Two-parameter sample path large deviations for infinite-server queues

Abstract

Let Qλ(t,y) be the number of people present at time t with y units of remaining service time in an infinite server system with arrival rate equal to λ>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 Qλ( · )/λ under the topology of uniform convergence on [0,T]×[0,∞). We illustrate our results by obtaining the most likely path, represented as a surface, to ruin in life insurance portfolios, and also we obtain the most likely surfaces to overflow in the setting of loss queues.

Keywords

• Large deviations
• infinite-server queues
• two-parameter processes
• rare-event tail estimation
• life insurance portfolio management