Conditions for the light-traffic insensitivity to loss probability in a \(\text{GI}/ \text{G}/m/0\) queueing system (Q1407087)

The authors consider the loss system \(\text{GI}/ \text{G}/m/0\) with service time distribution function \(B(x)\) having mean \(1/\mu\) and an interarrival time density \(a(x)\) that behaves like \(c\lambda^\alpha x^{\alpha -1}\) for small \(x\). They study the limiting behavior of the probability that the \(n\)th customer will be lost as \(\lambda/\mu \) tends to zero. Under certain conditions this loss probability turns out to be sensitive with respect to the form of \(a(x)\) and \(B(x)\) for \(\alpha \neq 1\) and insensitive for \(\alpha = 1\).