{"product_id":"queueing-modelling-fundamentals-9780470519578","title":"Queueing Modelling Fundamentals","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFully revised, this second edition of Queueing Modeling Fundamentals With Applications In Communication Networks contains a significant new chapter on Flow \u0026amp; Congestion Control and a section on Network Calculus among other new sections that have been added to other chapters.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\"The book is well written and nicely illustrated. I recommend it as an introduction for graduate students and telecommunications engineers.\" (\u003ci\u003eComputing Reviews\u003c\/i\u003e, November 24, 2008)  \u003cp\u003e\"This book would serve ideally as a text for an undergraduate course on network performance analysis.\" (\u003ci\u003eComputing Reviews,\u003c\/i\u003e July 2008)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eList of Tables xi\u003c\/p\u003e \u003cp\u003eList of Illustrations xiii\u003c\/p\u003e \u003cp\u003ePreface xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1. Preliminaries 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Probability Theory 1\u003c\/p\u003e \u003cp\u003e1.1.1 Sample Spaces and Axioms of Probability 2\u003c\/p\u003e \u003cp\u003e1.1.2 Conditional Probability and Independence 5\u003c\/p\u003e \u003cp\u003e1.1.3 Random Variables and Distributions 7\u003c\/p\u003e \u003cp\u003e1.1.4 Expected Values and Variances 12\u003c\/p\u003e \u003cp\u003e1.1.5 Joint Random Variables and Their Distributions 16\u003c\/p\u003e \u003cp\u003e1.1.6 Independence of Random Variables 21\u003c\/p\u003e \u003cp\u003e1.2 z-Transforms – Generating Functions 22\u003c\/p\u003e \u003cp\u003e1.2.1 Properties of z-Transforms 23\u003c\/p\u003e \u003cp\u003e1.3 Laplace Transforms 28\u003c\/p\u003e \u003cp\u003e1.3.1 Properties of the Laplace Transform 29\u003c\/p\u003e \u003cp\u003e1.4 Matrix Operations 32\u003c\/p\u003e \u003cp\u003e1.4.1 Matrix Basics 32\u003c\/p\u003e \u003cp\u003e1.4.2 Eigenvalues, Eigenvectors and Spectral Representation 34\u003c\/p\u003e \u003cp\u003e1.4.3 Matrix Calculus 36\u003c\/p\u003e \u003cp\u003eProblems 39\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2. Introduction to Queueing Systems 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Nomenclature of a Queueing System 44\u003c\/p\u003e \u003cp\u003e2.1.1 Characteristics of the Input Process 45\u003c\/p\u003e \u003cp\u003e2.1.2 Characteristics of the System Structure 46\u003c\/p\u003e \u003cp\u003e2.1.3 Characteristics of the Output Process 47\u003c\/p\u003e \u003cp\u003e2.2 Random Variables and their Relationships 48\u003c\/p\u003e \u003cp\u003e2.3 Kendall Notation 50\u003c\/p\u003e \u003cp\u003e2.4 Little’s Theorem 52\u003c\/p\u003e \u003cp\u003e2.4.1 General Applications of Little’s Theorem 54\u003c\/p\u003e \u003cp\u003e2.4.2 Ergodicity 55\u003c\/p\u003e \u003cp\u003e2.5 Resource Utilization and Traffic Intensity 56\u003c\/p\u003e \u003cp\u003e2.6 Flow Conservation Law 57\u003c\/p\u003e \u003cp\u003e2.7 Poisson Process 59\u003c\/p\u003e \u003cp\u003e2.7.1 The Poisson Process – A Limiting Case 59\u003c\/p\u003e \u003cp\u003e2.7.2 The Poisson Process – An Arrival Perspective 60\u003c\/p\u003e \u003cp\u003e2.8 Properties of the Poisson Process 62\u003c\/p\u003e \u003cp\u003e2.8.1 Superposition Property 62\u003c\/p\u003e \u003cp\u003e2.8.2 Decomposition Property 63\u003c\/p\u003e \u003cp\u003e2.8.3 Exponentially Distributed Inter-arrival Times 64\u003c\/p\u003e \u003cp\u003e2.8.4 Memoryless (Markovian) Property of Inter-arrival Times 64\u003c\/p\u003e \u003cp\u003e2.8.5 Poisson