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).

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 will be proposed during the class.

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.

RECOMMENDED READING/BIBLIOGRAPHY

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"

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.