Fundamentals of Stochastic Networks

Fundamentals of Stochastic Networks

by Oliver C. Ibe
Released September 2011
Publisher(s): Wiley
ISBN: 9781118065679

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Book description

An interdisciplinary approach to understanding queueing and graphical networks

In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physical sciences.

The author uniquely unites different types of stochastic, queueing, and graphical networks that are typically studied independently of each other. With balanced coverage, the book is organized into three succinct parts:

  • Part I introduces basic concepts in probability and stochastic processes, with coverage on counting, Poisson, renewal, and Markov processes

  • Part II addresses basic queueing theory, with a focus on Markovian queueing systems and also explores advanced queueing theory, queueing networks, and approximations of queueing networks

  • Part III focuses on graphical models, presenting an introduction to graph theory along with Bayesian, Boolean, and random networks

The author presents the material in a self-contained style that helps readers apply the presented methods and techniques to science and engineering applications. Numerous practical examples are also provided throughout, including all related mathematical details.

Featuring basic results without heavy emphasis on proving theorems, Fundamentals of Stochastic Networks is a suitable book for courses on probability and stochastic networks, stochastic network calculus, and stochastic network optimization at the upper-undergraduate and graduate levels. The book also serves as a reference for researchers and network professionals who would like to learn more about the general principles of stochastic networks.

Table of contents

  1. Cover
  2. Title page
  3. Copyright page
  4. PREFACE
    1. ACKNOWLEDGMENTS
  5. 1 BASIC CONCEPTS IN PROBABILITY
    1. 1.1 INTRODUCTION
    2. 1.2 RANDOM VARIABLES
    3. 1.3 TRANSFORM METHODS
    4. 1.4 COVARIANCE AND CORRELATION COEFFICIENT
    5. 1.5 SUMS OF INDEPENDENT RANDOM VARIABLES
    6. 1.6 RANDOM SUM OF RANDOM VARIABLES
    7. 1.7 SOME PROBABILITY DISTRIBUTIONS
    8. 1.8 LIMIT THEOREMS
  6. 2 OVERVIEW OF STOCHASTIC PROCESSES
    1. 2.1 INTRODUCTION
    2. 2.2 CLASSIFICATION OF STOCHASTIC PROCESSES
    3. 2.3 STATIONARY RANDOM PROCESSES
    4. 2.4 COUNTING PROCESSES
    5. 2.5 INDEPENDENT INCREMENT PROCESSES
    6. 2.6 STATIONARY INCREMENT PROCESS
    7. 2.7 POISSON PROCESSES
    8. 2.8 RENEWAL PROCESSES
    9. 2.9 MARKOV PROCESSES
    10. 2.10 GAUSSIAN PROCESSES
  7. 3 ELEMENTARY QUEUEING THEORY
    1. 3.1 INTRODUCTION
    2. 3.2 DESCRIPTION OF A QUEUEING SYSTEM
    3. 3.3 THE KENDALL NOTATION
    4. 3.4 THE LITTLE’S FORMULA
    5. 3.5 THE M/M/1 QUEUEING SYSTEM
    6. 3.6 EXAMPLES OF OTHER M/M QUEUEING SYSTEMS
    7. 3.7 M/G/1 QUEUE
  8. 4 ADVANCED QUEUEING THEORY
    1. 4.1 INTRODUCTION
    2. 4.2 M/G/1 QUEUE WITH PRIORITY
    3. 4.3 G/M/1 QUEUE
    4. 4.4 THE G/G/1 QUEUE
    5. 4.5 SPECIAL QUEUEING SYSTEMS
  9. 5 QUEUEING NETWORKS
    1. 5.1 INTRODUCTION
    2. 5.2 BURKE’S OUTPUT THEOREM AND TANDEM QUEUES
    3. 5.3 JACKSON OR OPEN QUEUEING NETWORKS
    4. 5.4 CLOSED QUEUEING NETWORKS
    5. 5.5 BCMP NETWORKS
    6. 5.6 ALGORITHMS FOR PRODUCT-FORM QUEUEING NETWORKS
    7. 5.7 NETWORKS WITH POSITIVE AND NEGATIVE CUSTOMERS
  10. 6 APPROXIMATIONS OF QUEUEING SYSTEMS AND NETWORKS
    1. 6.1 INTRODUCTION
    2. 6.2 FLUID APPROXIMATION
    3. 6.3 DIFFUSION APPROXIMATIONS
  11. 7 ELEMENTS OF GRAPH THEORY
    1. 7.1 INTRODUCTION
    2. 7.2 BASIC CONCEPTS
    3. 7.3 CONNECTED GRAPHS
    4. 7.4 CUT SETS, BRIDGES, AND CUT VERTICES
    5. 7.5 EULER GRAPHS
    6. 7.6 HAMILTONIAN GRAPHS
    7. 7.7 TREES AND FORESTS
    8. 7.8 MINIMUM WEIGHT SPANNING TREES
    9. 7.9 BIPARTITE GRAPHS AND MATCHINGS
    10. 7.10 INDEPENDENT SET, DOMINATION, AND COVERING
    11. 7.11 COMPLEMENT OF A GRAPH
    12. 7.12 ISOMORPHIC GRAPHS
    13. 7.13 PLANAR GRAPHS
    14. 7.14 GRAPH COLORING
    15. 7.15 RANDOM GRAPHS
    16. 7.16 MATRIX ALGEBRA OF GRAPHS
    17. 7.17 SPECTRAL PROPERTIES OF GRAPHS
    18. 7.18 GRAPH ENTROPY
    19. 7.19 DIRECTED ACYCLIC GRAPHS
    20. 7.20 MORAL GRAPHS
    21. 7.21 TRIANGULATED GRAPHS
    22. 7.22 CHAIN GRAPHS
    23. 7.23 FACTOR GRAPHS
  12. 8 BAYESIAN NETWORKS
    1. 8.1 INTRODUCTION
    2. 8.2 BAYESIAN NETWORKS
    3. 8.3 CLASSIFICATION OF BNs
    4. 8.4 GENERAL CONDITIONAL INDEPENDENCE AND d-SEPARATION
    5. 8.5 PROBABILISTIC INFERENCE IN BNs
    6. 8.6 LEARNING BNs
    7. 8.7 DYNAMIC BAYESIAN NETWORKS
  13. 9 BOOLEAN NETWORKS
    1. 9.1 INTRODUCTION
    2. 9.2 INTRODUCTION TO GRNs
    3. 9.3 BOOLEAN NETWORK BASICS
    4. 9.4 RANDOM BOOLEAN NETWORKS
    5. 9.5 STATE TRANSITION DIAGRAM
    6. 9.6 BEHAVIOR OF BOOLEAN NETWORKS
    7. 9.7 PETRI NET ANALYSIS OF BOOLEAN NETWORKS
    8. 9.8 PROBABILISTIC BOOLEAN NETWORKS
    9. 9.9 DYNAMICS OF A PBN
    10. 9.10 ADVANTAGES AND DISADVANTAGES OF BOOLEAN NETWORKS
  14. 10 RANDOM NETWORKS
    1. 10.1 INTRODUCTION
    2. 10.2 CHARACTERIZATION OF COMPLEX NETWORKS
    3. 10.3 MODELS OF COMPLEX NETWORKS
    4. 10.4 RANDOM NETWORKS
    5. 10.5 RANDOM REGULAR NETWORKS
    6. 10.6 CONSENSUS OVER RANDOM NETWORKS
    7. 10.7 SUMMARY
  15. REFERENCES
  16. Index
  17. Download CD/DVD content

Product information

  • Title: Fundamentals of Stochastic Networks
  • Author(s): Oliver C. Ibe
  • Release date: September 2011
  • Publisher(s): Wiley
  • ISBN: 9781118065679