After successful completion of this module component, the student is able to:
- formulate a Markov chain model for a given problem description and solve this model;
- formulate a Stochastic Dynamic Programming (SDP) model for a given problem description and solve this model;
- formulate a Markov Decision Process (MDP) model for a given problem description and solve this model;
- interpret the outcomes of an SDP and MDP model in order to construct an optimal strategy, which is applicable in a given practical situation;
- select an appropriate queueing model (M/M/1, M/M/c, etc.) for a given problem description and solve this model;
- interpret the implications of a queueing system’s performance on (given) performance indicators and formulate practical recommendations for system improvement.
In the module component Stochastic Models, students first learn the basics of Markov chains (in discrete and continuous time, and Poisson processes). Using that knowledge, they next learn about stochastic dynamic programming and about queueing theory. Stochastic dynamic programming can be used to solve sequential multistage decision problems under uncertainty, e.g., transportation planning for multiple time periods with uncertain order arrivals and transportation times. Queueing theory can be used to analyse queueing problems that occur, e.g., in production and logistics, traffic, and communication networks.