dc.contributor.author | Gamarnik, David | |
dc.contributor.author | Goldberg, David A. | |
dc.date.accessioned | 2013-12-23T20:46:47Z | |
dc.date.available | 2013-12-23T20:46:47Z | |
dc.date.issued | 2013-10 | |
dc.date.submitted | 2012-07 | |
dc.identifier.issn | 1050-5164 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/83256 | |
dc.description.abstract | We 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.sponsorship | National Science Foundation (U.S.) (Grant CMMI-0726733) | en_US |
dc.language.iso | en_US | |
dc.publisher | Institute of Mathematical Statistics | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1214/12-aap889 | en_US |
dc.rights | Article 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.source | Institute of Mathematical Statistics | en_US |
dc.title | On the rate of convergence to stationarity of the M/M/N queue in the Halfin–Whitt regime | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Gamarnik, 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 Statistics | en_US |
dc.contributor.department | Sloan School of Management | en_US |
dc.contributor.mitauthor | Gamarnik, David | en_US |
dc.relation.journal | The Annals of Applied Probability | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Gamarnik, David; Goldberg, David A. | en_US |
dc.identifier.orcid | https://orcid.org/0000-0001-8898-8778 | |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |