# SCS

## Seminar

### Limit theorems for bandwidth sharing networks with rate constraints

Seminar Room 1, Newton Institute

#### Abstract

Bandwidth-sharing networks as considered by Massouli'e & Roberts (1998) are an exciting class of models as their analysis requires techniques from both stochastic models and optimization. At the same time, such networks provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers in computer and communication systems, and can be used to develop, pricing/charging mechanisms.In this paper, we consider bandwidth sharing networks under the assumption that the number of users as well as the capacities are large, and the assumption that the traffic each user is allowed to submit is bounded by some rate, as is standard in practice. Under Markovian assumptions, we develop fluid and diffusion approximations which are quite tractable: for most parameter combinations, the invariant distribution is multivariate normal, with mean and diffusion coefficients that can be computed in polynomial time as function of the size of the network.

Joint work with Josh Reed (NYU).

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