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

B.H. Fralix, C. Knessl, J.S.H. Leeuwaarden, van

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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.
Originele taal-2Engels
Uitgeverijs.n.
Aantal pagina's11
StatusGepubliceerd - 2013

Publicatie series

NaamarXiv.org
Volume1302.3007 [math.PR]

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