DOCUMENTA MATHEMATICA, Extra Volume ICM III (1998), 213-222

Maury Bramson

Title: State Space Collapse for Queueing Networks

The diffusive limits of queueing networks, known as heavy traffic limits, are a topic of continuing interest. An important ingredient in such work is the demonstration of state space collapse, which says that, in the limit, the process must live on an appropriate subspace. In [Wi98b], conditions are given under which state space collapse suffices for heavy traffic limits. Here, we discuss how state space collapse can be reduced to the problem of showing stability for the fluid model which is the deterministic analog of the queueing networks under consideration. We discuss specific cases, such as first-in first-out (FIFO) networks of Kelly type and certain static priority networks.

1991 Mathematics Subject Classification: Primary 60K25.

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