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.
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