Buffer overflow asymptotics for a switch handling many traffic sources

C. Courcoubetis and R.R. Weber, to appear in Appl. Prob., 199-. Abstract

As a model for an ATM switch we consider the overflow frequency of a queue that
is served at a constant rate and 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 to 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.