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dc.contributor.authorVerloop, I.M.
dc.contributor.authorAyesta, U.
dc.contributor.authorNúñez-Queija, R.
dc.date.accessioned2017-02-21T08:11:14Z
dc.date.available2017-02-21T08:11:14Z
dc.date.issued2011-12-31
dc.identifier.issn0030-364X
dc.identifier.urihttp://hdl.handle.net/20.500.11824/379
dc.description.abstractWe analyze a generalization of the discriminatory processor-sharing (DPS) queue in a heavy-traffic setting. Customers present in the system are served simultaneously at rates controlled by a vector of weights. We assume that customers have phase-type distributed service requirements and allow that customers have different weights in various phases of their service. In our main result we establish a state-space collapse for the queue-length vector in heavy traffic. The result shows that in the limit, the queue-length vector is the product of an exponentially distributed random variable and a deterministic vector. This generalizes a previous result by Rege and Sengupta [Rege, K. M., B. Sengupta. 1996. Queue length distribution for the discriminatory processor-sharing queue. Oper. Res. 44(4) 653-657], who considered a DPS queue with exponentially distributed service requirements. Their analysis was based on obtaining all moments of the queue-length distributions by solving systems of linear equations. We undertake a more direct approach by showing that the probability-generating function satisfies a partial differential equation that allows a closed-form solution after passing to the heavy-traffic limit. Making use of the state-space collapse result, we derive interesting properties in heavy traffic: (i) For the DPS queue, we obtain that, conditioned on the number of customers in the system, the residual service requirements are asymptotically independent and distributed according to the forward recurrence times. (ii) We then investigate how the choice for the weights influences the asymptotic performance of the system. In particular, for the DPS queue we show that the scaled holding cost reduces as classes with a higher value for dk/E(B fwd k) obtain a larger share of the capacity, where dk is the cost associated to class k, and E(B fwd k) is the forward recurrence time of the class-k service requirement. The applicability of this result for a moderately loaded system is investigated by numerical experiments.
dc.formatapplication/pdf
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectDiscriminatory processor sharing
dc.subjectHeavy traffic
dc.subjectPhase-type service requirements
dc.subjectResidual service requirements
dc.subjectScheduling
dc.titleHeavy-traffic analysis of a multiple-phase network with discriminatory processor sharing
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1287/opre.1110.0914
dc.relation.publisherversionhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-79960550564&doi=10.1287%2fopre.1110.0914&partnerID=40&md5=e89f87a9f99965696f69303ac32aa7b7
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/publishedVersionen_US
dc.journal.titleOperations Researchen_US


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Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España