
Course unit
STOCHASTIC PROCESSES
INP9086676, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
INGINF/03 
Telecommunications 
6.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Prerequisites:

The course requires preliminary knowledge of: Mathematical Analysis, Probability, random variables and random processes, networks and protocols. For the examples treated, a basic course in networks and protocols is useful (through not required). 
Target skills and knowledge:

The training objective of the course involves the acquisition of the following knowledge and skills:
1. To understand and know how to use probability theory and random processes to model real systems and evaluate their performance.
2. To acquire advanced analytical tools for the performance assessment of systems and networks
3. To know how to translate a problem into a corresponding mathematical model
4. To know which performance metrics can be calculated (and how) from a mathematical/probabilistic representation
5. To be able to state precisely and to prove rigorously the most important theoretical results related to the main topics of the course (Markov chains, Poisson processes, renewal processes) 
Examination methods:

The assessment of the knowledge and skills acquired is carried out by means of a written test divided into two parts.
Part A, with a duration of 90 minutes and openbook, consists of eleven numerical questions grouped into four exercises. Each question has a value of three points.
Part B, with a duration of 60 minutes and closedbook, consists of three theoretical questions (typically proofs of theorems seen in class). Each question has a value of eleven points.
If the student scores at least 15 points in part A and the average score of part A and part B is at least 18, the latter can be accepted as the final grade. If the score in part A is less than 15 or the average of the two tests is less than 18, the exam is not passed.
Even if the final exam can be passed by a successful written exam (in two parts), the student can always ask to take an oral exam if he/she wants to improve the grade. In no case can the oral exam replace the written test.
Examples of exams are available on the elearning platform course website, and are extensively covered in class. 
Assessment criteria:

The evaluation of the acquired knowledge and skills will be carried out considering:
1. The completeness and depth of the knowledge of the topics covered during the course.
2. The ability to model a problem using one of the analytical tools seen in class
3. The ability to obtain correct numerical results in the proposed exercises
4. The ability to develop analytical reasoning in a rigorous and complete manner. 
Course unit contents:

1. Review of probability and random processes
2. Markov chains: definitions and main results
3. Markov chains: asymptotic behavior
4. Study of multiaccess systems and their stability properties
5. Poisson processes: definitions and main results
6. Renewal processes: definitions and main results, asymptotic behavior
7. Renewal reward, regenerative, and semiMarkov processes
8. Exercises and examples of applications
A detailed list of the topics covered during the course, with specific reference to chapters and pages of the texts, is available on the course website through the elearning platform. 
Planned learning activities and teaching methods:

Teaching is done through lectures on the blackboard, as it is believed that this method of delivery maintains the right presentation pace and keeps the students' attention, allowing interaction and involvement.
In order to verify the level of learning during the course, the students are proposed exercises or theoretical developments to be done at home, which will then be often carried out in class during a subsequent lecture. 
Additional notes about suggested reading:

The course follows a main textbook, with additions from other texts, notes and research articles.
With the exception of the main textbook, all the other teaching materials are made available to students on the elearning platform course website, including examples of exams and a list of proposed exercises from the text (with solutions). 
Textbooks (and optional supplementary readings) 

H. Taylor, S. Karlin, An introduction to stochastic modeling. : Academic Press (3rd or 4th edition), 1998. TESTO PRINCIPALE/PRIMARY TEXTBOOK

S. Karlin, H. Taylor, A first course in stochastic processes. : Acedemic Press (2nd ed.), 1975.

D. Bertsekas, R. Gallager, Data Networks. : PrenticeHall (2nd ed.), 1992.

S. Ross, Stochastic processes. : Wiley (2nd ed.), 1996.

S. Ross, Applied probability models with optimization applications. : Dover (2nd ed.), 1996.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Problem based learning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

