Probabilistic Methods In Or

AY2018/2019 Semester 1

1.Queueing Theory a Revision of Exponential and Poisson Distributions b Basic Queueing System, Birth-death Process c Little's Formula d The M/M/s, M/M/s/K models, Queue Length and Waiting Time 2.Simulation a Techniques for Simulating Continuous Random Variable b Simulating from Discrete Distributions c Variance Reduction Techniques d Generating from the Stationary Distribution of a Markov Chain e Monto Carlo Method 3. Stochastic Optimization: Prologue a Elements of Inventory and Production Models b Deterministic Optimization v.s. Stochastic Optimization c Expected Utility Criterion d Sample Average Approximation Method 4. Markov Decision Process a Formulating Markov Decision Model b Linear Programming Approach c Policy Improvement Algorithm d Successive Approximation approach