Arrivals During a Random Time Interval 66\u003c\/p\u003e \u003cp\u003eProblems 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3. Discrete and Continuous Markov Processes 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Stochastic Processes 72\u003c\/p\u003e \u003cp\u003e3.2 Discrete-time Markov Chains 74\u003c\/p\u003e \u003cp\u003e3.2.1 Definitions of Discrete-time Markov Chains 75\u003c\/p\u003e \u003cp\u003e3.2.2 Matrix Formulation of State Probabilities 79\u003c\/p\u003e \u003cp\u003e3.2.3 General Transient Solutions for State Probabilities 81\u003c\/p\u003e \u003cp\u003e3.2.4 Steady-state Behaviour of a Markov Chain 86\u003c\/p\u003e \u003cp\u003e3.2.5 Reducibility and Periodicity of a Markov Chain 88\u003c\/p\u003e \u003cp\u003e3.2.6 Sojourn Times of a Discrete-time Markov Chain 90\u003c\/p\u003e \u003cp\u003e3.3 Continuous-time Markov Chains 91\u003c\/p\u003e \u003cp\u003e3.3.1 Definition of Continuous-time Markov Chains 91\u003c\/p\u003e \u003cp\u003e3.3.2 Sojourn Times of a Continuous-time Markov Chain 92\u003c\/p\u003e \u003cp\u003e3.3.3 State Probability Distribution 93\u003c\/p\u003e \u003cp\u003e3.3.4 Comparison of Transition-rate and Transitionprobability Matrices 95\u003c\/p\u003e \u003cp\u003e3.4 Birth-Death Processes 96\u003c\/p\u003e \u003cp\u003eProblems 100\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4. Single-Queue Markovian Systems 103\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Classical M\/M\/1 Queue 104\u003c\/p\u003e \u003cp\u003e4.1.1 Global and Local Balance Concepts 106\u003c\/p\u003e \u003cp\u003e4.1.2 Performance Measures of the M\/M\/1 System 107\u003c\/p\u003e \u003cp\u003e4.2 PASTA – Poisson Arrivals See Time Averages 110\u003c\/p\u003e \u003cp\u003e4.3 M\/M\/1 System Time (Delay) Distribution 111\u003c\/p\u003e \u003cp\u003e4.4 M\/M\/1\/S Queueing Systems 118\u003c\/p\u003e \u003cp\u003e4.4.1 Blocking Probability 119\u003c\/p\u003e \u003cp\u003e4.4.2 Performance Measures of M\/M\/1\/S Systems 120\u003c\/p\u003e \u003cp\u003e4.5 Multi-server Systems – M\/M\/m 124\u003c\/p\u003e \u003cp\u003e4.5.1 Performance Measures of M\/M\/m Systems 126\u003c\/p\u003e \u003cp\u003e4.5.2 Waiting Time Distribution of M\/M\/m 127\u003c\/p\u003e \u003cp\u003e4.6 Erlang’s Loss Queueing Systems – M\/M\/m\/m Systems 129\u003c\/p\u003e \u003cp\u003e4.6.1 Performance Measures of the M\/M\/m\/m 130\u003c\/p\u003e \u003cp\u003e4.7 Engset’s Loss Systems 131\u003c\/p\u003e \u003cp\u003e4.7.1 Performance Measures of M\/M\/m\/m with Finite Customer Population 133\u003c\/p\u003e \u003cp\u003e4.8 Considerations for Applications of Queueing Models 134\u003c\/p\u003e \u003cp\u003eProblems 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5. Semi-Markovian Queueing Systems 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The M\/G\/1 Queueing System 142\u003c\/p\u003e \u003cp\u003e5.1.1 The Imbedded Markov-chain Approach 142\u003c\/p\u003e \u003cp\u003e5.1.2 Analysis of M\/G\/1 Queue Using Imbedded Markov-chain Approach 143\u003c\/p\u003e \u003cp\u003e5.1.3 Distribution of System State 146\u003c\/p\u003e \u003cp\u003e5.1.4 Distribution of System Time 147\u003c\/p\u003e \u003cp\u003e5.2 The Residual Service Time Approach 148\u003c\/p\u003e \u003cp\u003e5.2.1 Performance Measures of M\/G\/ 1 150\u003c\/p\u003e \u003cp\u003e5.3 M\/G\/1 with Service Vocations 155\u003c\/p\u003e \u003cp\u003e5.3.1 Performance Measures of M\/G\/1 with Service Vacations 156\u003c\/p\u003e \u003cp\u003e5.4 Priority Queueing Systems 158\u003c\/p\u003e \u003cp\u003e5.4.1 M\/G\/1 Non-preemptive Priority Queueing 158\u003c\/p\u003e \u003cp\u003e5.4.2 Performance Measures of