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## Stochastic Modelling

2019-2020

### Course Objective

In this course you will become acquainted with stochastic processes and
models for waiting lines (queueing models). The learning objectives are:
1. to know the assumptions and formulations of the fundamental
stochastic processes and queueing models mentioned above;
2. to be able to analyze and derive results for the fundamental models
mentioned above, and apply similar analysis techniques to related
models;
3. to formulate a model that can be used to analyze a given practical
situation, and/or recognize which model is applicable;
4. to be able interpret the results of these stochastic models, and
understand the practical implications (such as economies of scale,
impact of variability, and critical load).

### Course Content

Stochastic processes and queueing models are often applied to model
practical situations where uncertainty is involved. This course mainly
focuses on Markov chains and queueing models. A key element is the
theoretical development of such models with the emphasis on modeling and
its analysis. In addition, the models are motivated by applications.
More specifically, the fundamental stochastic processes and queueing
models that we study are: Markov chains in discrete and continuous time,
the Poisson process, the M/M/1 queue, the Erlang delay and loss model,
birth-death processes, the M/G/1 queue and the waiting-time paradox.

### Teaching Methods

Lectures and tutorials.

### Method of Assessment

A written midterm exam at the end of period 1 (40% of the grade), a
practical assignment in period 1 (10% of the grade) presented in the
fourth week and to be turned in two weeks later, and a written midterm
exam at the end of period 2 (50% of the grade).

The resit exam covers all material of the course. The practical
assignment still determines 10% of the grade in case of a resit, unless
the grade for the resit exam is higher, in which case the grade for the
resit is determined entirely by the resit exam. It is not possible to
take a resit for only one of the two midterm exams.

### Literature

Kulkarni, V.G., Introduction to Modeling and Analysis of Stochastic
Systems, Springer Texts in Statistics (also available as e-book via
UBVU).
Adan, I.J.B.F., and Resing, J.A.C., Queueing Theory, online lecture

2BA

### Recommended background knowledge

Probability Theory (in particular, the binomial, Poisson, exponential
and uniform distributions and the law of total probability), Calculus 1
and 2 (in particular, power series and Taylor series), Linear Algebra

### General Information

Course Code X_400646 6 EC P1+2 200 English Faculty of Science dr. W. Kager dr. W. Kager dr. W. Kager

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Seminar, Lecture
Target audiences

This course is also available as: