Steady-state GI/GI/n Queue in the Halfin-Whitt Regime

@inproceedings{Gamarnik2011SteadystateGQ,
  title={Steady-state GI/GI/n Queue in the Halfin-Whitt Regime},
  author={David Gamarnik and David Alan Goldberg},
  year={2011}
}
We consider the FCFS $GI/GI/n$ queue in the so-called Halfin-Whitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by $n^(1/2)$, is tight. We derive an upper bound on the large deviation exponent of the limiting steady-state queue length matching that conjectured by Gamarnik and Momcilovic in \cite{GM.08}. We also prove a matching lower bound when the arrival process is Poisson. Our main proof… CONTINUE READING

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