Two-parameter Sample Path Large Deviations for Infinite Server Queues

2012/07/21 by J. Blanchet, X. Chen, Blanchet, J. +3
Business, Management and Accounting · Decision Sciences · Mathematics · #60F10 #60K25 #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1207.5164

openalex publication_date 2012/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Q_λ(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 Q_λ(⋅) /λ under the topology of uniform convergence on [0,T]×\lbrack0,∞). 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.

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