On the Rate of Convergence to Stationarity of the $M/M/n$ Queue

DATE: September 1, 2009

TIME: 11:00 AM – 12:00 PM

LOCATION: Executive Classroom

FEES: none

EVENT CONTACT:

Ton Dieker, ISyE
Contact Ton Dieker
404-385-3140

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*.