Learning objectives
The goals of the course, in terms of knowledge and comprehension, are the following:
- to allow the student to master mathematical techniques for telecommunication networks' performance analysis;
- to provide the student the ability to abstract real application scenarios of telecommunication networks.
The abilities to use the knowledge and comprehension skills outline above can be summarized as follows:
- to analyze and describe a telecommunication network;
- to evaluate the performance of telecommunication networks.
Prerequisites
Course unit content
Little’s law. Poisson processes. PASTA property. Renewal processes. M/G/1 queue. LAN performance analysis (Ideal controller. TDMA/FDMA. Aloha. Slotted Aloha). WAN performance analysis. Discrete-Time Markov Chains (DTMCs). Geo/geo/1 queue. Geo/geo/1/B queue. Slotted Aloha network. M/G/1 queue. M/G/1/B queue. (Mini)slotted Ethernet network. Absorbent Markov Chains (AMCs). Continous Time Markov Chains (CTMCs). Overview of semi-Markov processes. M/M/1 queue.performance analysis (Ideal controller. TDMA/FDMA. Aloha. Slotted Aloha). WAN performance analysis.
Discrete-Time Markov Chains (DTMCs). Geo/geo/1 queue. Geo/geo/1/B queue. Slotted Aloha network.
M/G/1 queue. M/G/1/B queue. (Mini)slotted Ethernet network. Absorbent Markov Chains (AMCs).
Continous Time Markov Chains (CTMCs). Overview of semi-Markov processes. M/M/1 queue.
Full programme
Classes (2 hours each):
1) Course introduction and probability refresher.
2-3) Introduction to network performance analysis: Littl'es law, stability condition, lost clients, saturation throughput, and exercises.
4-5) Poisson arrival process properties. Renewals process: renewal theorem, age and residual life, the inspector paradox.
6-7) M/G/1 queue: Pollaczek-Khinchin’s formula, variations with vacations and setup times. Exercises.
8-9) Analysis of shared medium networks: TDMA, FDMA, Aloha, slotted Aloha, Ethernet, Token Ring, Polling system.
10-11) Mesh networks and exercises.
12-15) Discrete Time Markov Chain (DTMC) introduction, properties, and exercises.
16-22) Network performance analysis based on DTMCs (Geo/Geo/1, Geo/Geo/1/B, M/G/1, M/G/1/B, slotted Aloha, CSMA-CD).
23-24) Exercises.
Bibliography
[1] D. P. Bertsekas, R. Gallager, Data networks, 2nd Ed. Prentice Hall, 1992.
[2] J. L. Hammond, P. J.P. O'Reilly, Performance analysis of Local Computer Networks. Addison Wesley, 1986.
[3] A. Leon-Garcia, Probability and random processes for electrical engineering, 2nd Ed. Addison Wesley, 1994.
[4] S. Ross, Stochastic Processes. Wiley, 1983.
[5] A. S. Tanenbaum, Computer Networks, 2nd Ed. Prentice-Hall, 1989.
[6] M. Schwartz, Telecommunication Networks. Addison-Wesley, 1987.
[7] J. G. Kemeny, H. Mirkil, J. L. Snell, G. L. Thompson, Finite mathematical structures. Prentice Hall, 1959.
[8] D. Gross, C. M. Harris, Fundamentals of Queuing Theory. Wiley, 1985.
[9] H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation. Volume III: Discrete-time Systems. North-Holland, Amsterdam, Holland, 1991.
Teaching methods
During the lectures variou topics related to performance analysis of telecommunication networks, as detailed in the program, will be covered. During the course exercises will also be given
Assessment methods and criteria
Written exam with open answers. During each written test all questions have the same weight. It is not allowed to bring any support material during the tests.
Other information
The teaching and suppport material will be provided by the teacher.
