Kolloquium Wintersemester 1998/99
Die Dozenten der Informatik
Prof. Dr. Francois Baccelli, INRIA und ENS, Sophia Antipolis, Frankreich
spricht über
The Algebra of Networks
| Datum: | Montag, 19. Oktober 1998
| | Zeit: | 16:15 Uhr
| | Ort: | Hörsaal 1, Römerstr. 164
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ZusammenfassungIn this talk, we will stress the key role played by idempotent semi--rings in the performance analysis of computer and communication networks.
The first part of the talk will focus on the so--called $(\max,+)$ semi--ring, We will in particular study the spectral theory of matrices, and the solutions of vectorial affine equations in this algebraic structure. We will stress their applications to the temporal analysis of computer systems, via examples ranging from parallel executions on multiprocessor architectures to flow control in communication networks.
We will also consider semi--rings of functions where the multiplication operation is the so-called $\inf$--convolution, a class which became quite actively studied lately because of its use in the modeling of integrated service networks.
The analysis of time--inhomogeneous (and in particular stochastic) linear systems in such algebras is of central importance in all the above applications. We will also review a few basic notions within this setting such as Lyapunov exponents and their relations with network throughputs, and the solutions of certain random fixed point problems allowing one to capture the statistical variations of response times in networks.
(Der Vortrag findet statt anläßlich des 70. Geburtstages von em. Prof. Dr. Wolfgang Everling.)
Letzte Änderung:
6. Oktober 1998, 8:57:03
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Wintersemester 1998/99
Everling2