Introduction to stochastic methods in Operational Research: Overview of the tools from Probability (Conditional mean, Probability Generators, Laplace-Stieltjes Transformation). Exponential distribution.
Poisson process. Times of events in Poisson process.
Renewal Theory: definition of the renewal process and basic computations.
The renewal function – Renewal theorem. The renewal equation, its solution and the basic renewal theorem. Forward and backward recurrence times.
General renewal process. Renewal processes with costs, rewards. Renewal properties.
Introduction to queueing theory. Basic results in queuing systems. Overview of continuous-time Markov chains. Simple Markov queues.
Bibliography
Taha A. H., Operations Research: An Introduction, Pearson, 10th ed., 2017
Hillier F. S., Lieberman G. J., Introduction to Operations Research, MacGraw-Hill, 8th ed., 2004