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Moderate deviations of many-server queues via idempotent processes

Part of: Limit theorems Special processes

Published online by Cambridge University Press:  20 December 2024

Anatolii Puhalskii
Anatolii Puhalskii*
Affiliation:
Institute for Problems in Information Transmission (IITP)
*
*Postal address: 19 B. Karetny, Moscow, Russia, 127051. Email address: puhalski@iitp.ru
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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 inter-arrival and service times under a heavy-traffic scaling akin to the Halfin–Whitt regime. The deviation function is expressed in terms of the solution to a Fredholm equation of the second kind. A key element of the proof is the large-deviation principle in the scaling of moderate deviations for the sequential empirical process. The techniques of large-deviation convergence and idempotent processes are used extensively.

Keywords

Halfin–Whitt regimeheavy trafficlarge-deviation principlesequential empirical process

MSC classification

Primary: 60F10: Large deviations
Secondary: 60K25: Queueing theory

Information

Type
Original Article
Information
Advances in Applied Probability , Volume 57 , Issue 2 , June 2025 , pp. 708 - 742
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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