Queueing Systems: Queueing models use basic probability concepts and stochastic processes (Poisson processes, Markov chains, birth-death processes, random walks) to describe and analyze congestion effects in terms of queue lengths and waiting times. In this course, we introduce the most common models in queueing theory, such as M/M/1, M/M/C, M/G/1 and G/M/1, discuss their fundamental properties, and explain how these models arise in various scenarios of interest. The focus is on mathematical techniques for deriving the stationary queue length distribution and waiting-time distribution, and calculating several specific performance measures. We also discuss how these methods and results can be applied for improving   the efficiency or evaluating the performance of real-life service facilities.
Markov decision processes (MDPs): Refers to class of problems that involve repeated decision making in stochastic environments. MDPs allow us to alter the evolution of stochastic systems by exercising control to achieve a certain objective. Finite Horizon MDPs, Infinite Horizon Discounted MDPs, Infinite Horizon Total and Average Cost MDPs.
Inventory control: Components of Inventory Models, Deterministic Continuous-Review Models, A Deterministic Periodic-Review Model, A Stochastic Continuous-Review Model, A Stochastic Single-Period Model for Perishable Products.
Stochastic models in biology and social sciences: Volterra and Lanchester models, basic epidemic processes.
Ruin theory: Basic elements of renewal theory, Cramer-Lundberg and Gerber-Shiu models.