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Stochastic Network Calculus (Lecture, WS 2011/12)

The stochastic network calculus is a relatively new theory for the performance analysis of queueing based systems such as communication networks. Being based on hybrid concepts and methods from (max,+) linear systems theory and large deviations theory, its prospect is that it can deal with a broad class of intrinsically hard and yet previously open problems. The goal of this course is to expose students to this branch of fundamental mathematical research and its practical relevance to the pervasive field of communication networks. As an example of bridging the theory-practice gap, the course will discuss a new approach to the network capacity problem, which is the notoriously long standing open problem in information theory.

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Overview

Information
Lecturer:
Florin Ciucu
Event type:
Lecture with tutorial (VL+UE)
Part of
Berlin Mathematical School
SWS:
2 VL + 2 UE
LP (ECTS):
Time:
wednesdays, 2–4pm
First Meeting:
19 October 2011
Room:
MA 542
Tutorial:
Time: wednesdays, 4–6pm
Room: MA 542
There will be weekly homeworks.
Course ID:
0432 L 818
Audience:
Students of the BMS
Prerequisites:
Students should feel comfortable with linear algebra and stochastic processes.
Exam:
written
Further information:
see ISIS

Course Outline

  • (max,+) Algebra, dioids, and linear systems
  • Markov arrival processes, self-similar and heavy-tailed processes
  • Service processes
  • Large deviations theory
  • Queueing metrics
  • Martingale inequalities
  • Applications

Resources

Lecture Slides

Excercises

References

  • C.-S. Chang, Performance Guarantees in Communication Networks, Springer-Verlag, 2000
  • A. Dembo and O. Zeitouni, Large Deviations. Techniques and Applications, Springer, 1998
  • F. L. Baccelli, G. Cohen, G. J. Olsder and J.-P. Quadrat, Synchronization and Linearity: An Algebra for Discrete Event Systems, Wiley, 1993

Zusatzinformationen / Extras

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Auxiliary Functions

Stochastic Network Calculus

Stochastic Network Calculus
0432 L 818
Integrierte LV (VL mit UE)

Lecturer: Dr. Florin Ciucu

Period:
19.10.2011 to 15.02.2012

We 14:00 - 16:00 o'clock

Location: MA 542

Website
Course overview (LSF)
ISIS

Hint:
Tutorial: Wednesday, 16:00--18:00 in MA 542 Part of the curriculum of the Berlin Mathematical School (BMS)