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Transient behavior of the Halfin-Whitt diffusion

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  • van Leeuwaarden, Johan S.H.
  • Knessl, Charles
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    Abstract

    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 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 transient behavior of this hybrid diffusion process, including the transient density, approach to equilibrium, and spectral properties. The transient behavior is shown to depend on whether [beta] is smaller or larger than the critical value [beta]*[approximate]1.85722, which confirms the recent result of Gamarnik and Goldberg (2008) [8].

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 7 (July)
    Pages: 1524-1545

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:7:p:1524-1545

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    Related research

    Keywords: GI/M/s queue M/M/s queue Halfin-Whitt regime Queues in heavy traffic Diffusion Asymptotic analysis;

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