An integrated presentation of theory, applications and algorithms that demonstrates how useful simple stochastic (random) models can be for gaining insight into the behaviour of complex stochastic systems. The methods described can be used to obtain solutions to problems in statistics, operations research, finance, economics and engineering. An integrated presentation of theory, applications and algorithms that demonstrates how useful simple stochastic (random) models can be for gaining insight into the behaviour of complex stochastic systems. The methods described can be used to obtain solutions to problems in statistics, operations research, finance, economics and engineering. Preface. The Poisson Process and Related Processes. Renewal Reward Processes. Discrete Time Markov Chains. Continuous Time Markov Chains. Markov Chains and Queues. Discrete Time Markov Decision Processes. Semi Markov Decision Processes. Advanced Renewal Theory. Algorithmic Analysis of Queueing Models. Appendix A: Useful Tools in Applied Probability. Appendix B: Useful Probability Distributions. Appendix C: Generating Functions. Appendix D: The Discrete Fast Fourier Transform. Appendix E: Laplace Transform Theory. Appendix F: Numerical Laplace Inversion. Appendix G: The Root Finding Problem. References. Index.