Jose Blanchet, Xinyun Chen, Henry Lam (2014) Two-parameter Sample Path Large Deviations for Infinite-Server Queues. Stochastic Systems 4(1):206-249. https://doi.org/10.1287/12-SSY080

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Abstract

Let Qλ(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 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 paths, represented as surfaces, to overflow in the setting of loss queues, and also to ruin in life insurance portfolios.

Authors
Jose Blanchet, Xinyun Chen, Henry Lam
Publication date
2014/9
Journal
Stochastic Systems
Volume
4
Issue
1
Pages
206-249
Publisher
INFORMS