|
Date |
Topics
|
Where to study
(B = book; LN = lecture notes)
|
Additional material |
|
October 1, 2018 (2h) |
- Presentation of the course
|
|
- Slides
|
|
October 4, 2018 (4h) |
- Basics of system theory
- Concept of system
- Static vs dynamical systems
- Concept of state
- Continuous vs discrete state
- Concept of event
- Time-driven vs event-driven 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 8, 2018 (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 11, 2018 (4h) |
- Exercises (state automata)
- Introduction to event timing
- Example: FIFO vs Round-Robin queueing
| [B] Section 5.1
[LN] Section 3.1
|
- Exercises
|
|
October 15, 2018 (2h) |
- Definition of clock structure
- Timed models of DES: timed automata
- Basic examples of event timing dynamics
| [B] Section 5.2 (only §5.2.1)
| |
|
October 18, 2018 (4h) |
- Algorithm for event timing dynamics
- Exercises (timed automata)
| [B] Section 5.2 (only §5.2.2, §5.2.4 and §5.2.5)
|
- Exercises (with solutions)
|
|
October 22, 2018 (2h) |
- Review of basic concepts of probability theory
| [B] Appendix I (except §I.7 and §I.8)
|
- Note di calcolo delle probabilità (in Italian)
|
|
October 25, 2018 (4h) |
- Uncertainty sources in models of DES
- Models of DES with uncertainty: stochastic timed automata
- Example of analysis of a stochastic timed automaton
| [B] Sections 6.1, 6.3 and 6.4
|
- Example
|
|
October 29, 2018 (2h) |
- Exercises (stochastic timed automata)
|
|
- Exercises (with solutions)
|
|
November 5, 2018 (2h) |
- The exponential distribution: definition and properties
|
|
|
|
November 8, 2018 (4h) |
- The Poisson counting process
- Stochastic timed automata with Poisson clock structure
- Distribution of residual lifetimes
- Distribution of interevent times
- Event probabilities
- State probabilities
- Distribution of state holding times
| [B] Sections 6.6, 6.7 and 6.8
|
|
|
November 12, 2018 (2h) |
- Exercises (stochastic timed automata with Poisson clock structure)
|
|
- Exercises (with solutions)
|
|
November 15, 2018 (4h) |
- Basics of stochastic processes
- Markov property and Markov processes
- Continuous-time homogeneous Markov chains
- Chapman-Kolmogorov equations
- Transition rate matrix and its properties
- Graphical representation
- State holding times
| [B] Section 6.2
[B] Sections 7.1 and 7.3 (only §7.3.1, from §7.3.4 to §7.3.6)
|
|
|
November 19, 2018 (2h) |
- Continuous-time homogeneous Markov chains
- Transition probabilities
- Estimation of transition rates
- State probabilities
- Classification of states
| [B] Section 7.3 (from §7.3.7 to §7.3.9)
|
|
|
November 22, 2018 (4h) |
- Continuous-time homogeneous Markov chains
- Birth-death chains
- Steady state analysis
- Equivalences between classes of models
- Stochastic timed automata with Poisson clock structure
- Continuous-time homogeneous Markov chains
| [B] Section 7.3 (only §7.3.10)
[B] Section 7.4
|
|
|
November 26, 2018 (2h) |
- Queueing theory
- Specification of queueing models
- A/B/m/K notation
- Transient and steady state analysis
- Characterization of steady state
- Performance indexes
| [B] Sections from 8.1 to 8.4
|
|
|
November 29, 2018 (4h) |
- Seminar "Design of a new production line using discrete event simulation"
Dr. Laura Tordini, PRAMAC s.r.l.
- Queueing theory
- Ergodicity
- Little's law
- PASTA property
| [B] Sections 8.5 and 8.6
|
|
|
December 3, 2018 (2h) |
- Review of basic concepts of statistics and their applications
- Law of large numbers
- Probability estimation
- Histograms and probability distribution estimation
- Random number generation
- Generation of discrete random variables
- Generation of continuous random variables via the inverse method
|
|
|
|
December 6, 2018 (4h) |
- Simulation of stochastic timed automata
|
|
- Matlab files
|
|
December 10, 2018 (2h) |
- Exercises (queueing systems)
|
|
- Exercises
|
