Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 74603, 22 pages
The single server queue and the storage model: Large deviations and fixed points
Statistical Laboratory, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
Received 16 February 2005; Revised 19 August 2005; Accepted 30 August 2005
Copyright © 2006 Moez Draief. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider the coupling of a single server queue and a storage
model defined as a queue/store model. We establish that if the
input variables, arrivals at the queue and store, satisfy large
deviations principles and are linked through an
exponential tilting, then the output variables
(departures from each system) satisfy large deviations principles
with the same rate function.