## Stochastic Systems

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

#### 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.

#### Article information

Source
Stoch. Syst., Volume 4, Number 1 (2014), 206-249.

Dates
First available in Project Euclid: 18 September 2014

https://projecteuclid.org/euclid.ssy/1411044996

Digital Object Identifier
doi:10.1214/12-SSY080

Mathematical Reviews number (MathSciNet)
MR3353218

Zentralblatt MATH identifier
1327.60066

#### Citation

Blanchet, Jose; Chen, Xinyun; Lam, Henry. Two-parameter sample path large deviations for infinite-server queues. Stoch. Syst. 4 (2014), no. 1, 206--249. doi:10.1214/12-SSY080. https://projecteuclid.org/euclid.ssy/1411044996

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