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

TL;DR

This paper derives logarithmic asymptotics for moderate deviations in many-server queues under the Halfin-Whitt regime, using weak convergence and Fredholm equations to characterize the deviation function.

Contribution

It introduces a novel approach to analyze moderate deviations in many-server queues with general interarrival and service time distributions, employing weak convergence methods.

Findings

Logarithmic asymptotics of moderate deviations obtained

Deviation function expressed via Fredholm equation

Method applicable to general service time distributions

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.