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

2023/05/02 by Anatolii A. Puhalskii, Puhalskii, Anatolii · 2 citations
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2305.01612

openalex publication_date 2023/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On large queue lengths in generalised Jackson networks
• Sample Path Moderate Deviation Principle for Queues with Waiting-time Dependent Interarrival and Service Times

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