Subexponential Loss Rates in a GI/GI/1 Queue with Applications

Consider a single server queue with i.i.d. arrival and service processes, {A, An,n > 0} and {C, Cn,n > 0}, respectively, and a finite buffer B. The queue content process {Qn , n > 0} is recursively defined as Qn+1 = min((Qn + An+1 − Cn+1),B), q = max(0, q). When E(A−C) < 0, and A has a subexponential distribution, we show that the stationary expected loss rate for this queue E(Qn +An+1−Cn+1−B) has the following explicit asymptotic characterization: