General Mathematics Colloquium
Speaker: Bert Zwart (CWI)
Title: Diffusion approximations of Bandwidth Sharing Networks
A Bandwidth Sharing Network is a mathematical abstraction of a communication network like the Internet and is a canonical example of a complex stochastic dynamic network. The dynamics of the network are governed by the solution of a family of convex optimization functions, of which the solution can be implemented in a decentralized manner. To assess the performance of such networks, classical queueing techniques are not suitable, which motivates to consider diffusion approximations.
For a network with proportial fairness we establish a diffusion limit through a state space collapse result: a high dimensional system will reside, in the limit, on a lower-dimensional invariant manifold.
A key intermediate result is uniform convergence to the invariant manifold for a deterministic fluid model, which will be established by constructing a suitable Lyapounov function.
Joint work with M. Vlasiou (TU/e) and J. Zhang (HKUST)
Location: KdVI meeting room, SP 105-107, F3.20