Probability Stochastic Processes and Queueing Theory

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. Language: English