Abstract
Let $Q_{\lambda}(t,y)$ be the number of people present at time $t$ with at least $y$ units of remaining service time in an infinite server system with arrival rate equal to $\lambda>0$. In the presence of a non-lattice renewal arrival process and assuming that the service times have a continuous distribution, we obtain a large deviations principle for $Q_{\lambda}(\cdot)/\lambda$ under the topology of uniform convergence on $[0,T]\times[0,\infty)$. We illustrate our results by obtaining the most likely paths, represented as surfaces, to overflow in the setting of loss queues, and also to ruin in life insurance portfolios.
Citation
Jose Blanchet. Xinyun Chen. Henry Lam. "Two-parameter sample path large deviations for infinite-server queues." Stoch. Syst. 4 (1) 206 - 249, 2014. https://doi.org/10.1214/12-SSY080
Information