B031292 - STOCHASTIC MODELS

English

- Stochastic models and formalisms

- Markovian stochastic models and processes

- Non-Markovian stochastic models and processes

- Advanced concepts on models and methods for quantitative evaluation of stochastic systems

References to scientific papers are reported in the course slides which will be made available on the Moodle web page during the course.

Reference tools: ORIS, PRISM, Java Modeling Tools, PHFit, Wolfram Mathematica, ...

- Knowledge of methods for quantitative modeling and analysis of stochastic systems.

- Knowledge of tools for quantitative modeling and analysis of stochastic systems.

- Practical experience in application of quantitative modeling and analysis methods to design and development of stochastic systems in specific domains.

A good understanding of software engineering principles, prior knowledge on mathematics, and aptitude to the formalization of concepts will largely help the comprehension of the topics covered in the course, but they are not prerequisites.

Lectures are given by presenting the course topics through slides, blackboard, and practical exercitations.

Students are invited to view the course page on Moodle (https://e-l.unifi.it) for more information.

The examination is designed to assess the theoretical and practical skills acquired on the course topics. Students may develop an assignment individually or in group, or they may develop a small assignment individually and take an oral test on a subset of the course contents, or thet may take an oral test on all the course contents.

Stochastic models and formalisms:
- Probability space and random variables, continuous and discrete random variables, moments and coefficients, multivariate random variables, conditional probabilities, independence.
- The special case of the exponential random variable, hyper- and hypo-exponential distribution, Erlang distribution, Whitt approximants, geometric distribution, Poisson distribution.
- Generalized Stochastic Petri Nets (GSPN).

Markovian stochastic models and processes:
- Stochastic Processes, discrete space chains, discrete and continuous time chains,
embedded chains, homogeneous chains, Markov condition.
- Discrete Time Markov Chains (DTMC), Chapman Kolomgorov equations, transient analysis,
steady state analysis for aperiodic and irreducible chains, first passage time distribution and absorption probabilities.
- Continuous Time Markov Chains (CTMC), Chapman Kolomgorov equations, steady state
analysis, transient analysis by uniformization.
- Underlying stochastic process of a GSPN.

Non-Markovian stochastic models and processes:
- Stochastic Time Petri Nets (STPN).
- Classes of non-Markovian stochastic processes, regeneration points, Semi Markov Processes (SMP), Markov Regenerative Processes (MRP), local and global kernel and generalized Markov renewal equations, Generalized semi Markov Processes (GSMP), simulation for non-Markovian processes, basic concepts on rare events simulation.
- Continuous Time Phase Type Distributions.
- The method of stochastic state classes.

Advanced concepts on models and methods for stochastic systems:
- Markov Decision Processes (MDP): reachability.
- Probabilistic Model Checking of Markov Chains, Probabilistic Computation Tree Logic
(PCTL), Continuous time stochastic logic (CSL), probabilistic model checking for Markov
Regenerative Processes (MRP).
- Hidden Markov Models (HMM): evaluation, inference, learning.
- Markovian Arrival Processes (MAP) and Marked Markov-Modulated Poisson Processes (M3PP).

Application of quantitative modeling and evaluation methods:
- Integration of stochastic models through Model Driven Engineering (MDE) practices.
- Modeling and evaluation of stochastic workflows, with applications in services computing.
- Matching algorithms to solve assignment problems by obtaining stable solutions.