Stochastic Systems

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

Jose Blanchet, Xinyun Chen, and Henry Lam

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ssy/1411044996

Digital Object Identifier
doi:10.1214/12-SSY080

Mathematical Reviews number (MathSciNet)
MR3353218

Zentralblatt MATH identifier
1327.60066

Subjects
Primary: 60F10: Large deviations 60K25: Queueing theory [See also 68M20, 90B22]

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

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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