Publication:
Maximum queue lengths during a fixed time interval in the M/M/c retrial queue

Simple item page
dc.contributor.authorGómez-Corral, Antonio
dc.contributor.authorLópez-García, M.
dc.date.accessioned2023-06-19T13:24:53Z
dc.date.available2023-06-19T13:24:53Z
dc.date.issued2014
dc.description.abstractWe are concerned with the problem of characterizing the distribution of the maximum number Z(t(0)) of customers during a fixed time interval [0, t(0)] in the M/M/c retrial queue, which is shown to have a matrix exponential form. We present a simple condition on the service and retrial rates for the matrix exponential solution to be explicit or algorithmically tractable. Our methodology is based on splitting methods and the use of eigen-values and eigenvectors. A particularly appealing feature of our solution is that it allows us to obtain global error control. Specifically, we derive an approximating solution p(x; t(0)) = p(x; t(0); epsilon) verifying [P(Z(t(0)) <= x vertical bar X(0) = (i,j)) - p(x; t(0))] < epsilon uniformly in x >= i + j, for any epsilon > 0 and initial numbers i of busy servers and j of customers in orbit.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipGovernment of Spain (Ministry of Economy and Competitiveness)
dc.description.sponsorshipEuropean Commission
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/26204
dc.identifier.doi10.1016/j.amc.2014.02.074
dc.identifier.issn0096-3003
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S0096300314003221
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33603
dc.journal.titleApplied Mathematics and Computation
dc.language.isoeng
dc.page.final136
dc.page.initial124
dc.publisherElsevier
dc.relation.projectIDMTM-2011-23864
dc.relation.projectIDBES-2009-018747
dc.rights.accessRightsrestricted access
dc.subject.cdu519.2
dc.subject.keywordAbsorbing Markov chain
dc.subject.keywordEigenvalues/eigenvectors
dc.subject.keywordMaximum queue length
dc.subject.keywordRetrial queue
dc.subject.keywordSplitting method
dc.subject.ucmEstadística matemática (Matemáticas)
dc.subject.unesco1209 Estadística
dc.titleMaximum queue lengths during a fixed time interval in the M/M/c retrial queue
dc.typejournal article
dc.volume.number235
dspace.entity.typePublication
Files
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
GomezCorral200.pdf
Size:
604.35 KB
Format:
Adobe Portable Document Format
Download
Collections
Artículos