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Course details 2012-2013  
    
Introduction to performance modelling
Course Code :2001WETSMT
Study domain:Computer Science
Semester:Semester: 2nd semester
Contact hours:45
Credits:6
Study load (hours):168
Contract restrictions: No contract restriction
Language of instruction :English
Exam period:exam in the 2nd semester
Lecturer(s)Benny Van Houdt

 


1. Prerequisites

At the start of this course the student should have acquired the following competences:
Specific prerequisites for this course:
This course introduces various fundamental concepts to develop stochastic models used to make design decisions in communication systems. These include the Bernoulli/Poisson process, renewal theory and Markov chains,  Erlang loss models, etc. Some elementary knowledge of probability theory is a plus, but not a prerequisite.


2. Learning outcomes

Apart from making the students acquainted with some elementary modeling techniques, such as the Bernoulli/Poisson process, branching processes and Markov chains, our main focus lies on understanding the practical relevance of various mathematical results and techniques. The students must be able to identify suitable problem situations where the proposed techniques are viable as a solution technique, both within and outside the area of communication systems. Developing this ability is the main purpose of the exercise sessions.




3. Course contents

This course introduces various fundamental concepts when developing stochastic models, such as the Bernoulli/Poisson process, renewal theory and Markov chains,  Erlang loss models, etc. A table of contents of the course notes is given below:

BERNOULLI AND POISSON PROCESS
- Bernoulli process
- The Poisson process
- Superposition, random split, random selection
BRANCHING PROCESSES
- Branching Processes Theory
- Single type branching processes
- Multitype branching processes
- An Application of Branching Processes
- Basic Binary Tree Algorithm
- Modi ed Binary Tree Algorithm

DISCRETE-TIME MARKOV CHAINS
- Definition and Basic Properties
- Communicating States and Classes
- A Fast Algorithm to check the Irreducibility of a FiniteMarkov Chain
- Hitting Probabilities and Hitting Times
- Transient and Recurrent States
- Invariant Vectors and Distributions
- Convergence to the Steady State
- A Fast Algorithm to determine the Period of a Finite Markov Chain
- Lemma of Pakes and Kaplan
- Birth-and-Death Markov chains
APPLICATIONS
- Dimensioning Telephone Systems
- Erlang B formula
- Engset Formula
- Erlang C Formula
- Bianchi’s 802.11 model
- Blocking probability in an OPS/OBS switching element



4. Teaching method

Class contact teaching:
  • Lectures
  • Practice sessions



  • 5. Assessment method and criteria

    Examination:
  • Written without oral presentation
  • Closed book
  • Open book

  • Continuous assessment:
  • Assignments


  • 6. Study material

    Required reading

    Detailed English course notes are available for the students.


    Optional reading

    The following study material can be studied on a voluntary basis:
    Not available.



    7. Contact information
    For questions and remarks, please contact Benny Van Houdt  in room G222 (after making an appointment by email).
    (+)last update: 30/04/2012 11:27 benny.vanhoudt