First passage times to congested states of many-server systems in the Halfin-Whitt regime

We consider the heavy-traffic approximation to the \(GI/M/s\) queueing system in the Halfin-Whitt regime, where both the number of servers \(s\) and the arrival rate \(\lambda\) grow large (taking the service rate as unity), with \(\lambda=s-\beta\sqrt{s}\) and \(\beta\) some constant. In this asymp...

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Bibliographic Details
Published in:arXiv.org 2013-02
Main Authors: Fralix, Brian H, Knessl, Charles, Johan S H van Leeuwaarden
Format: Article
Language:English
Subjects:
Brownian motion
Markov analysis
Ornstein-Uhlenbeck process
Queues
Queuing theory
Online Access:Get full text
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Summary:We consider the heavy-traffic approximation to the \(GI/M/s\) queueing system in the Halfin-Whitt regime, where both the number of servers \(s\) and the arrival rate \(\lambda\) grow large (taking the service rate as unity), with \(\lambda=s-\beta\sqrt{s}\) and \(\beta\) some constant. In this asymptotic regime, the queue length process can be approximated by a diffusion process that behaves like a Brownian motion with drift above zero and like an Ornstein-Uhlenbeck process below zero. We analyze the first passage times of this hybrid diffusion process to levels in the state space that represent congested states in the original queueing system.
ISSN:2331-8422