On the steady-state probability of delay and large negative deviations for the $GI/GI/n$ queue in the Halfin-Whitt regime

@inproceedings{Goldberg2013OnTS,
  title={On the steady-state probability of delay and large negative deviations for the \$GI/GI/n\$ queue in the Halfin-Whitt regime},
  author={David Alan Goldberg},
  year={2013}
}
as the associated excess parameter B →∞; and by 1− ǫB as B → 0. We also prove that the tail of the steady-state number of idle servers has a Gaussian decay, and use known results to show that our bounds are tight (in an appropriate sense). Our main proof technique is the derivation of new stochastic comparison bounds for the FCFS GI/GI/n queue, which are of a structural nature, hold for all n and times t, and build on the recent work of Gamarnik and Goldberg [21]. 

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