Introduction to performance modelling

Course Code :2001WETSMT
Study domain:Computer Science
Academic year:2019-2020
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