### Buffer Overflow Asymptotics for a Buffer Handling many Traffic Sources

C. Courcoubetis (University of Crete)

R. R. Weber (Statistical Laboratory, University of Cambridge)

Journal
of Applied Probability, vol. 33, 1996.
Available here [.ps.gz]

**Abstract**

As a model for an ATM switch we consider the overflow frequency
of a queue that is served at a constant rate in which the arrival
process is the superposition of $N$ traffic streams. We consider an asymptotic
as $N \rightarrow \infty$ in which the service rate
$Nc$ and buffer size $Nb$ also increase linearly in $N$. In this
regime, the frequency of buffer overflow is
approximately $exp(-NI(c,b))$, where $I(c,b)$ is given by the
solution of an optimization problem posed in terms of time-dependent
logarithmic moment generating functions. Experimental
results for Gaussian and Markov modulated fluid source
models show that this asymptotic provides a better estimate of the
frequency of buffer overflow than ones based on large buffer asymptotics.

Keywords: ATM switches, buffer overflow asymptotics,
effective bandwidths, large deviations, markov modulated fluid

AMS 1991 subject class: Primary: 90K30; Secondary: 60F10, 60K25, 68M20,
90B10,90B22

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