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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.

## News

- This course is part of the Berlin Mathematical School (BMS).

## Overview

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, 4–6pmRoom: MA 542There 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

## 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