Dr. Paolo Lollini, associate professor, Department of Mathematics and Informatics, University of Florence, Italy

Since the course will also review basics when needed, only foundational knowledge of computer science is required, and in particular some basics of procedural programming (e.g., C).

The course aims at providing solid knowledge and competences to model, evaluate and analyze critical dependable systems. In particular, the focus is put on the quantitative assessment of key system's dependability properties like reliability, safety, availability. At the end of the course, students will be able: i) to identify the key system aspects to be modelled, ii) to select the appropriate modeling methodology, and iii) to develop and solve stochastic models for the quantitative evaluation of system's dependability properties.

The course consists of five main pillars: foundational elements, combinatorial methods, Markovian processes, Petri Nets and extensions, Stochastic Activity Networks.

1.      Foundational elements - it will discuss the basic and foundational concepts on dependability, the role played by stochastic modeling approaches as a system validation technique, and it will recall some basics on probability theory. Topics covered:

a.       Basics on dependability, on performance and reliability analysis of systems and on systems validation.

b.      Definitions of performances and reliability indicators.

c.       Rules for building and validating models.

d.      Fundamentals of probability theory.

2.      Combinatorial methods - it will focus on several combinatorial approaches for quantitative and qualitative dependability assessment. Topics covered:

a.       Boolean methods.

b.      Fault Trees, Reliability Block Diagrams, Reliability Graphs.

c.       Examples and guided exercises.

3.      Markovian Processes - it focuses on the usage of the Markovian processes for describing a system state and its evolution, covering both transient and steady-state analysis of Discrete and Continuous Time Markov Chains. Topics covered:

a.       Introduction to Random Processes and to Markovian Processes.

b.      Discrete Time Markov Chains - Transient and Steady-state analysis.

c.       Continuous Time Markov Chains - Transient and Steady-state analysis.

d.      Examples and guided exercises.

4.      Petri Nets (PN) and extensions - it will focus on Petri Nets models, starting from the basic PN and considering several PN extensions. Topics covered:

a.       Intro to PN.

b.      Priority and Timed PN.

c.       Stochastic Petri Nets.

d.      Generalized Stochastic Petri Nets.

e.       Examples and guided exercises.

5.      Stochastic Activity Networks (SAN) - it will focus on Stochastic Activity Networks as a general and powerful stochastic modeling formalisms widely adopted for performability analysis, and on its supporting tool Möbius for the practical modeling exercises during the lectures. Topics covered:

a.       Introduction, Definition, Completion rules, Stabilizing and Well-Specified SAN. Underlying stochastic process.

b.      Automatic supporting tools: Möbius.

c.       Guided practical modelling experiences using SAN and Möbius tool.

Lectures.

The assessment is organized into two parts: a project and an oral interview.

a. During the semester:
Students are requested to prepare a project on stochastic modelling using SAN. The text of the project will be assigned during lectures, and it can be carried out in groups of up to 2 people. The project consists in the development of a SAN model and in the preparation of a short report on the performed activities, including the description of the obtained results. The development of the project will start during the lectures as a practical guided exercise, and then it will be completed by the students.

b. In the examination period:

The project must be submitted at least 1 week before the date of the oral interview. Criteria for the project evaluation are: capability of the models to capture the key elements of the use-case wrt the metrics of interest, quality of the analyses, quality of the report on the performed activities.

At the examination, a discussion on the developed project is followed by questions related to the applied modeling methodology.

c. Early exams before the examination period:
None.

As per the applicable regulations of the faculty and the university.

Appointments shall be made with the lecturers on a case-by-case basis.

The main relevant resources are the slides that will be presented during the lectures. Additional teaching material including articles will be suggested during the course. Slides, web-based sources, and links to download the Möbius tool will be made available to the students during the course. 

Dr. Paolo Lollini associate professor, University of Florence