Large Deviations for Small Buffers: An Insensitivity Result
Queueing Systems: Theory and Applications
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We consider a fluid queue fed by a superposition of $n$ homogeneous on-off sources with generally distributed on- and off-periods. We scale buffer space $B$ and link rate $C$ by $n$, such that we get $nb$ and $nc$, respectively. Then we let $n$ grow large. In this regime, the overflow probability decays exponentially in the number of sources $n$; we specifically examine the situation in which also $b$ is large. We explicitly compute asymptotics for the case in which the on-periods have a subexponential distribution, e.g., Pareto, Lognormal, or Weibull. We provide a detailed interpretation of our results. Crucial is the shape of the function $v(t) := - log Pr( A^*