Blanchet, J., Glynn, P. & Meyn, S. Large deviations for the empirical mean of an M/M/1 queue. Queueing Syst 73, 425–446 (2013). https://doi.org/10.1007/s11134-013-9349-7
Abstract
Let be an queue with traffic intensity Consider the quantity $$\begin{aligned} S_{n}(p)=\frac{1}{n}\sum _{j=1}^{n}Q\left( j\right) ^{p} \end{aligned}$$for any The ergodic theorem yields that , where is geometrically distributed with mean It is known that one can explicitly characterize such that $$\begin{aligned} \lim \limits _{n\rightarrow \infty }\frac{1}{n}\log P\big (S_{n}(p)0. \end{aligned}$$In this paper, we show that the approximation of the right tail asymptotics requires a different logarithm scaling, giving $$\begin{aligned} \lim \limits _{n\rightarrow \infty }\frac{1}{n^{1/(1+p)}}\log P\big (S_{n} (p)>\mu \big (p\big )+\varepsilon \big )=-C\big (p\big ) \varepsilon ^{1/(1+p)}, \end{aligned}$$where is obtained as the solution of a variational problem. We …
Authors
Jose Blanchet, Peter Glynn, Sean Meyn
Publication date
2013/4
Journal
Queueing Systems
Volume
73
Issue
4
Pages
425-446
Publisher
Springer US
