Course Code : | 2001WETSMT |

Study domain: | Computer Science |

Academic year: | 2020-2021 |

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:

an active knowledge of

an active knowledge of

- English

- English

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, Markov chains, Erlang loss models, etc. A table of contents of the course notes is given below:

BERNOULLI AND POISSON PROCESS

1 Bernoulli Process

2 The Poisson Process

3 Superposition, Random Split, Random Selection

4 Exercise

DISCRETE-TIME MARKOV CHAINS

1 De nition and Basic Properties

2 Communicating States and Classes

3 A Fast Algorithm to check the Irreducibility of a Finite Markov Chain

4 Hitting Probabilities and Hitting Times

5 Transient and Recurrent States

6 Invariant Vectors and Distributions

7 Convergence to the Steady State

8 A Fast Algorithm to determine the Period of a Finite Markov Chain

9 Lemma of Pakes and Kaplan

10 Birth-and-Death Markov chains

11 Summary

12 Exercises

CONTINUOUS-TIME MARKOV CHAINS

1 De nition and Basic Properties

2 Limiting Behavior

3 Uniformization and Embedded Markov Chain

4 Birth-and-Death Markov Chains

5 PASTA Property

6 Exercises

APPLICATIONS

1 Some Fundamental Queueing Systems

1.1 The M/M/1 queue

1.2 The M/M/1 queue

1.3 Insensitivity

2 Dimensioning the Plain Old Telephone System

2.1 Erlang B Formula (M/M/C/C queue)

2.2 Engset Formula

2.3 Erlang C Formula (M/M/C/C+Q queue)

3 Jackson Networks

4 Bianchi's 802.11 Model

4.1 802.11 DCF Operation

4.2 A Markovian Model for the 802.11 Saturation Throughput

4.2.1 Packet Transmission Probability

4.2.2 Throughput

5 Blocking Probability in an OPS/OBS Switching Element

6 Exercises

The course has an international dimension.

Class contact teachingLectures Practice sessions

ExaminationWritten examination without oral presentation Closed book Open book

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).