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Second Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)


The course aims to provide an introduction to stochastic models commonly used in telecommunications for the modelling and management of traffic, sizing and planning of shared resources.

--- Knowledge and comprehension skills
The student will learn to model, analize and optimize complex interconnected systems, subject to stochastic inputs and characterized by stochastic performance.

--- Knowledge and applied comprehension skills
The theoretical training will be complemented by a series of examples and applications (from the domain of telecommunication) to stimulate the active participation of the students and develop skills for autonomous reasoning.

--- Making judgements
Students will be capable to critically evaluate the results of the analysis and the design.

--- Communication skills
Practical exercises could be solved in small groups so as to develop the ability to collaborate and critically discuss the encountered problems.

--- Learning skills
The aim of the course is also to help the student integrate the knowledge coming from other, thus acquiring a broader vision of the problems connected with the design and management of telecommunications networks.


For an effective approach to the study of this course, students should have the following skills.

--- Knowledge
Basics of linear algebra. Esponential and logarithmic functions and their properties. Oridinary linear differential equations. Integrals. Polynomials. Geometric series. Laplace transformation.

--- Capacity
Algebraic and differential calculus. Analysis and representation of functions depending on one or more variables. Variable transformations.

--- Competence
To be able to apply the methods of algebra, differential calculus and function analysis.


--- Presentation of the course
Introduction to traffic problems and advantages and disadvantages coming from their solution in a discrete event system framework. The importance of formal methods in the telecommunication framework.

--- Probability and stochastic processes
Basic definitions on probability and stochastic processes, fundamental for the understanding of queueing networks and traffic models.

--- Markov chains
Basic definitions. Evolution equations. State classification. Stationary and limit distribution. Ergodicity. Birth-death processes.

--- Queuing theory and basic notions on teletraffic
Basic notions on queuing theory. Classification according to the Kendall notation. Deterministic queues. Stochastic queues with infinity capacity. Stochastic queues with limited capacity and problems of buffers dimensioning. The Engset formula. Stationary and limit distributions. Ergodicity and Little law.

--- Queuing networks
Open queueing networks: traffic equations, Jackson theorem, Little law. Closed queuing networks: equivalent continuous time Markov chain, Gordon and Newell theorem. Examples in the telecommunication framework.

--- Simulation tools
Use of tools for the simulation and analysis of the proposed models, with special focus on tools in a Matlab environment.

Teaching Methods

32 hours devoted to theory
18 hours devoted to exercises and practical case studies

Verification of learning

The final evaluation consists in an oral exam during which the students should show the knowledge of the basic techniques and methods for dealing with the modelling of a stochastic process, while demonstrating the ability of carrying on a critical analysis of its evolution and properties.

He has also to show and adequate expertise in solving resource allocation design problems related with the dimensioning and management of traffic, sizing and planning of systems with shared resources, under given Quality-of-Service specifications.

To pass the exam the student has to demonstrate an appropriate and correct knowledge of the mathematical tools and methods of analysis and design seen during the course, while showing, during the solution of simple exercises, autonomy in making judgments in regard to its design choices.

Furthermore, the student has to show adequate skills in speaking and using a technical language as well as a sufficient synthesis and critical analysis ability.

The final oral examination begins by asking the candidate to present, in English, a topic of his/her choice among the main ones of the course. Based on his/her presentation, the exam will continue by asking the candidate to answer other questions related to the course topics and/or by submitting exercises similar to those seen during classroom exercises.

The oral exam evaluates:
1. The knowledge of the topics of the course (30% final mark)
2. The application of the obtained knowledge to approach the solution of exercises and design problems related with the course topics (30% final mark)
3. The autonomy in making judgments in regard to design choices (30% final mark)
4. The use of technical language (10% final mark)

(*) Students can always ask, via email, to do the final oral exam.
(**) During the final oral examination, under request, the student is allowed to consult the file available at the next url:
and consisting of a collection of most of the formulas of interest about Markovian systems.


--- Notes prepared by prof. A. Pilloni, prof. A. Giua and prof. C. Seatzu
--- Book (available online and free): Zukerman, Moshe. “Introduction to queueing theory and stochastic teletraffic models.” arXiv preprint arXiv:1307.2968 (2013).
--- Chapter 3 and Appendices B, C and D of the book: A. Di Febbraro, A. Giua. “Sistemi ad Eventi Discreti” MvGraw-Hill, 2002, 88-386-0863-6.

More Information

Parts of the lessons will be devoted to numerical exercises that will be solved in class and discussed with the instructor.

The text of the classwork will be regularly provided to the students during the course, or send by email to the students upon specific request.

Questionnaire and social

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