Week 1: Concepts of probability: random variables, probability distributions, expectations. Stopping times and examples.

Week 2: Concepts of probability: conditional probability, conditional expectations.

Week 3: Generation of random variables and introduction to simulation.

Week 4: Markov chains introduction, classification of states and properties.

Week 5: Simulation models: tick-based and event-based methods.

Week 6: Simulation models: Reduced models. Examples: Petri nets, aggregated models.

Week 7: Analysis of absorbing Markov chains, examples. Branching processes and time to extinction.

Week 8:  Analysis of stationary Markov chains, examples. Reversible chains.

Week 9: Statistical analysis of simulation output. Confidence intervals, stopping tests. 

Week 10: Continuous Time Markov Chains and Regenerative Processes.

Week 11: Simulation efficiency and variance reduction methods.

Week 12: (optional) Markov Chain Monte Carlo methods and random search methods.

Week 13: (optional) Markov Decision Processes and Dynamic Programming.

Week 14: Student presentations.

Week 15: Final Exam.