Algorithms and Models for Network Analysis and Design

Algorithms and Models for Network Analysis and Design R. G. Addie July 18, 2011 ii Contents Front Matter vi Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Preface 1 1 Overview of Network Analysis and Design 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Examples of Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 A Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 A Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.3 A School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.4 A University Campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.5 A State-wide Retail Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.6 A National Internet Service Provider (ISP) . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3.7 A National Carrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Modeling and Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.5 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.6 Requirements Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.8 Equipment Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.9 Design (quantities, placement, and routing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2 Reliability 17 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Analysis of Network Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.1 An Enumeration Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.2 Another Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Network Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.1 Layering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Definition of Layering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.3 A Transmission Facility Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.4 SONET and the Synchronous Digital Hierarchy . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.5 Add-drop Multiplexors and Network Reconfiguration . . . . . . . . . . . . . . . . . . . . 30 2.4 Design for Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 iii iv CONTENTS 2.4.1 Design of a Network of Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 WDM Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.5.1 Networks of WDM Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.5.2 Reliable Routing for WDM Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.6 Further Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.7 Closing Comments and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3 Performance Analysis and Modeling 45 3.1 Probability Theory and Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1.1 Mathematical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.1.2 Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.3 Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.4 Conditional Mean and Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.1.5 The Gaussian Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.6 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.1.7 Statistics of Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2 The Causes of Loss and Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.1 The Causes of Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.2 The Causes of Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3 Traffic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.1 Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.2 Poisson Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.3 Telephone Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3.4 Gaussian Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.5 Long-range Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3.6 Fractional Brownian Motion and Fractional Gaussian Noise . . . . . . . . . . . . . . . . 64 3.3.7 The Poisson-Pareto Burst Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Application of the Gaussian Traffic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.1 A Simple Link . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.2 The Normal Loss Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.3 The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.4.4 Traffic with Infinite Variance∗ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.5 Analysis of Loss and Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.5.1 Queueing Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.2 Loss Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.5.3 End-to-end Control of Traffic in TCP/IP networks . . . . . . . . . . . . . . . . . . . . . . 72 3.5.4 Dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.5.5 Differentiated Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.5.6 Estimation of Performance of Separate Streams . . . . . . . . . . . . . . . . . . . . . . . 75 3.5.7 Benefits of Differentiation of Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.6 Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6.1 Definition of Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.6.2 Analysis of Security Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.6.3 A Simple Model of Security and Its Analysis . . . . . . . . . . . . . . . . . . . . . . . . 80 3.7 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.8 Closing Comments and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4 Measurements 91 4.1 Traffic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.1.1 Measuring the variance or standard deviation of traffic . . . . . . . . . . . . . . . . . . . 92 4.1.2 Interrelationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.1.3 Connections and Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.2 Estimation of Traffic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 CONTENTS v 4.2.1 Estimation of mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.2.2 Estimation of variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.2.3 Estimation of the Hurst Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.2.4 Estimation of variance (part II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.3 Performance Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.3.1 Measurement of Loss and Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.3.2 Reliability and Security Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5 Routing and Control 107 5.1 Routing and control in the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.1.1 Finding the shortest path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.1.2 Subnetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.1.3 Routing Domains in the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.1.4 Router Protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.1.5 Network Address Translation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.1.6 Router Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 5.1.7 Virtual LANs (vLANs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.1.8 IP Version 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.1.9 Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.1.10 End-to-end Congestion Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.2 Routing in Telephone and ATM Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.2.1 Connection Admission Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.2.2 Routing and CAC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.2.3 State-based Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.3 New Approaches to Congestion Control in the Internet . . . . . . . . . . . . . . . . . . . . . . . 121 5.3.1 Congestion and its Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.3.2 Random Early Discard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.3.3 DiffServ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.3.4 Service Level Agreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.3.5 Random Early Dropping of In and Out Packets (RIO) . . . . . . . . . . . . . . . . . . . . 123 5.4 New Approaches to Routing in the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.4.1 Layered Routing – MPLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.4.2 Resource ReSerVation Protocol (RSVP) . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.6 Closing Comments and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6 Requirements Analysis 133 6.1 Traffic Streams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.2 Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.2.1 Tabulation of Demand for Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.3 Growth and Forecasting of future traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.4 Closing Comments and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7 Architecture 141 7.1 Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 7.2 Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.2.1 Hierarchy in Telephone Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 7.2.2 Hierarchy in the Internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 7.3 Networking Philosophies and their Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 7.3.1 Philosophy of TCP/IP Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 7.3.2 Philosophy of ATM Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.3.3 Philosophy of SONET/SDH Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 7.3.4 Cross-fertilization of ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 7.3.5 Multi-Protocol Label Switching (MPLS) . . . . . . . . . . . . . . . . . . . . . . . . . . 150 vi CONTENTS 7.4 Security Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 7.4.1 Key Concepts in Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.4.2 Public key encryption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 7.4.3 Kerberos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.4.4 Lightweight Directory Access Protocol (LDAP) . . . . . . . . . . . . . . . . . . . . . . . 157 7.4.5 IPSEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.4.6 SSL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.4.7 Pretty Good Privacy (PGP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.4.8 Secure Shell (SSH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.4.9 Key Distribution and Certificate Services . