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2014 Two-parameter sample path large deviations for infinite-server queues
Jose Blanchet, Xinyun Chen, Henry Lam
Stoch. Syst. 4(1): 206-249 (2014). DOI: 10.1214/12-SSY080

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

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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

Published: 2014
First available in Project Euclid: 18 September 2014

zbMATH: 1327.60066
MathSciNet: MR3353218
Digital Object Identifier: 10.1214/12-SSY080

Subjects:
Primary: 60F10, 60K25

Rights: Copyright © 2014 INFORMS Applied Probability Society

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Vol.4 • No. 1 • 2014
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