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dc.contributor.authorDieker, A. B.
dc.contributor.authorGao, Xuefeng
dc.date.accessioned2016-10-12T07:08:49Z
dc.date.available2016-10-12T07:08:49Z
dc.date.issued2011
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1245
dc.descriptionOWLF 2011en_US
dc.description.abstractWe study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to `overload' and `underload'. The two regimes cause standard techniques for proving positive recurrence to fail. Using and extending the framework of common quadratic Lyapunov functions from the theory of control, we construct Lyapunov functions for the diffusion approximations corresponding to systems with and without abandonment. With these Lyapunov functions, we prove that piecewise OU processes have a unique stationary distribution.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2011,26
dc.subjectStabilityen_US
dc.subjectCommon quadratic Lyapunov functionen_US
dc.subjectLyapunov functionen_US
dc.subjectPiecewise Ornstein-Uhlenbeck processen_US
dc.subjectMulti-server queueen_US
dc.subjectCustomer abandonmenten_US
dc.subjectHalfin-Whitt regimeen_US
dc.subjectPhasetype distributionen_US
dc.titlePositive recurrence of piecewise Orntein-Uhlenbeck processes and common quadratic Lyapunov functionsen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2011-26
local.scientificprogramOWLF 2011en_US
local.series.idOWP-2011-26
dc.identifier.urnurn:nbn:de:101:1-201109305089
dc.identifier.ppn1651043167


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