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On the Rate of Convergence to Stationarity of the $M/M/n$ Queue
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TITLE: On the Rate of Convergence to Stationarity of the $M/M/n$ Queue in the Halfin-Whitt Regime
SPEAKER: David Goldberg
ABSTRACT:
We study the rate of convergence to stationarity of the M/M/n queue in the Halfin-Whitt Regime. We prove that there is an interesting phase transition in the system's behavior, occurring when a critical parameter B reaches B* sim 1.85772. For B < B*, the exponential rate of convergence is B2/4; above B* it is the solution to an equation involving the Parabolic Cylinder functions. We also bound the prefactor governing the rate of convergence uniformly over n, for B < B*.
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- Workflow Status:Published
- Created By:Anita Race
- Created:10/12/2009
- Modified By:Fletcher Moore
- Modified:10/07/2016
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