the state transition diagram (Example 8.4)

Figure 8.4 The state space and the modified state transition diagram (Example 8.4)

Figure 8.5 The state space and the state transition diagram (Example 8.6)

Figure 8.6 The state space and the state transition diagram (Example 8.9)

Figure 8.7 TC probabilities for service‐class 1 b.u.) (Example 8.11)

Figure 8.8 TC probabilities for service‐class 1 ( b.u.) (Example 8.11)

Figure 8.9 TC probabilities for service‐class 2 (T = 90 b.u.) (Example 8.11) 

Figure 8.10 TC probabilities for service‐class 2 (T = 100 b.u.) (Example 8.11) 

Figure 8.11 TC probabilities for service‐class 3 (T = 90 b.u.) (Example 8.11) 

Figure 8.12 TC probabilities for service‐class 3 (T = 100 b.u.) (Example 8.11) 

Figure 8.13 The reference C‐RAN architecture

Figure 8.14 Enabling a hybrid SON

Figure 9.1 The state transition diagram of the f‐ON–OFF model

Figure 9.2 TC probabilities for service‐class 1 when a) , (b) , and (c) (Example 9.4)

Figure 9.3 TC probabilities for service‐class 2 when (a) , (b) , and (c) (Example 9.4)

Figure 9.4 BBP for both service‐classes when (a) and (b) (Example 9.4)

Figure 9.5 A basic configuration of an OCDMA PON

Figure 10.1 Call arrivals according to (a) a Poisson process and (b) a batched Poisson process

Figure 10.2 The state transition diagram in (a) the EMLM and (b) the BP‐EMLM (Example 10.1)

Figure 10.3 Graphical representation of 10.13 (Example 10.3)

Figure 10.4 Difference between CC and TC probabilities (Example 10.5)

Figure 10.5 TC probabilities of service‐class 1 (Example 10.11)

Figure 10.6 CC probabilities of service‐class 1 (Example 10.11)

Figure 10.7 TC probabilities of service‐class 2 (Example 10.11)

Figure 10.8 CC probabilities of service‐class 2 (Example 10.11)

Figure 10.9 A rectangular cell model for the LEO‐MSS network

Figure 11.1 Equalized TC probabilities (Example 11.5)

Figure 11.2 CC probabilities for service‐class 1 (Example 11.5)

Figure 11.3 CC probabilities for service‐class 2 (Example 11.5)

Figure 11.4 CC probabilities for service‐class 3 (Example 11.5)

Figure 11.5 Equalized TC probabilities (Example 11.10)

Figure 11.6 CC probabilities for service‐class 1 (Example 11.10)

Figure 11.7 CC probabilities for service‐class 2 (Example 11.10)

Figure 11.8 CC probabilities for service‐class 3 (Example 11.10)

Figure 11.9 CC probabilities for service‐class 4 (Example 11.10)

Figure 11.10 Link utilization (in b.u.) (Example 11.10)

Figure 11.11 Congestion probabilities of all service‐classes (elastic/adaptive) (Example 11.10)

Figure A.1 Interdependency of the teletraffic models of Part I of this book

Figure A.2 Interdependency of the teletraffic models of Part II of this book

Figure A.3 Interdependency of the teletraffic models of Part III of this book

List of Tables

Table I.1 Measurements on b.u. .

Table I.2 Measurements of arrivals .

Table 1.1 Equalized CBP under the BR policy in the network of Figure 1.25 

Table 2.1 CBP of Example 2.5 (SRM, b.u. and b.u.) 

Table 2.2 CBP of Example 2.5 (SRM/BR, b.u. and b.u.) 

Table 2.3 CBP of Example 2.10 (MRM, b.u.) 

