Traffic Engineering: A Practical Approach

Description

This textbook discusses the principles of queuing theory and teletraffic engineering in telecommunication networks. The book lays out the rigorous theoretical background while keeping strong links to practical applications and real-life scenarios. The overall goal of this textbook is to provide students with in-depth and broad understanding of the operational framework of teletraffic problems, and therefore the capability to select the most suitable and effective method to solve traffic engineering problems that may arise in real-life. The student will learn to pick and choose from a spectrum of tools, ranging from the simplest mathematical treatment to sophisticated models. The book features practical examples derived from real life, presented and discussed, establishing the links with the theoretical results. Pedagogical materials include end-of-chapter exercises and problems. Foreword Preface Contents 1 Introduction to Teletraffic Engineering 1.1 What Is Traffic Engineering? Some Basic Concepts andDefinitions 1.1.1 The Definition of Traffic 1.2 An Important and Very General Rule of Teletraffic Systems: Little's Theorem 1.3 A More Detailed Model of the Teletraffic System: A Queuing System 1.3.1 Naming a Queuing System 1.3.2 Little's Theorem for Queuing Systems Exercises 2 An Introduction to Queuing System Modeling 2.1 Introduction 2.2 Modeling Service Requests 2.2.1 The Poisson Process 2.2.1.1 Average Arrival Rate 2.2.1.2 Inter-arrival Time 2.2.1.3 Merging and Splitting Poisson Arrival Processes 2.3 Modeling Service Time 2.3.1 Exponential Service Time 2.3.2 Deterministic Service Time 2.3.3 Uniform Service Time 2.3.4 Erlang Service Time 2.3.5 Pareto Service Time 2.4 Link the Time of Arrivals with the Service Time 2.5 Residual Service Time 2.5.1 The Residual Exponential Service Time and Its Memoryless Property 2.5.2 The Residual Deterministic Service Time 2.5.3 The Residual Uniform Service Time 2.6 Examples and Case Studies 2.6.1 Time Related Tariffs 2.6.1.1 Calculating the Average Cost of the Calls 2.6.2 Deriving the Poisson Formula from Exponential Inter-arrivals 2.6.3 Time to Complete Multiple Services 2.6.3.1 Case 1: Deterministic Service Time 2.6.3.2 Case 2: Exponential Service Time Exercises 3 Formalizing the Queuing System: State Diagrams and Birth–Death Processes 3.1 Stateful and Time Dependent Systems 3.2 Defining Congestion as a Sample State 3.2.1 The PASTA Property 3.3 Birth–Death Processes 3.4 Queuing Systems, Memoryless Property, and BD Processes 3.5 Examples and Case Studies 3.5.1 The Poisson Process as a Birth-Only Process 3.5.2 Alarm Reporting 3.5.3 Taxis at the Airport Exercises 4 Engineering Circuit-Switched Networks 4.1 Introduction 4.2 Modeling Circuit Switching Systems Without Waiting Space 4.2.1 Performance Metrics 4.2.2 An Ideal System with Infinite Circuits 4.2.2.1 Average Values 4.2.2.2 What About Congestion? 4.2.3 The Real System with a Finite Number of Circuits 4.2.3.1 Congestion: The Erlang B Formula 4.2.3.2 Average Values and Utilization 4.2.4 Utilization of Ordered Servers 4.2.5 Comparing the M/M and the M/M/m/0 Systems 4.2.6 Insensitivity to Service Time Distribution 4.2.7 How Good Is the Erlang B Model 4.2.8 Examples and Case Studies 4.2.8.1 Dimensioning the Number of Circuits in a PABX 4.2.8.2 Planning the Dimensioning of a Trunk Group Between Two Central Offices 4.2.8.3 Dimensioning Interconnections in a Private Telephone Network 4.2.8.4 Utilization of the Last Server and Network Cost Optimization 4.2.8.5 Coping with Traffic Increases 4.3 Modeling Circuit Switching Systems with Waiting Space 4.3.1 Performance Metrics 4.3.2 The M/M/m System 4.3.2.1 Congestion: The Erlang C Formula 4.3.2.2 Average Number of Customers 4.3.2.3 Average Waiting Time 4.3.3 Waiting Time Probability Distribution for a FIFO Queue 4.3.4 Examples and Case Studies 4.3.4.1 Dimensioning the Number of Operators in a Call Center 4.3.4.2 Adopting a Unique Emergency Telephone Number 4.3.4.3 Planning Lines and Operators in a Call Center 4.3.4.4 A Call Center with Impatient Customers 4.4 Multi-Dimensional BD Processes 4.4.1 The Multi-Service Link 4.4.2 Circuit-Switched Networks with Fixed Routing 4.4.3 Examples and Case Studies 4.4.3.1 QoS Comparison for Two Traffic Classes with Different Bandwidth Requirements 4.4.3.2 Strategies for QoS Management: Bandwidth Sharing, Bandwidth Partitioning and Trunk Reservation 4.4.3.3 A Simple Circuit Switching Network 4.4.3.4 Dimensioning a Small Private Telephone Network Exercises 5 Engineering Packet-Switched Networks 5.1 Introduction 5.2 Single Server Queuing 5.2.1 Performance Metrics 5.2.2 A General Result for Single Server Systems with Infinite Waiting Space 5.3 Memoryless Single Sever Queuing Systems 5.3.1 Infinite Queuing Space: The M/M/1 System 5.3.1.1 Congestion: The Probability of Being Queued 5.3.1.2 Delay: The Time Spent Waiting in the Queue 5.3.1.3 The Output Traffic Process: Burke's Theorem 5.3.2 Finite Queuing Space, the M/M/1/L System 5.3.2.1 Blocking Probability 5.3.2.2 Average Performance Metrics 5.3.3 Examples and Case Studies 5.3.3.1 LAN Interconnection with a VPN 5.3.3.2 IoT Data Collection 5.3.3.3 Load Balancing Between Two Output Links 5.3.3.4 A Voice over IP Interconnection 5.3.3.5 Multiplexing Multi-Service Traffic 5.3.3.6 Queue Length Measured in Number of Bits 5.4 A Look at Some More General Cases 5.4.1 Poisson Arrivals May Be Fine, But What About Service Time? The M/G/1 Queue 5.4.1.1 The Average Waiting Time with FIFO Scheduling 5.4.1.2 Some Relevant Cases of the M/G/1 Queue 5.4.2 Packet Switching and Quality of Service: When One Pipe Does Not Fit All 5.4.2.1 Priority Queuing 5.4.2.2 Shortest Job Next (SJN) Scheduling 5.4.2.3 Kleinrock's Conservation Law 5.4.3 Examples and Case Studies 5.4.3.1 Stop-and-Wait with Errors 5.4.3.2 Packet Payload Padding 5.4.3.3 Non-preemptive Priority Scheduling with Two Classes 5.4.3.4 Priority Scheduling for Multimedia Traffic 5.4.3.5 Data, Voice, and Video Traffic with Priority 5.4.3.6 Token Bucket Scheduling Exercises A Brief Introduction to Markov Chains A.1 Discrete Time Markov Chains A.1.1 Transition and Steady State Probabilities A.1.2 Irreducible Markov Chains A.1.3 The Chapman–Kolmogorov Equations A.1.4 The Markov Chain Behavior as a Function of Time A.1.5 Time Spent in a Given State A.2 Continuous Time Markov Chain A.2.1 The Time Spent in a State B The Embedded Markov Chain for the M/G/1 System B.1 Steady State Probabilities of the Number of Customers in the System at Departure Times B.2 Steady State Probabilities at Generic Time Instants Index