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Systems with Discrete Events

Code: PDEEC0068     Acronym: SED

Classification Keyword
OFICIAL Electrical and Computer Engineering

Instance: 2019/2020 - 1S

Active? Yes
Responsible unit: Department of Electrical and Computer Engineering
Course/CS Responsible: Doctoral Program in Electrical and Computer Engineering

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
PDEEC 0 Syllabus since 2015/16 1 - 7,5 70 202,5

Teaching Staff - Responsibilities

Teacher Responsibility
Fernando Manuel Ferreira Lobo Pereira

Teaching - Hours

Recitations: 3,00
Type Teacher Classes Hour
Recitations Totals 1 3,00
Fernando Manuel Ferreira Lobo Pereira 3,00

Teaching language

Portuguese and english
Obs.: Portuguese and English


An unified modeling and analysis formal framework for discrete event driven dynamic systems and some associated key analytical tools are introduced and discussed. For the class of Markov processes, which are amenable to more traditional analytic methods, control issues will be also addressed. For more general classes of systems, simulation methods will be considered and sensitivity analysis and sample path constructive techniques are presented.
The spectrum of topics is very vast and not all the items might be covered with the same intensity. This enables to focus on issues selected to suit the interests of the students' research plans.
Methods for the modeling, analysis and synthesis of discrete event systems.

Learning outcomes and competences

Mastery of systematic methods for the analysis, design and verification of control systems for Discrete Event Systems.
The systemic approach encompasses untimed, timed, deterministic and stochastic systems, providing the basis to handle systems specified by networks of queues

Working method


Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Algebra, Mathemaical Analysis, Probability Theory


1. Introduction - Discrete-Event Systems, System Classification.
2. Untimed Models of Discrete-Event Systems - Languages and Automata Theory, Petri Nets, Analysis of Untimed Models.
3. Timed Models of Discrete-Event Systems - Timed State Automata, Timed Petri Nets, Algebra max-plus.
4. Stochastic Timed Models for Discrete-Event Systems - Introduction to Stochastic Processes, Stochastic Timed State Automata, Generalized Semi-Markov Process, Poisson Process, Extensions of Generalized Semi-Markov Process.
5. Markov Chains - Models, Transition Probability Matrix, Transient and Steady State Analysis for Discrete-Time Markov Chains and Continuous-time Markov.
6. Controlled Markov Chains - Markov Decision Processes, Approaches to the Synthesis for Markov Decision Problems.
7. Queueing Theory - Queueing Models, Performance and Dynamics of a Queuing System, Analysis of Markovian Queueing Systems, Markovian Queueing Networks, Control of Queueing Systems. (5h)
8. Discrete-Event Simulation - The Event Scheduling Simulation Scheme, The Process-Oriented Simulation Scheme, Discrete-Event Simulation Languages, Output Analysis.
9. Sensitivity Analysis.

Mandatory literature

Christos G. Cassandras; Introduction to discrete event systems

Complementary Bibliography

Y. C. Ho and X. R. Cao; Perturbation Analysis of Discrete Event Dynamic Systems, Kluwer Academic Publishers, 1991
P. Kozák and S. Balemi and R. Smedinga (eds.); Discrete Event Systems: Modelling and Control, Birkhäuser, 1993

Teaching methods and learning activities

Short exposition of strategic nature for each one of the main chapters.
Presentation of a number of themes by each one of the students followed by a discussion by the group.
Challenging exercises to be addressed by the students.
Discussion of the exercises so that studentes receive proper feedback to enhance their studying methods.
Optionally the student might engage in a design project involving the topics above.


Technological sciences > Engineering > Control engineering > Automation

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation Weight (%)
Participação presencial 20,00
Apresentação/discussão de um trabalho científico 20,00
Trabalho escrito 30,00
Trabalho prático ou de projeto 30,00
Total: 100,00

Amount of time allocated to each course unit

Designation Time (hours)
Apresentação/discussão de um trabalho científico 3,00
Estudo autónomo 30,00
Frequência das aulas 42,00
Trabalho escrito 30,00
Total: 105,00

Eligibility for exams

75% participation in classes + 50% execution of the project

Calculation formula of final grade

D - discussion
PP - participation in the classes
TE -written report
TP - reserach project

Final grading= [2D+2PP+3TE+3TP]/10

being the items D, PP, TE, TP graded from 0 to 20

Special assessment (TE, DA, ...)

Work to be performed within 5 days compatible with the school calendar

Classification improvement

Work to be performed within 5 days compatible with the school calendar
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