Fundamentals of Stochastic Networks (ePub)

Preface xi Acknowledgments, xii 1 Basic Concepts in Probability 1 1.1 Introduction, 1 1.2 Random Variables, 1 1.3 Transform Methods, 5 1.4 Covariance and Correlation Coefficient, 8 1.5 Sums of Independent Random Variables, 8 1.6 Random Sum of Random Variables, 9 1.7 Some Probability Distributions, 11 1.8 Limit Theorems, 21 2 Overview of Stochastic Processes 26 2.1 Introduction, 26 2.2 Classification of Stochastic Processes, 27 2.3 Stationary Random Processes, 27 2.4 Counting Processes, 28 2.5 Independent Increment Processes, 29 2.6 Stationary Increment Process, 29 2.7 Poisson Processes, 30 2.8 Renewal Processes, 32 2.9 Markov Processes, 37 2.10 Gaussian Processes, 56 3 Elementary Queueing Theory 61 3.1 Introduction, 61 3.2 Description of a Queueing System, 61 3.3 The Kendall Notation, 64 3.4 The Little's Formula, 65 3.5 The M/M/1 Queueing System, 66 3.6 Examples of Other M/M Queueing Systems, 71 3.7 M/G/1 Queue, 79 4 Advanced Queueing Theory 93 4.1 Introduction, 93 4.2 M/G/1 Queue with Priority, 93 4.3 G/M/1 Queue, 99 4.4 The G/G/1 Queue, 105 4.5 Special Queueing Systems, 109 5 Queueing Networks 124 5.1 Introduction, 124 5.2 Burke's Output Theorem and Tandem Queues, 126 5.3 Jackson or Open Queueing Networks, 128 5.4 Closed Queueing Networks, 130 5.5 BCMP Networks, 132 5.6 Algorithms for Product-Form Queueing Networks, 138 5.7 Networks with Positive and Negative Customers, 144 6 Approximations of Queueing Systems and Networks 150 6.1 Introduction, 150 6.2 Fluid Approximation, 151 6.3 Diffusion Approximations, 155 7 Elements of Graph Theory 172 7.1 Introduction, 172 7.2 Basic Concepts, 172 7.3 Connected Graphs, 177 7.4 Cut Sets, Bridges, and Cut Vertices, 177 7.5 Euler Graphs, 178 7.6 Hamiltonian Graphs, 178 7.7 Trees and Forests, 179 7.8 Minimum Weight Spanning Trees, 181 7.9 Bipartite Graphs and Matchings, 182 7.10 Independent Set, Domination, and Covering, 186 7.11 Complement of a Graph, 188 7.12 Isomorphic Graphs, 188 7.13 Planar Graphs, 189 7.14 Graph Coloring,

OLIVER C. IBE, ScD, is Associate Professor in the Department of Electrical and Computer Engineering at the University of Massachusetts at Lowell. He has more than thirty years of experience in academia and the telecommunications industry in various technical and management capacities. Dr. Ibe's research interests include stochastic systems modeling, bioinformatics, and communication network performance modeling. He is the author of Converged Network Architectures: Delivering Voice over IP, ATM, and Frame Relay (Wiley).

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