Introduction to performance modelling

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

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