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.4.10 Security of Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.5 Network Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8 Equipment Choice 167 8.1 Categories of Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 8.2 A Cost Model of Switching and Transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.3 Switching and Routing Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.3.1 Layer 2 Switching Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 8.3.2 Layer 1 Switching Choices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 9 Design 177 9.1 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 9.1.1 Minimal Spanning Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 9.1.2 Maximum Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 9.1.3 Linear Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 9.1.4 Integer Programming and Mixed Integer Programming . . . . . . . . . . . . . . . . . . . 183 9.1.5 Non-linear Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9.1.6 Travelling Salesman Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 9.2 Present Value Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 9.3 Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 9.4 Design for Service Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 9.5 Design Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 A Netml, A Language for Describing Networks and Traffic 203 A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 A.2 Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 A.3 Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 A.4 Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 A.5 Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 A.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 CONTENTS vii List of Examples Example 1.1 A Network where cost depends upon traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Example 1.2 A Network where cost depends distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Example 2.1 Signalling Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Example 2.2 Unavailability Calculation Using the Enumeration Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Example 2.3 The Parallel Serial Reduction Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Example 2.4 The method of the perfect middle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Example 2.1 A Signalling Network (continued) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Example 2.5 A Connection-oriented Packet Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Example 2.6 A network of SDH Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Example 2.7 Adding Two Nodes while Preserving Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Example 2.8 Large WDM Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Example 3.1 Variance of a Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Example 3.2 Calculation of a mean and variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Example 3.3 From Australia to Silicon Valley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Example 3.4 A Simple Gaussian traffic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Example 3.5 Statistics of Bytes per packet for Uniform packet lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Example 3.6 Loss Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Example 3.7 Fractional Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Example 3.8 The Poisson-Pareto Burst Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Example 3.9 Estimation of Different Performance for Different Classes of Traffic . . . . . . . . . . . . . . . . . . . . . . . . . 75 Example 3.10 Benefits of Differentiated Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Example 3.11 A More Secific Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Example 3.12 A Home . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Example 3.13 A Laboratory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Example 3.14 A School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Example 3.15 A University Campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Example 3.16 A State-wide Retail Organization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Example 3.17 A National Internet Service Provider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Example 3.18 A National Carrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Example 4.1 Telephone Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Example 4.2 Internet Traffic Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Example 4.3 Evaluation of a Security Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Example 5.1 Finding the shortest paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Example 5.2 Subnetworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Example 5.3 A Laboratory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Example 5.4 A School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Example 5.5 A Campus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Example 5.6 A Statewide Retail Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Example 5.7 A National ISP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Example 6.1 Traffic Streams in a Campus Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Example 6.2 A Campus Traffic Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Example 7.1 N +1 Service Protection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Example 7.2 Service Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Example 7.3 IP Over IP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 Example 7.4 Digital Signatures and Certificates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Example 7.5 Denial of Service Attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Example 7.6 SPAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Example 7.7 Authority in PGP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Example 7.8 Secure DNS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Example 7.9 Verisign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Example 7.10 Security in a Campus Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 viii CONTENTS Example 7.11 Layers in a National Carrier Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Example 8.1 The Cost of a download . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Example 8.2 Multi-Protocol Label Switching (MPLS) with TCP/IP over ATM . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Example 8.3 IP over SONET / SDH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 Example 8.4 Why ATM is used in Access Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Example 9.1 Find a Minimal Spanning Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 Example 9.2 Shortest Path Problem as Linear Programming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Example 9.3 Dimensioning a Link. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Example 9.4 Linking two Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Example 9.5 Major Network Upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 Example 9.6 Service Protection in a Campus Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Example 9.7 Design as Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Example 9.8 Design Optimization taking into account traffic variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Example 9.9 Design Optimization for Service Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 CONTENTS ix List of Exercises Exercise 1.1 Network Design – a Difficult Case? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Exercise 2.1 Availability expressed in minutes per year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Exercise 2.2 Analyze the reliability of a network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Exercise 2.3 Another network availability problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Exercise 2.4 Analyze the reliability of another network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Exercise 2.5 Availability Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Exercise 2.6 Design for Reliability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Exercise 2.7 Design for Reliability – Part II. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Exercise 2.8 Design of SDH Ring Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Exercise 2.9 Wavelength Assignment for a 6 Node Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Exercise 3.1 Calculation of a variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Exercise 3.2 Using Ping to display Transmission Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Exercise 3.3 The Rate of a Gaussian Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Exercise 3.4 The distribution of file sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Exercise 3.5 A Simple Network, and its Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Exercise 3.6 Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Exercise 3.7 Delay Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Exercise 3.8 Dimensioning a Simple Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Exercise 3.9 Dimensioning a Simple Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Exercise 3.10 The Benefits of Differential Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Exercise 3.11 Security Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Exercise 4.1 Packet Voice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Exercise 4.2 Use Ping and Traceroute to estimate performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Exercise 4.3 Use of Ping to measure link transmission speed, propagation delay, and throughput . . . . . . . . . . . . 98 Exercise 4.4 Set up MRTG . . . . . . . .

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