Large Deviations for the Empirical Mean of an M/M/1 QueueJ. Blanchet , P. W. Glynn, and S. Meyn Submitted for publication Let (Q(k):k≥0) be an M/M/1 queue with traffic intensity ρ∈(0,1). Consider the quantity for any p>0. The ergodic theorem yields that S_{n}(p)→μ(p):=E[Q(∞)^{p}], where Q(∞) is geometrically distributed with mean ρ/(1ρ). It is known that one can explicitly characterize I(ε)>0 such that In this paper, we show that the approximation of the right tail asymp totics requires a diĀ¤erent logarithm scaling, giving where C(p)>0 is obtained as the solution of a variational problem. We discuss why this phenomenon  Weibullian right tail asymptotics rather than exponential asymptotics  can be expected to occur in more general queueing systems.

