Table of Contents

1 Introduction.- I Probability.- 2 Randomness and Probability.- 3 Combinatorics.- 4 Random Variables and Distributions.- 5 Expectation and Fundamental Theorems.- II Stochastic Processes.- 6 The Poisson Process and Renewal Theory.- 7 The M/G/1 Queue.- 8 Markov Processes.- 9 Matrix Geometric Solutions.- 10 Queueing Networks.- 11 Epilogue and Special Topics.- A Types of Randomness.- A.1 Randomness: Physical Systems.- A.1.1 Intrinsic Probability.- A.2 Randomness: Deterministic Systems.- A.2.1 The Baker’s Transformation.- A.2.2 Dynamical Systems.- A.3 Deterministic Randomness**.- A.3.1 Isomorphism Between Systems.- A.3.2 Random Newtonian Systems.- A.4 Summary of Appendix A.- A.5 Problems for Appendix A.- B Combinatorial Equalities and Inequalities.- B.1 Noninteger Combinatorial Expressions.- B.2 Binomial Formula.- B.3 Stirling’s (de Moivre’s) Formula.- B.4 Bounds on Factorial Expressions.- B.5 Noninteger Factorials**.- C Tables of Laplace Transforms and Generating Functions.- C.0.1 Laplace Transforms.- C.1 Generating Functions.- D Limits and Order Relationships.- D.1 Limits.- D.2 Order Relationships.- E List of Common Summations.- References.- Index of Notation.