Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

Simple item page
dc.contributor.authorArtalejo Rodríguez, Jesús Manuel
dc.contributor.authorLi, Quan-Lin
dc.date.accessioned2023-06-20T00:10:45Z
dc.date.available2023-06-20T00:10:45Z
dc.date.issued2010-09
dc.description.abstractIn this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phase-type (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the UL-type RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMEC
dc.description.sponsorshipNational Grand Fundamental
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15001
dc.identifier.citation1. A.S. Alfa, Matrix-geometric solution of discrete time MAP/PH/1 priority queue, Naval Research Logistics, 45 (1998) 23-50. 2. C. Blondia , O. Casals, Statistical multiplexing of VBR sources: a matrix-analytic approach, Performance Evaluation, v.16 n.1-3, p.5-20, Nov. 1992 [doi>10.1016/0166-5316(92)90064-N] 3. C. Blondia, A discrete time batch Markovian arrival process as B-ISDN traffic model, Belgian Journal of Operations Research, Statistics and Computer Science, 32 (1993), 3-23. 4. K. Claffy, WAN packet size distribution, (1996), http://www. nlanr.net/NA/Learn/packetsizes.html. 5. I. Frigui, A.S. Alfa and X.Y. Xu, Algorithms for computing waiting time distributions under different queue disciplines for the D-BMAP/PH/1 , Naval Research Logistics, 44 (1997), 559-576. 6. W.K. Grassmann and D.A. Stanford, Matrix analytic methods, in: Computational probability, (Kluwer Academic Publishers, Norwell, MA, 1999), 153-203. 7. Q.-M. He, Queues with marked customers, Advances in Applied Probability, 28 (1996), 567-587. 8. Q.-M. He and M.F. Neuts, Markov chains with marked transitions, Stochastic Processes and their Applications, 74 (1998), 37-52. 9. D.M. Lucantoni, K.S. Meier-Hellstern and M.F. Neuts, A single-server queue with server vacations and a class of non-renewal arrival processes, Advances in Applied Probability, 22 (1990), 676-705. 10. D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Stochastic Models, 7 (1991), 1-46. 11. David M. Lucantoni, The BMAP/G/1 QUEUE: A Tutorial, Performance Evaluation of Computer and Communication Systems, Joint Tutorial Papers of Performance '93 and Sigmetrics '93, p.330-358, May 10-14, 1993 12. D.G. Miller, Computation of steady-state probabilities for M/M/1 priority queues, Operations Research, 29 (1981), 945-958. 13. M.F. Neuts, Matrix-geometric solutions in stochastic models - an algorithmic approach, (The Johns Hopkins University Press, 1981). 14. M.F. Neuts, Structured stochastic matrices of M/G/1 type and their applications, (Marcel Dekker Inc., New York, 1989). 15. Nachum Sacham, Multipoint communication by hierarchically encoded data, Proceedings of the eleventh annual joint conference of the IEEE computer and communications societies on One world through communications (Vol. 3), p.2107-2114, May 1992, Florence, Italy 16. H. Takagi, Queueing analysis: a foundation of performance evaluation, Vol 1: vacation and priority systems, (North-Holland, 1993). 17. J.-A. Zhao, B. Li and I. Ahmad, Traffic model for layered video: an approach on Markovian arrival process, in: Packet Video 2003, Universite de Nantes, Nantes, France, (2003). 18. Ji-An Zhao , Bo Li , Chi-Wah Kok , Ishfaq Ahmad, MPEG-4 Video transmission over wireless networks: a link level performance study, Wireless Networks, v.10 n.2, p.133-146, March 2004 [doi>10.1023/B:WINE.0000013078.74259.13] 19. Y.Q. Zhao, Censoring technique in studying block-structured Markov chains, in: The Third International Conference on Matrix Analytic Methods in Stochastic Models, Leuven, Belgium, (2000).
dc.identifier.doi10.1007/s10626-009-0075-6
dc.identifier.issn0924-6703
dc.identifier.officialurlhttp://www.springerlink.com/content/3522g14536j4351v/fulltext.pdf
dc.identifier.relatedurlhttp://www.springerlink.com
dc.identifier.urihttps://hdl.handle.net/20.500.14352/42138
dc.issue.number3
dc.journal.titleDiscrete Event Dynamic Systems
dc.language.isoeng
dc.page.final347
dc.page.initial325
dc.publisherSpringer
dc.relation.projectIDMTM2005-01248
dc.relation.projectID2006CB805901
dc.rights.accessRightsrestricted access
dc.subject.cdu517
dc.subject.keywordService
dc.subject.keywordSystem
dc.subject.keywordQueueing
dc.subject.keywordDiscrete-time
dc.subject.keywordStructured Markov chain
dc.subject.keywordRetrial
dc.subject.keywordLU-factorizations
dc.subject.keywordWaiting time
dc.subject.ucmAnálisis matemático
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titlePerformance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals
dc.typejournal article
dc.volume.number20
dspace.entity.typePublication
relation.isAuthorOfPublicationdb4b8a04-44b0-48e9-8b2c-c80ffae94799
relation.isAuthorOfPublication.latestForDiscoverydb4b8a04-44b0-48e9-8b2c-c80ffae94799
Download
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
arta04.pdf
Size:
476.76 KB
Format:
Adobe Portable Document Format
Download
Collections
Artículos