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Large deviations and fluid approximations in control of stochastic
systems

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R.R. Weber,
In F.P. Kelly, editor, *Probability Statistics and Optimization,
a Tribute to Peter Whittle*, pages 159-171. Wiley, 1994.

Abstract

Large deviation and fluid approximations can provide valuable insight to the
behaviour of stochastic systems. This paper summarises some of the key ideas
and discusses a number of examples, including a probabilistic analysis of the
first-fit decreasing bin packing algorithm, and comments on ideas of Whittle
relating to risk-sensitive control of Markov processes. In a final example, a
large deviations analysis is used to estimate the frequency of overflow when a
number of stationary traffic sources are routed through a switch with a finite
buffer. we show that the buffer overflow frequency is asymptotically less that a
specified amount if an only if the sum of the effective bandwidths for the
different traffic sources is less than the bandwidth of the switch and we
suggest a simple approximation for these effective bandwidths.

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