A Scaling Framework for the Many Flows Asymptotic, through Large Deviations.
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If you have a question about this talk, please contact Neil Walton.
We introduce a new framework of scalings for the many flows asymptotic
for queueing systems. This asymptotic was first introduced by Alan
Weiss. This asymptotic is useful in estimating drop probabilities for
modelling congestion control protocols as well as providing insight into
observed phenomenon.
To introduce the framework we re-examine the previously studied results
and see how the scalings naturally generalise. Within the framework we
consider a simple Markovian example and followed by the sample path
large deviations for fractional Brownian motion. This allows us to
demonstrate the versatility and salient features of the framework.
In addition we briefly introduce results with in this framework for
point processes which extend previous small buffer results. As well as
presenting some open problems thrown up by the new framework.
This talk is part of the Optimization and Incentives Seminar series.
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