MVE170 and MSG800
Basic Stochastic Processes
7.5 credit points, 2009/2010

This is a first course in stochastic models for senior undergraduate students in engineering, mathematical statistics, and applied mathematics. The students are assumed to be familiar with the elementary theory of probability.

The theoretical part of the course provides a solid framework in which a variety of applications will be considered.

Course Content

The Poisson process and related topics

The Poisson process

The memoryless property

Merging and splitting of Poisson processes

The M|G|infinity queue

The Poisson process and the uniform distribution

Renewal-reward processes

The renewal process. The renewal function and the excess variable

The renewal-reward process. Limit theorems. Examples on application

The formula of Little

Poisson arrivals see time averages

Discrete-time Markov chains

The model. Examples

Transient analysis

The equilibrium probabilities

Computation of the equilibrium probabilities

Continuous-time Markov chains

The model. Examples

The balance equations. Interpretation of the equilibrium probabilities.

The flow rate equation method

Continuous-time Markov chains with rewards

Computation of the equilibrium probabilities: Kolmogoroff's forward differential equations

Markov chains and queues

The Erlang delay model: the M/M/1 queue.

Course Book
A First Course in Stochastic Models by Henk C. Tijms. The book may be bought by Internet at Bokus Publishing House. Probably it will be available for purchasing at Chalmers students' bookstore Cremona

The course comprises lectures, classes with exercises and discussions, one take home problem-solving examination and a written examination on both theoretical and problem solving questions.

MVE170 and MSG800
Basic Stochastic Processes
7,5 credit points, 2009/2010

Lecturers and exercises
Rossitza Dodunekova

Course material. Examinations and course evaluation