# Mathematics Colloquia and Seminars

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### Application of fluid models to recurrence and central limits for queueing networks

**Colloquium**

Speaker: | Maury Bramson, University of Minnesota |

Location: | 693 Kerr |

Start time: | Fri, May 26 2000, 4:10PM |

NOTE: research seminar.

Over the last several years, there has been significant progress on understanding the qualitative of queueing networks. Two topics of interest, recurrence and central limit theorems, have analogs in traditional models in probability.

In the context of queueing networks, recurrence corresponds to the lines, on the average, remaining bounded in time. The central limit theorem has the form of standard central limit theorems, but with the limit being a Brownian motion restricted to the positive orthant. In both cases, fluid models permit reduction of these problems to a simpler, deterministic setting, and the resolution of outstanding questions. We will provide a survey of this material.