Probability markov chains queues and simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling the detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role the textbook is relevant to a wide variety of fields including computer science . Probability markov chains queues and simulationprovides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. Probability markov chains queues and simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling the detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role the textbook is relevant to a wide variety of fields including computer science . Part ii markov chains 191 chapter 9 discrete and continuous time markov chains 193 91 stochastic processes and markov chains 193 92 discrete time markov chains definitions 195 93 the chapman kolmogorov equations 202 94 classification of states 206 95 irreducibility 214 96 the potential fundamental and reachability matrices 218. Probability markov chains queues and simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling the detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role the textbook is relevant to a wide variety of fields including computer science