Moderate deviations of many-server queues in the Halfin-Whitt regime and weak convergence methods

Anatolii Puhalskii

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arXiv · 2305.01612

Moderate deviations of many-server queues in the Halfin-Whitt regime and weak convergence methods

Anatolii Puhalskii

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Abstract

This paper obtains logarithmic asymptotics of moderate deviations of the stochastic process of the number of customers in a many--server queue with generally distributed interarrival and service times in the Halfin--Whitt heavy traffic regime. The deviation function is expressed in terms of the solution to a Fredholm equation of the second kind. The proof uses characterisation of large deviation relatively compact sequences of probability measures as exponentially tight ones.

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BibTeX RIS

Anatolii Puhalskii. 2023-05-02. Moderate deviations of many-server queues in the Halfin-Whitt regime and weak convergence methods. https://arxiv.org/abs/2305.01612

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