2008/2009
MVE170 Basic Stochastic
Processes, 7.5 credit points
MSG800 Basic Stochastic
Processes, 7.5 credit points
TMS125 Stochastic
Processes, 4.5 credit points
MSG860 Basic Stochastic Processes, 4.5 credit points
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 MGinfinity queue
The Poisson
process and the uniform distribution
Renewalreward processes
The renewal process. The renewal function and the excess variable
The renewalreward process. Limit theorems. Examples on
application
The formula of Little
Poisson arrivals see
time averages
Discretetime Markov chains
The model. Examples
Transient analysis
The equilibrium probabilities
Computation of the equilibrium probabilities
Continuoustime Markov chains
The model. Examples
The balance equations. Interpretation of the equilibrium probabilities.
The flow rate equation method
Continuoustime 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
Organization
The course is run on two levels, worth 7.5 and 4.5 credit points
respectively. It comprises
lectures, classes with exercises and
discussions, two take home problemsolving examinations,
and a written examination in the theory.
