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
Organization
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.
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