Date 
Topics

Where to study
(B = book; LN = lecture notes)

Additional material 
October 5, 2015 (2h) 
 Presentation of the course


 Slides

October 6, 2015 (2h) 
 Basics of system theory
 Concept of system
 Static vs dynamical systems
 Concept of state
 Continuous vs discrete state
 Concept of event
 Timedriven vs eventdriven systems
 Systems vs (mathematical) models
 Definition of Discrete Event System (DES)
 [B] Chapter 1 (except §1.2.7, §1.2.8 and §1.3.5)
[LN] Chapter 1 (except Examples 1.4 and 1.5)
 
October 7, 2015 (3h) 
 Examples of DES:
 queueing system
 cart system
 Untimed models of DES: state automata (with outputs)
 Graphical representation of state automata
 Exercises
 [B] Section 2.2.2
[B] Examples 2.10 and 2.11
[LN] Examples 1.4 and 1.5
[LN] Chapter 2

 Exercises (with solutions)

October 12, 2015 (2h) 
 Introduction to event timing
 Example: FIFO vs RoundRobin queueing
 [B] Section 5.1
[LN] Section 3.1
 
October 13, 2015 (2h) 
 Definition of clock structure
 Timed models of DES: timed automata
 Examples of event timing dynamics
 [B] Section 5.2 (only §5.2.1)
 
October 14, 2015 (3h) 
 Algorithm for event timing dynamics
 Example: FIFO vs RoundRobin queueing (revisited)
 [B] Section 5.2 (only §5.2.2, §5.2.4 and §5.2.5)


October 19, 2015 (2h) 


 Exercises (with solutions)

October 20, 2015 (2h) 
 Review of probability theory
 [B] Appendix I (except §I.7 and §I.8)

 Test on probability

October 21, 2015 (3h) 
 Uncertainty sources in models of DES
 Models of DES with uncertainty: stochastic timed automata
 Analysis of stochastic timed automata
 Example
 [B] Sections 6.1, 6.3 and 6.4

 Example

October 26, 2015 (2h) 
 The exponential distribution: definition and properties



October 27, 2015 (2h) 
 Stochastic timed automata with Poisson clock structure
 Distribution of events
 Distribution of states
 Distribution of interevent times
 Distribution of state holding times
 [B] Section 6.8


October 28, 2015 (3h) 
 The Poisson counting process
 Exercises
 [B] Sections 6.6 and 6.7

 Exercises (with solutions)

November 2, 2015 (2h) 



November 3, 2015 (2h) 


 Exercises (with solutions)

November 4, 2015 (3h) 


 Exercises (with solutions)

November 9, 2015 (2h) 
 Use of simulation for analysis of stochastic timed automata
 Law of large numbers
 Estimation of state and event probabilities



November 10, 2015 (2h) 
 Use of simulation for analysis of stochastic timed automata
 Histograms
 Estimation of probability density functions



November 11, 2015 (3h) 


 Exercises (with solutions)

November 16, 2015 (2h) 



November 17, 2015 (2h) 
 Basics of stochastic processes
 Markov property and Markov processes
 Continuoustime homogeneous Markov chains
 ChapmanKolmogorov equations
 [B] Section 6.2
[B] Sections 7.1 and 7.3 (only §7.3.1 and §7.3.4)


November 18, 2015 (3h) 
 Continuoustime homogeneous Markov chains
 Transition rate matrix and its properties
 State holding times
 Transition probabilities
 Estimation of transition rates
 [B] Section 7.3 (only §7.3.5, §7.3.6 and §7.3.7)


November 23, 2015 (2h) 
 Continuoustime homogeneous Markov chains
 State probabilities
 Graphical representation
 Classification of states
 [B] Section 7.3 (only §7.3.8 and §7.3.9)


November 24, 2015 (2h) 
 Continuoustime homogeneous Markov chains
 Equivalences between classes of models
 Stochastic timed automata with Poisson clock structure
 Continuoustime homogeneous Markov chains
 [B] Section 7.3 (only §7.3.10)


November 25, 2015 (3h) 
 Queueing theory
 Specification of queueing models
 A/B/m/K notation
 Transient and steady state analysis
 Characterization of steady state
 Performance of queueing systems
 Little's law
 PASTA property
 Examples of Markovian queueing systems
 [B] Sections from 8.1 to 8.6 (except §8.2.5)


November 30, 2015 (2h) 
 Introduction to Matlab (lab tutorial)



December 1, 2015 (2h) 
 Simulation of stochastic timed automata (lab tutorial)


 Matlab files

December 2, 2015 (2h) 


 Exercises (with solutions)

December 9, 2015 (3h) 
 Discretetime homogeneous Markov chains
 ChapmanKolmogorov equations
 Transition probability matrix and its properties
 Example: a simplified telephone call process
 State holding times
 [B] Sections 7.1 and 7.2 (from §7.2.1 to §7.2.5)


December 14, 2015 (2h) 
 Discretetime homogeneous Markov chains
 State probabilities
 Graphical representation
 Classification of states
 [B] Section 7.2 (from §7.2.6 to §7.2.8)


December 15, 2015 (2h) 
 Discretetime homogeneous Markov chains
 [B] Section 7.2 (from §7.2.9 to §7.2.10)


December 16, 2015 (3h) 


 Exercises (with solutions)

December 21, 2015 (2h) 
 Application: control of a machine subject to failures


