Course Code : | 2001WETSMT |

Study domain: | Computer Science |

Academic year: | 2018-2019 |

Semester: | 1st semester |

Contact hours: | 45 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | English |

Exam period: | exam in the 1st semester |

Lecturer(s) | Benny Van Houdt |

At the start of this course the student should have acquired the following competences:

specific prerequisites for this course

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.

- The students become acquainted with some elementary modeling techniques, such as the Bernoulli/Poisson process, Markov chains and queueing theory. The 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.

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

- Modied 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

The course has an international dimension.

Class contact teachingLectures Practice sessions

ExaminationWritten examination without oral presentation Closed book Open book

Continuous assessmentAssignments

Continuous assessment

Detailed English course notes are available for the students.

Not available.

For questions and remarks, please contact Benny Van Houdt in room G222 (after making an appointment by email).