Non-preemptive Priority 160\u003c\/p\u003e \u003cp\u003e5.4.3 M\/G\/1 Pre-emptive Resume Priority Queueing 163\u003c\/p\u003e \u003cp\u003e5.5 The G\/M\/1 Queueing System 165\u003c\/p\u003e \u003cp\u003e5.5.1 Performance Measures of GI\/M\/ 1 166\u003c\/p\u003e \u003cp\u003eProblems 167\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6. Open Queueing Networks 169\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Markovian Queries in Tandem 171\u003c\/p\u003e \u003cp\u003e6.1.1 Analysis of Tandem Queues 175\u003c\/p\u003e \u003cp\u003e6.1.2 Burke’s Theorem 176\u003c\/p\u003e \u003cp\u003e6.2 Applications of Tandem Queues in Data Networks 178\u003c\/p\u003e \u003cp\u003e6.3 Jackson Queueing Networks 181\u003c\/p\u003e \u003cp\u003e6.3.1 Performance Measures for Open Networks 186\u003c\/p\u003e \u003cp\u003e6.3.2 Balance Equations 190\u003c\/p\u003e \u003cp\u003eProblems 193\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7. Closed Queueing Networks 197\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Jackson Closed Queueing Networks 197\u003c\/p\u003e \u003cp\u003e7.2 Steady-state Probability Distribution 199\u003c\/p\u003e \u003cp\u003e7.3 Convolution Algorithm 203\u003c\/p\u003e \u003cp\u003e7.4 Performance Measures 207\u003c\/p\u003e \u003cp\u003e7.5 Mean Value Analysis 210\u003c\/p\u003e \u003cp\u003e7.6 Application of Closed Queueing Networks 213\u003c\/p\u003e \u003cp\u003eProblems 214\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8. Markov-Modulated Arrival Process 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Markov-modulated Poisson Process (MMPP) 218\u003c\/p\u003e \u003cp\u003e8.1.1 Definition and Model 218\u003c\/p\u003e \u003cp\u003e8.1.2 Superposition of MMPPs 223\u003c\/p\u003e \u003cp\u003e8.1.3 MMPP\/G\/ 1 225\u003c\/p\u003e \u003cp\u003e8.1.4 Applications of MMPP 226\u003c\/p\u003e \u003cp\u003e8.2 Markov-modulated Bernoulli Process 227\u003c\/p\u003e \u003cp\u003e8.2.1 Source Model and Definition 227\u003c\/p\u003e \u003cp\u003e8.2.2 Superposition of N Identical MMBPs 228\u003c\/p\u003e \u003cp\u003e8.2.3 ΣMMBP\/D\/ 1 229\u003c\/p\u003e \u003cp\u003e8.2.4 Queue Length Solution 231\u003c\/p\u003e \u003cp\u003e8.2.5 Initial Conditions 233\u003c\/p\u003e \u003cp\u003e8.3 Markov-modulated Fluid Flow 233\u003c\/p\u003e \u003cp\u003e8.3.1 Model and Queue Length Analysis 233\u003c\/p\u003e \u003cp\u003e8.3.2 Applications of Fluid Flow Model to ATM 236\u003c\/p\u003e \u003cp\u003e8.4 Network Calculus 236\u003c\/p\u003e \u003cp\u003e8.4.1 System Description 237\u003c\/p\u003e \u003cp\u003e8.4.2 Input Traffic Characterization–Arrival Curve 239\u003c\/p\u003e \u003cp\u003e8.4.3 System Characterization – Service Curve 240\u003c\/p\u003e \u003cp\u003e8.4.4 Min-Plus Algebra 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9. Flow and Congestion Control 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 243\u003c\/p\u003e \u003cp\u003e9.2 Quality of Service 245\u003c\/p\u003e \u003cp\u003e9.3 Analysis of Sliding Window Flow Control Mechanisms 246\u003c\/p\u003e \u003cp\u003e9.3.1 A Simple Virtual Circuit Model 246\u003c\/p\u003e \u003cp\u003e9.3.2 Sliding Window Model 247\u003c\/p\u003e \u003cp\u003e9.4 Rate Based Adaptive Congestion Control 257\u003c\/p\u003e \u003cp\u003eReferences 259\u003c\/p\u003e \u003cp\u003eIndex 265\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402353844567,"sku":"9780470519578","price":91.76,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470519578.jpg?v=1730480155","url":"https:\/\/bookcurl.com\/products\/queueing-modelling-fundamentals-9780470519578","provider":"Book Curl","version":"1.0","type":"link"}