Table 2.4 CBP of Example 2.15 (STM, or b.u., and ) 

Table 2.5 CBP of Example 2.15 (STM, or b.u., and ) 

Table 2.6 CBP of Example 2.15 (STM/BR, or b.u., and ) 

Table 2.7 Analytical and simulation CBP results for Set 1 (Example 2.19) 

Table 2.8 Analytical and simulation CBP results for Set 2 (Example 2.19) 

Table 2.9 Analytical and simulation CBP results for Set 3 (Example 2.19) 

Table 2.10 Equalized CBP for Example 2.20 

Table 2.11 Various parameters and CBP results of Example 2.23 

Table 3.1 The state space and the occupied link bandwidth (Example 3.1) 

Table 3.2 The values of the state dependent compression factors (Example 3.3) 

Table 3.3 The state space and the occupied link bandwidth (Example 3.9) 

Table 3.4 The values of the state dependent compression factors (Example 3.9) 

Table 3.5 The values of the state dependent factors (Example 3.14) 

Table 3.6 The values of the state dependent factors (Example 3.20) 

Table 4.1 The state space and the occupied link bandwidth (Example 4.1) 

Table 4.2 The values of the state‐dependent compression factors and (Example 4.2) 

Table 4.3 The state space and the occupied link bandwidth (Example 4.6) 

Table 4.4 The values of the state‐dependent compression factors and (Example 4.7) 

Table 4.5 The state space and the occupied link bandwidth (Example 4.9) 

Table 4.6 The values of the state‐dependent compression factors and (Example 4.10) 

Table 4.7 The values of the state‐dependent compression factors and (Example 4.14) 

Table 4.8 The values of the state‐dependent compression factors and (Example 4.19) 

Table 4.9 The values of the state‐dependent compression factors and (Example 4.21) 

Table 5.1 State space and occupied real and fictitious link bandwidth (Example 5.1) 

Table 5.2 Analytical and simulation BBP results (Example 5.5) 

Table 5.3 Analytical and simulation BBP of the ON–OFF model (Example 5.6) 

Table 5.4 Analytical and simulation BBP of the ON–OFF/BR model (Example 5.6) 

Table 5.5 Simulation CBP results when and b.u. (Example 5.7) 

Table 5.6 Simulation CBP results when and b.u. (Example 5.7) 

Table 5.7 Simulation CBP results when and b.u. (Example 5.7) 

Table 5.8 Analytical utilization results for the first link (real and fictitious) (Example 5.7) 

Table 5.9 Analytical utilization results for the second link (real and fictitious) (Example 5.7) 

Table 6.1 Steady state probabilities (Example 6.1) 

Table 6.2 State space and occupied link bandwidth (Example 6.4) 

Table 6.3 State space, , jeq and blocking states (Example 6.5) 

Table 6.4 State space and occupied link bandwidth (Example 6.7) 

Table 6.5 State space and occupied link bandwidth (Example 6.10) 

Table 7.1 State space, , jeq, and blocking states (Example 7.2) 

Table 7.2 The state space, , jeq, and the blocking states (Example 7.10) 

Table 7.3 Analytical and simulation results of TC probabilities (Example 7.10) 

Table 7.4 The state space, , jeq, and the blocking states (Example 7.12) 

Table 7.5 Sets of sources and offered traffic‐loads per idle source (Example 7.16) 

Table 7.6 The state space, , , and the blocking states (Example 7.16) 

Table 7.7 Analytical and simulation results of the TC probabilities () (Example 7.16) 

Table 7.8 Analytical and simulation results of the TC probabilities () (Example 7.16) 

Table 7.9 Analytical and simulation results of the TC probabilities () (Example 7.16) 

Table 8.1 Excerpt of the results of Figure 8.7, when (Example 8.11) 

Table 8.2 Excerpt of the results of Figure 8.8, when (Example 8.11) 

Table 9.1 State space,

Preface

The title: In the title of this book, the term efficient means effective computer implementation of the teletraffic model that is achieved through recursive formulas. A sine qua non of nowadays multi‐dimensional telecom traffic is the term multirate, which shows that not only a single traffic service‐class is accommodated in a service system but many traffic‐classes. The term teletraffic loss models certainly reflects the content of this book, since it comprises mainly loss models where ‘lost calls are cleared’ (not queueing models). Relying on the fact that the Erlang‐B formula was the most famous and useful formula (teletraffic model) in the past, we have added the term beyond Erlang hoping that the models of this book will also become pretty useful. On the other hand, although Erlang had not studied multirate loss models, we have named ‘Erlang Multirate Loss Model (EMLM)’, the basic multirate loss model which became the springboard of developing all other models presented in this book. The name EMLM can be justified from the fact that it provides the same results with the Erlang‐B formula for a single service‐class; however, the main inventors of this key model are J. S. Kaufman (Bell Laboratories, 1981) and J. W. Roberts (France Telecom, 1981).

