Loss Rate Asymptotics in aGI/G/1 Queue with Finite Buffer

We consider the stationary loss rate ℓ K of a GI/G/ 1 queue with finite buffer of size K. Let X n = U n −T n , n ≥ 1 where U n is the service time, T n is the interarrival time and let ρ be the traffic intensity. We derive sharp asymptotics for the loss rate as K → ∞ in the cases (i): ρ > 1 , and (ii): ρ < 1 and X n non–lattice with light tails. We also look at another reflection, related to Moran's dam model. As an example, we look at the PH/PH/ 1 case, where we show how to compute the asymptotic loss rate as well as the exact one and illustrate our results numerically.