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).

• Preface xi Acknowledgments, xii1 Basic Concepts in Probability 11.1 Introduction, 11.2 Random Variables, 11.3 Transform Methods, 51.4 Covariance and Correlation Coefficient, 81.5 Sums of Independent Random Variables, 81.6 Random Sum of Random Variables, 91.7 Some Probability Distributions, 111.8 Limit Theorems, 212 Overview of Stochastic Processes 262.1 Introduction, 262.2 Classification of Stochastic Processes, 272.3 Stationary Random Processes, 272.4 Counting Processes, 282.5 Independent Increment Processes, 292.6 Stationary Increment Process, 292.7 Poisson Processes, 302.8 Renewal Processes, 322.9 Markov Processes, 372.10 Gaussian Processes, 563 Elementary Queueing Theory 613.1 Introduction, 613.2 Description of a Queueing System, 613.3 The Kendall Notation, 643.4 The Little’s Formula, 653.5 The M/M/1 Queueing System, 663.6 Examples of Other M/M Queueing Systems, 713.7 M/G/1 Queue, 794 Advanced Queueing Theory 934.1 Introduction, 934.2 M/G/1 Queue with Priority, 934.3 G/M/1 Queue, 994.4 The G/G/1 Queue, 1054.5 Special Queueing Systems, 1095 Queueing Networks 1245.1 Introduction, 1245.2 Burke’s Output Theorem and Tandem Queues, 1265.3 Jackson or Open Queueing Networks, 1285.4 Closed Queueing Networks, 1305.5 BCMP Networks, 1325.6 Algorithms for Product-Form Queueing Networks, 1385.7 Networks with Positive and Negative Customers, 1446 Approximations of Queueing Systems and Networks 1506.1 Introduction, 1506.2 Fluid Approximation, 1516.3 Diffusion Approximations, 1557 Elements of Graph Theory 1727.1 Introduction, 1727.2 Basic Concepts, 1727.3 Connected Graphs, 1777.4 Cut Sets, Bridges, and Cut Vertices, 1777.5 Euler Graphs, 1787.6 Hamiltonian Graphs, 1787.7 Trees and Forests, 1797.8 Minimum Weight Spanning Trees, 1817.9 Bipartite Graphs and Matchings, 1827.10 Independent Set, Domination, and Covering, 1867.11 Complement of a Graph, 1887.12 Isomorphic Graphs, 1887.13 Planar Graphs, 1897.14 Graph Coloring, 1917.14.1 Edge Coloring, 1917.14.2 The Four-Color Problem, 1927.15 Random Graphs, 1927.16 Matrix Algebra of Graphs, 1957.17 Spectral Properties of Graphs, 1987.18 Graph Entropy, 2017.19 Directed Acyclic Graphs, 2017.20 Moral Graphs, 2027.21 Triangulated Graphs, 2027.22 Chain Graphs, 2037.23 Factor Graphs, 2048 Bayesian Networks 2098.1 Introduction, 2098.2 Bayesian Networks, 2108.3 Classification of BNs, 2148.4 General Conditional Independence and d-Separation, 2158.5 Probabilistic Inference in BNs, 2158.6 Learning BNs, 2278.7 Dynamic Bayesian Networks, 2319 Boolean Networks 2359.1 Introduction, 2359.2 Introduction to GRNs, 2369.3 Boolean Network Basics, 2369.4 Random Boolean Networks, 2389.5 State Transition Diagram, 2399.6 Behavior of Boolean Networks, 2409.7 Petri Net Analysis of Boolean Networks, 2429.8 Probabilistic Boolean Networks, 2509.9 Dynamics of a PBN, 2519.10 Advantages and Disadvantages of Boolean Networks, 25210 Random Networks 25510.1 Introduction, 25510.2 Characterization of Complex Networks, 25610.3 Models of Complex Networks, 26110.4 Random Networks, 26510.5 Random Regular Networks, 26710.6 Consensus over Random Networks, 26810.7 Summary, 274References 276Index 280

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).

• Preface xi Acknowledgments, xii1 Basic Concepts in Probability 11.1 Introduction, 11.2 Random Variables, 11.3 Transform Methods, 51.4 Covariance and Correlation Coefficient, 81.5 Sums of Independent Random Variables, 81.6 Random Sum of Random Variables, 91.7 Some Probability Distributions, 111.8 Limit Theorems, 212 Overview of Stochastic Processes 262.1 Introduction, 262.2 Classification of Stochastic Processes, 272.3 Stationary Random Processes, 272.4 Counting Processes, 282.5 Independent Increment Processes, 292.6 Stationary Increment Process, 292.7 Poisson Processes, 302.8 Renewal Processes, 322.9 Markov Processes, 372.10 Gaussian Processes, 563 Elementary Queueing Theory 613.1 Introduction, 613.2 Description of a Queueing System, 613.3 The Kendall Notation, 643.4 The Little’s Formula, 653.5 The M/M/1 Queueing System, 663.6 Examples of Other M/M Queueing Systems, 713.7 M/G/1 Queue, 794 Advanced Queueing Theory 934.1 Introduction, 934.2 M/G/1 Queue with Priority, 934.3 G/M/1 Queue, 994.4 The G/G/1 Queue, 1054.5 Special Queueing Systems, 1095 Queueing Networks 1245.1 Introduction, 1245.2 Burke’s Output Theorem and Tandem Queues, 1265.3 Jackson or Open Queueing Networks, 1285.4 Closed Queueing Networks, 1305.5 BCMP Networks, 1325.6 Algorithms for Product-Form Queueing Networks, 1385.7 Networks with Positive and Negative Customers, 1446 Approximations of Queueing Systems and Networks 1506.1 Introduction, 1506.2 Fluid Approximation, 1516.3 Diffusion Approximations, 1557 Elements of Graph Theory 1727.1 Introduction, 1727.2 Basic Concepts, 1727.3 Connected Graphs, 1777.4 Cut Sets, Bridges, and Cut Vertices, 1777.5 Euler Graphs, 1787.6 Hamiltonian Graphs, 1787.7 Trees and Forests, 1797.8 Minimum Weight Spanning Trees, 1817.9 Bipartite Graphs and Matchings, 1827.10 Independent Set, Domination, and Covering, 1867.11 Complement of a Graph, 1887.12 Isomorphic Graphs, 1887.13 Planar Graphs, 1897.14 Graph Coloring, 1917.14.1 Edge Coloring, 1917.14.2 The Four-Color Problem, 1927.15 Random Graphs, 1927.16 Matrix Algebra of Graphs, 1957.17 Spectral Properties of Graphs, 1987.18 Graph Entropy, 2017.19 Directed Acyclic Graphs, 2017.20 Moral Graphs, 2027.21 Triangulated Graphs, 2027.22 Chain Graphs, 2037.23 Factor Graphs, 2048 Bayesian Networks 2098.1 Introduction, 2098.2 Bayesian Networks, 2108.3 Classification of BNs, 2148.4 General Conditional Independence and d-Separation, 2158.5 Probabilistic Inference in BNs, 2158.6 Learning BNs, 2278.7 Dynamic Bayesian Networks, 2319 Boolean Networks 2359.1 Introduction, 2359.2 Introduction to GRNs, 2369.3 Boolean Network Basics, 2369.4 Random Boolean Networks, 2389.5 State Transition Diagram, 2399.6 Behavior of Boolean Networks, 2409.7 Petri Net Analysis of Boolean Networks, 2429.8 Probabilistic Boolean Networks, 2509.9 Dynamics of a PBN, 2519.10 Advantages and Disadvantages of Boolean Networks, 25210 Random Networks 25510.1 Introduction, 25510.2 Characterization of Complex Networks, 25610.3 Models of Complex Networks, 26110.4 Random Networks, 26510.5 Random Regular Networks, 26710.6 Consensus over Random Networks, 26810.7 Summary, 274References 276Index 280