Ateneo - UPO

The course focuses on some non functional requirements that must be considered when designing systems, in particular computing systems and computer networks. Some mathematical models are presented allowing one to describe and analyze the performance and dependability of systems. Models can be built and analyzed either in early design phases, or later when the system under study is operational. The course also includes practical exercises using software packages supporting the design of system models and their analysis through analytical or numerical methods or simulation. Some connections are also highlighted with models from the field of Artificial Intelligence, in particular Probabilistic Graphical Models.

J. Banks, J. S. Carson II, B. L. Nelson, David M. Nicol, Discrete-Event System Simulation , Fifth edition, Pearson Education 2010
K. Trivedi, A. Bobbio, "Reliability and Availability: Modeling, Analysis and Applications" - Cambridge University Press, 2017
Lecture notes or scientific publications to be downloaded from DIR

Knowledge and understanding: know and understand: (a) some formalisms for the representation of mathematical models (which may also have a graphical representation) that can be used to study system dependability and performance properties; (b) the main computational methods for model analysis (closed form solution, numerical solution, or simulation); (c) some basic models and be able to discuss examples of application of such models. Apply knowledge and understanding: Have the ability to: (a) provide an interpretation of a model expressed in a known formalism, and of the results that can be obtained by analyzing it; (b) build the model of a system using a given formalism and define its performance/reliability indices of interest; (c) compute the indices using an existing software tool or building a new ad-hoc software analysis tool. (d) validate a model comparing the analysis results again those obtained from alternative models or measured on a real system.The students will achieve autonomy in judgement about what is the most appropriate formalism and analysis method to face a given problem. Will be able to choose the most appropriate detail level in describing the model and its performance indices, and choose the software tools that better support the chosen formalism and analysis method. Finally students shall be able to communicate and explain the mathematical basis on which the models and corresponding analysis algorithms have been developed. Moreover they will be able to describe the models they have built, justify the choices made in building the model and present an interpretation of the results of model analysis. The student shall acquire the methodological knowledge to learn new formalisms and analysis methods published in the scientific literature.

Basic course in probability and statistics

Class lectures, exercises in class and in laboratory, in particular using a few software tools for the design, simulation and solution of models. Homework are assigned consisting in practical exercises and/or autonomous study of research papers.

It is possible to download electronic copy of all slides of the lectures, perform self-assessment tests, read general information on the course and news about the lectures and the exam organization on the e-learning platform DIR. Besides the reference textbooks some scientific publications in English are proposed, to study in more detail some of the topics presented during the course.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the "Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti", consulting the University webpage: https://www.uniupo.it/en/services/services-students-physical-or-learning-disabilities. Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The achievement of learning outcomes is evaluated through a written or oral examination after the end of the course, including about five questions (which in turn may comprise several points and include specific exercises) on the topics studied in the course.
The examination comprises also a second part (mandatory), consisting either in a practical exercise including the modelling of a case study and the model analysis performed using existing software tools or directly developing the appropriate software artifact, or in the autonomous study of a theoretical topic. In both cases the practical or theoretical topic is presented in an oral discussion.
The final evaluation is mainly dependent on the theory part of the exam, which can be increased according to the quality of the practical part.

Review of the basics of probability theory and statistics needed to understand the mathematical models discussed within the course. Definition of non functional requirements of systems: performance and dependability indices.
Discrete event simulation: basic principles, random numbers and random variate generation, transient and steady state analysis, obtaining a sample of the measures of interest through simulation experiment repetitions or batch method; simulation output analysis through statistical methods. Validation of a simulation model.
Formalisms:
* Formalisms to describe the behavior of dynamic and stochastic models (queueing networks, Petri nets with and without timing, Markov chains).
* Formalisms for studying the dependability of systems, in particular Fault Trees and extensions.
* Definition of performance and dependability indices through reward functions.
Analysis methods:
* Markov chains: analytical and numerical solution, simulation.
* Queueing Networks: operational analysis and simulation.
* (Stochastic) Petri Nets: state space based analysis for studying the model qualitative and quantitative behavior; quantitative analysis and Markov chains; simulation.
* Fault tree: analysis through combinatorial or state space methods (including extensions of the formalisms).
Notes on the relationship between Fault trees and Probabilistic Graphical Models (Bayesian Networks).
* Demonstration and lab experimentation of some software tools and development of a simulator.

Knowledge and understanding:
Know the main formalisms for the representation of mathematical models, which can be used to study system dependability and performance properties;
Know the main computational methods for model analysis know some basic models
Competence and Skills
Explain the concept of modeling and the use of abstraction to focus on the aspects relevant to a given problem. Devise a (simple) mathematical model of a system and show how its dynamics can be recreated through simulation. Build the model of a system using a specific formalism (presented in the course) and implement it through a programming language or through a software tool. Evaluate the adequacy of a given formalism (among those presented in the course) to model a specific system. Explain the benefits of using models and simulation in various application domains. Explain the meaning of model verification and validation, also providing practical examples. Present the results of the analysis (possibly through simulation) of a model. Provide an interpretation of quantitative results of model analysis or simulation, drive some conclusions on the behavior of the modelled system and possibly suggest changes in the system under study to improve its performance and/or dependability indices.