CODE 90146 2024/2025 5 cfu anno 2 INTERNET AND MULTIMEDIA ENGINEERING 10378 (LM-27) - GENOVA ING-INF/03 English GENOVA 2° Semester Questo insegnamento è un modulo di: AULAWEB

## OVERVIEW

The class aims at the introduction of the basic elements for understanding and applying the mathematical instruments commonly utilized for performance analysis of telecommunication networks and for teletraffic engineering.

## AIMS AND CONTENT

### LEARNING OUTCOMES

• Methods of network performance evaluation: analytical models, simulation, experimental measurements • Packet-level and flow-level models • Elementary queueing theory: elements of a queue, statistics of input and service, general results on infinite- and finite-buffer queues, Little’s Theorem, Kendall’s notation • Markovian queues: Poisson arrivals, exponential distribution, stationary distribution of general birth-death systems; M/M/1, M/M/1/K, M/M/m/m, M/M/m • Discrete- and continuous-time Markov Chains • M/G/1 and Pollaczek-Kinchin formula; Pareto distribution; M/G/1 with vacations; priority queueing • Networks of queues: Jackson networks, independence hypothesis, Kleinrock’s delay formula

### AIMS AND LEARNING OUTCOMES

The main goal of the class is to provide the elements for understanding and applying queueing models for the representation, performance analysis and control of telecommunication networks. At the end of the class the student should be able to to use dynamic models based on Markov chains and Markovian queueing models in equilibrium, as well as to represent and evaluate various performance indexes of telecommunication networks (throughput, delay, loss probability).

### PREREQUISITES

To understand the topics covered, some knowledge is required of basic Mathematical Analysis, Probability Theory and Random Variables (discrete and continuous).

### TEACHING METHODS

The class is taught basically with face-to-face lectures. Numerous exercizes will be solved, relating to the application of the methodology to the derivation of performance indexes of networks and network elements. The exam consists of a written problem solution, along with the oral discussion of it. The written part can be substituted by the positive completion of the periodic tests that might be proposed during the class. Working students and students with a certification of Specific Learning Disturbances (DSA), disabilty or other special educational needs are advised to contact the lecturer at the beginning of the class to agree upon teaching and verification modalities that, respecting anyway the course objectives, may be tailored to the individual learning capabilities.

Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities.

### SYLLABUS/CONTENT

Methods of network performance evaluation: analytical models, simulation, experimental measurements. Packet-level and flow-level models. Elementary queueing theory: elements of a queue, statistics of input and service, general results on infinite- and finite-buffer queues, Little’s Theorem, Kendall’s notation. Markovian queues in equilibrium: properties of the exponential distribution, Poisson process, stationary distribution of general birth-death systems, M/M/1, M/M/1/K, M/M/infinity, M/M/m/m, M/M/m, M/M/m/m/N. Discrete- and continuous-time Markov Chains. M/G/1 queue. Pollaczek-Kinchin formula. Pareto distribution and M/Pareto/1. Server vacation. M/G/1 with pre-emptive priority. Networks of queues. Jackson networks, Product Form Solution, independence hypothesis, Kleinrock’s delay formula and applications.

The class is based on the first part of the lecture notes on Aulaweb:

- F. Davoli, "Lecture Notes for the Courses of Telecommunication Networks: Queueing Theory and Teletraffic", 2nd ed., July 2021.

Other useful material can be found on:

- L. Kleinrock, Queueing Systems, Vol. I, Wiley, New York, 1975.

- M. Zukerman, Introduction to Queueing Theory and Stochastic Teletraffic Models, 2017; online: https://arxiv.org/pdf/1307.2968.pdf.

- J. Virtamo, Queueing Theory, Lecture Notes, 2005; online: http://www.netlab.tkk.fi/opetus/s383143/kalvot/english.shtml.

## LESSONS

### LESSONS START

https://corsi.unige.it/10378/p/studenti-orario

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

The exam is written and usually consists of two problems on the topics of the class. The student who wants to improve the mark of the written test can do an oral that consists of a discussion of some of the topics relating to the written problems. Obviously, depending on the outcome, the mark obtained in the written part may also decrease.

### ASSESSMENT METHODS

Written examination.

### FURTHER INFORMATION

Students who have a valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework, and exams should speak both with the instructor and with Professor Federico Scarpa (federico.scarpa@unige.it ), the School's disability liaison.