Many real-world systems—such as those found in robotics, factory automation, communication networks, and economic environments—combine continuous dynamics with discrete events. Discrete dynamics arise from asynchronous events (e.g., a component failure or a system reset) that can abruptly alter a system’s state. While traditional courses on systems and control theory primarily focuses on continuous behavior, the analysis of discrete event systems requires tools and models that are quite different from the ones used in the traditional study of systems with continuous states. The main purpose of this course is to introduce the foundational concepts and tools for modeling and analyzing Discrete Event Systems. Students will explore both deterministic and stochastic frameworks to understand how these systems evolve over time and they will learn to analyze quantitatively the system behavior, via an analytic approach or via a computer simulation one. By the end of the course, students will have a strong foundation in the principles and tools needed to work with discrete event systems across a range of real-world applications.

The student shall acquire the following knowledge and develop the following abilities: - Knowledge of analytical tools for the representation of dynamic systems with discrete events, in both deterministic and stochastic contexts; - Ability to model simple problems commonly encountered in automated production processes and management; - Ability to evaluate system performance, both analytically and numerically, and to define the system parameters during the design phase; - Knowledge of the key characteristics of networks of interconnected systems.

Elements of basic probability theory, mathematical analysis, and linear algebra.

1) Introduction to the course. Basic notions of probability theory and linear algebra (1.5 hours) 2) Discrete event systems, timed discrete event systems (9 hours); 3) Stochastic processes, Poisson processes (4.5 hours); 4) Discrete-time Markov chains, continuous-time Markov chains (13.5 hours); 5) Birth-death chains (4.5 hours); 6) Queueing theory (12 hours); 7) Open queueing networks, closed queueing networks (15 hours).

The course is organized in a series of lectures (about 2/3 of the course) and practice sessions (about 1/3 of the course).

Selected chapters from: C. G. Cassandras and S. Lafortune, “Introduction to Discrete Event Systems”, Kluwer; G. Grimmett and D. Stirzaker, "Probability and Random Processes", Oxford university press. Lecture slides are available as well as laboratory practice handouts.

Slides; Libro di testo; Esercizi risolti;

Modalità di esame: Prova scritta (in aula);

Exam: Written test;

... The final exam consists of a written test, which will contain a mixture of multiple-choice questions and numerical open-answer problems (to be executed with pen and paper; use of a simple calculator is allowed). For multiple-choice questions, a (small) negative score is assigned to wrong answers. Use of didactic material ONLY ON PAPER (books, notes, etc.) is allowed. The exam will last 1h30m approximately.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.