Date 
Topics

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

Additional material 
October 3, 2016 (2h) 
 Presentation of the course


 Slides

October 4, 2016 (3h) 
 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
 
October 5, 2016 (2h) 
 Untimed models of DES: state automata (with outputs)
 Graphical representation of state automata
 Example: queueing system
 [B] Section 2.2.2
[B] Example 2.11
[LN] Chapter 2
 
October 10, 2016 (2h) 


 Exercises (with solutions)

October 11, 2016 (3h) 
 Introduction to event timing
 Example: FIFO vs RoundRobin queueing
 Definition of clock structure
 Timed models of DES: timed automata
 [B] Section 5.1
[B] Section 5.2 (only §5.2.1)
[LN] Section 3.1
 
October 12, 2016 (2h) 
 Basic examples of event timing dynamics
 Algorithm for event timing dynamics
 [B] Section 5.2 (only §5.2.2, §5.2.4 and §5.2.5)
 
October 17, 2016 (2h) 
 Example: FIFO vs RoundRobin queueing (revisited)



October 18, 2016 (3h) 


 Exercises (with solutions)

October 19, 2016 (2h) 
 Review of probability theory
 [B] Appendix I (except §I.7 and §I.8)

 Note di calcolo delle probabilità (in Italian)

October 24, 2016 (2h) 
 Uncertainty sources in models of DES
 Models of DES with uncertainty: stochastic timed automata
 [B] Sections 6.1, 6.3 and 6.4


October 25, 2016 (3h) 
 Analysis of stochastic timed automata
 Example


 Example

October 26, 2016 (2h) 
 The exponential distribution: definition and properties



November 7, 2016 (2h) 
 Stochastic timed automata with Poisson clock structure
 Distribution of residual lifetimes
 Distribution of interevent times
 Distribution of events
 Distribution of states
 [B] Section 6.8


November 8, 2016 (3h) 
 The Poisson counting process
 Stochastic timed automata with Poisson clock structure
 Distribution of state holding times
 Example
 [B] Sections 6.6 and 6.7


November 9, 2016 (2h) 


 Exercise (with solutions)

November 14, 2016 (2h) 


 Exercises (with solutions)

November 15, 2016 (3h) 


 Exercises (with solutions)

November 16, 2016 (2h) 


 Exercises (with solutions)

November 21, 2016 (2h) 



November 22, 2016 (3h) 
 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 23, 2016 (2h) 
 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 28, 2016 (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 29, 2016 (3h) 
 Continuoustime homogeneous Markov chains
 Birthdeath chains
 Steady state analysis
 Equivalences between classes of models
 Stochastic timed automata with Poisson clock structure
 Continuoustime homogeneous Markov chains
 Example
 [B] Section 7.3 (only §7.3.10)
[B] Section 7.4

 Exercises (with solutions)
 Matlab files

November 30, 2016 (2h) 
 Use of simulation for analysis of stochastic timed automata
 Law of large numbers
 Estimation of state and event probabilities



December 6, 2016 (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
 [B] Sections from 8.1 to 8.5


December 7, 2016 (2h) 
 Examples of Markovian queueing systems
 Exercises
 [B] Section 8.6

 Exercises (with solutions)

December 19, 2016 (2h) 
 Simulation of stochastic timed automata (lab tutorial)


 Matlab files

December 21, 2016 (2h) 
 Simulation of stochastic timed automata (lab tutorial)


 Exercise
 Matlab files

January 9, 2017 (2h) 
 Discretetime homogeneous Markov chains
 ChapmanKolmogorov equations
 Transition probability matrix and its properties
 Graphical representation
 [B] Sections 7.1 and 7.2 (from §7.2.1 to §7.2.4)


January 10, 2017 (3h) 
 Discretetime homogeneous Markov chains
 State probabilities
 State holding times
 Classification of states
 [B] Section 7.2 (from §7.2.5 to §7.2.8)


January 16, 2017 (2h) 
 Discretetime homogeneous Markov chains
 Steady state analysis
 Applications to robotics
 [B] Section 7.2 (from §7.2.9 to §7.2.10)


January 17, 2017 (3h) 


 Exercises (with solutions)

January 18, 2017 (2h) 
 [B] Example 7.2

 Exercises (with solutions)

January 31, 2017 (1h) 
 Endterm test (CAER&A only)