The Subject: Teletraffic models are an inseparable part of the telecommunications and Information and Communication Technology (ICT) infrastructure from the very beginning of their existence. No matter what changes new networking technologies toward 5G may bring, the essential task of teletraffic models remains the same: To determine and evaluate the relationship between (1) the QoS parameters (i.e., call blocking probability), (2) the parameters that determine the intensity of connection requests and the demanded resources (traffic load), and (3) the parameters that describe available network resources (capacity). The global network of either 4G or 5G consisting of many interacting heterogeneous systems supports widely used broadband mobile devices and cloud computing that have given rise not only to a tremendous growth of network traffic but also to a high diversity of traffic streams. The latter more than ever necessitates the development of specialized teletraffic models according to the input traffic stream.

As we describe in the Introduction, Section ‘I.13 Classification of Teletraffic Loss Models’ (reading this Section is strongly recommended), the models are distinguished according to the:

call arrival process

call bandwidth requirements upon arrival, (i.e., service‐classes) and

call behavior while they are in service.

The combination of the characteristics of (i), (ii) and (iii) lead to different teletraffic models. We only present those combinations/models which are realistic and therefore interesting.

The Motivation: The motivation for developing new teletraffic models was the fact that the accuracy of network optimization/dimensioning strongly depends on the accuracy of the incorporated teletraffic model which, in turn, depends on the accurate modelling of the service‐classes of network traffic. Dimensioning is considered an endless, on‐going process of network performance analysis and design. To accomplish it effectively, it is necessary to work out models that incorporate the parameters of a designed network in a reliable way. Besides, teletraffic models are of great assistance for call admission control (CAC), that is, the access control of different service‐classes to network resources and the bandwidth allocation among service‐classes. The latter has been widely recognized as a necessary solution for QoS guarantee both in existing and future networks. Call‐level multi‐rate teletraffic loss models aim at assessing the call‐level QoS of networks with resource reservation capabilities, as well as of the emerging and future all‐optical core networks. Our ultimate aim is to contribute (through this book) to the upgrading of teletraffic models incorporated in commercial packages/tools for network configuration, optimization and planning. To the best of our knowledge, most of such tools utilize only basic (old) teletraffic models. Comparison of new teletraffic models against the basic teletraffic models is included in the book to show the necessity of the new models.

The Audience: This book is directed primarily at telecommunication engineers, professionals who are experienced with optimization and dimensioning of telecom networks, and especially to those who are responsible for QoS assessment/guarantee, or for planning and designing transmission networks. The book is also useful for telecom operators or managers on the higher and average levels, because it will help them to assess the network performance (e.g., of a transmission link), and take proper decisions on network dimensioning and traffic management that result in an increase profit, or investment savings; thus, they can gain competition advantage.

On the other hand, thinking that this book has been resulted from academic research over many years, we certainly recommend this book to PhD students (and modelers) who are involved in related research, as a valuable reference book. Besides, given that we write it in a very simple and explanatory manner, we propose this book as a textbook. It can be adopted as a textbook for a specialized course on a master/PhD level.

Our Vision: Having a bad experience of reading several contemporary books which do not offer more information than one can find, for instance, in the cited journals, we envisioned our book being unique by providing to a reader not only a collection of teletraffic models but also a detailed explanation on how efficient multirate teletraffic loss models are extracted and applied, as well as complete numerical examples. We also guide the readers through many network technologies and services. However, this is accomplished at the end of each chapter as an application example. When presenting a teletraffic model, we do not refer to technologies. The reason is that the models are abstracted from various network technologies and are not dedicated to a specific technology.

Starting from the basics, the book steadily increases in difficulty to include complex teletraffic models so as to keep the book self‐contained and to provide a better understanding to those who might be new to the subject. Readers who are not familiar with the teletraffic theory may find helpful the following analogy: For a sales store, the traffic load (i.e., the number of available products each day) is a key element of its size (number of cashiers/servers, store and parking place, etc.). Traffic load is an important element for network/system dimensioning and can be estimated through a teletraffic model. The sales store example is even more important than for understanding purposes, because of the fact that the same teletraffic model can be used to estimate the traffic‐load offered either to a communication system or to the sales store. Thus, we can recommend this book to a wider audience, because of the applicability of traffic theory to many other scientific fields (for instance, we mention the applicability of teletraffic models to smart grid in chapters 1, 2 and 6).

The Structure: