Show simple item record

dc.contributor.authorGamarnik, David
dc.contributor.authorGoldberg, David A.
dc.date.accessioned2013-12-23T20:46:47Z
dc.date.available2013-12-23T20:46:47Z
dc.date.issued2013-10
dc.date.submitted2012-07
dc.identifier.issn1050-5164
dc.identifier.urihttp://hdl.handle.net/1721.1/83256
dc.description.abstractWe prove several results about the rate of convergence to stationarity, that is, the spectral gap, for the M/M/n queue in the Halfin–Whitt regime. We identify the limiting rate of convergence to steady-state, and discover an asymptotic phase transition that occurs w.r.t. this rate. In particular, we demonstrate the existence of a constant B[superscript ∗] ≈ 1.85772 s.t. when a certain excess parameter B ∈ (0,B[superscript ∗]], the error in the steady-state approximation converges exponentially fast to zero at rate B[superscript 2 over 4]. For B > B[superscript ∗], the error in the steady-state approximation converges exponentially fast to zero at a different rate, which is the solution to an explicit equation given in terms of special functions. This result may be interpreted as an asymptotic version of a phase transition proven to occur for any fixed n by van Doorn [Stochastic Monotonicity and Queueing Applications of Birth-death Processes (1981) Springer]. We also prove explicit bounds on the distance to stationarity for the M/M/n queue in the Halfin–Whitt regime, when B < B[superscript ∗]. Our bounds scale independently of n in the Halfin–Whitt regime, and do not follow from the weak-convergence theory.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant CMMI-0726733)en_US
dc.language.isoen_US
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1214/12-aap889en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceInstitute of Mathematical Statisticsen_US
dc.titleOn the rate of convergence to stationarity of the M/M/N queue in the Halfin–Whitt regimeen_US
dc.typeArticleen_US
dc.identifier.citationGamarnik, David, and David A. Goldberg. “On the rate of convergence to stationarity of the M/M/N queue in the Halfin–Whitt regime.” The Annals of Applied Probability 23, no. 5 (October 2013): 1879-1912. © Institute of Mathematical Statisticsen_US
dc.contributor.departmentSloan School of Managementen_US
dc.contributor.mitauthorGamarnik, Daviden_US
dc.relation.journalThe Annals of Applied Probabilityen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsGamarnik, David; Goldberg, David A.en_US
dc.identifier.orcidhttps://orcid.org/0000-0001-8898-8778
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record