This information sheet indicates how the course will be organized at pandemic code level yellow and green.
If the colour codes change during the academic year to orange or red, modifications are possible, for example to the teaching and evaluation methods.

# Introduction to performance modelling

 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

### 3. Course contents *

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