## 2DI60 - Stochastic operations research

This is an introductory course in stochastic operations research. As such, you cannot avoid being introduced to several basic ideas and principles that can prove quite challenging at first. However, regardless whether you plan to go to industry after finishing your degree or if you are planning on further studies, you will certainly use material from this class.

**Learning objectives:**

The objective of the course is to help the students master the basic tools used in analysing systems that operate in the presence of randomness. At the end of the course, students should be able to:

- ◘ Model real life/practical problems using Markov chains (MC) and renewal processes (RP) –
**Modelling** - ◘ Use the theory of Markov chains, renewal processes, and queueing theory to solve practical problems –
**Solving** - ◘ Calculate the performance measures of a system through the study of MC and RP –
**Calculating**Toolbox outcomes: solve linear systems, calculate integrals and summations, master computations of expectations, use power and geometric series - ◘ Define appropriate cost structures and efficiently optimize the behaviour of the system–
**Optimizing** - ◘ Use mathematical software (Mathematica) for large scale numerical calculations –
**Coding**

**Short promotional description of the course:**

We focus on model-based process analysis using Operation Research. Students can formulate discrete and continuous time Markov chains and queuing models for several practical situations. For discrete-time chains, we compute transient and limiting distributions, costs and first passage times. For continuous-time chains, we compute the limiting distribution, long-term costs and first passage times. Students can calculate and interpret several performance measures in a number of queuing models.

The course is designed to help you master this material. To this purpose, the course material is divided into theory, exercises/instructions and pc instructions. During all sessions, you are strongly advised to bring your laptop. It will help with solving the exercises.

**Content:**

Topics taught in 2DI60 include discrete and continuous time Markov chains, Poisson process, renewal processes, introduction to queueing systems (M/M/1, M/M/s, finite population models, birth and death queues, M/G/1, G/M/1, G/G/1), and open and closed networks of queues (Jackson networks). More generally, this course deals with the modelling and analysis of systems that operate in the presence of randomness/uncertainty. The goal of the course is to set the mathematical foundations so as the students understand, analyse, and ultimately optimize the behaviour of such systems.

Syllabus