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Algorithmic analysis of the Geo/Geo/c retrial queue

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dc.contributor.authorArtalejo Rodríguez, Jesús Manuel
dc.contributor.authorEconomou, A.
dc.contributor.authorGómez-Corral, Antonio
dc.date.accessioned2023-06-20T09:34:08Z
dc.date.available2023-06-20T09:34:08Z
dc.date.issued2008-09-16
dc.description.abstractIn this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipKapodistrias 70/4/6415 (University of Athens)
dc.description.sponsorshipEPEAEKII-Pythagoras 70/3/7388 (European social fund and national resources)
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15225
dc.identifier.doi10.1016/j.ejor.2007.01.060
dc.identifier.issn0377-2217
dc.identifier.officialurlhttp://www.sciencedirect.com/science/article/pii/S037722170700519X
dc.identifier.relatedurlhttp://www.sciencedirect.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49926
dc.issue.number3
dc.journal.titleEuropean journal of operational research
dc.language.isoeng
dc.page.final1056
dc.page.initial1042
dc.publisherElsevier Science
dc.relation.projectIDMTM2005-01248
dc.rights.accessRightsrestricted access
dc.subject.cdu519.248
dc.subject.keywordDiscrete-time
dc.subject.keywordSize distribution
dc.subject.keywordQueueing
dc.subject.keywordGeo/Geo/c queue
dc.subject.keywordRetrials
dc.subject.keywordStationary Distribution
dc.subject.keywordBusy period
dc.subject.keywordWaiting time
dc.subject.keywordMatrix-analytic methods
dc.subject.ucmInvestigación operativa (Matemáticas)
dc.subject.unesco1207 Investigación Operativa
dc.titleAlgorithmic analysis of the Geo/Geo/c retrial queue
dc.typejournal article
dc.volume.number189
dcterms.referencesJ.R. Artalejo. Accessible bibliography on retrial queues. Mathematical and Computer Modelling, 30 (1999), pp. 1–6 J.R. Artalejo, A. Gómez-Corral. Waiting time in the M/M/c queue with finite retrial group. Bulletin of Kerala Mathematics Association, 2(2005), pp. 1–17 Artalejo, J.R., Lopez-Herrero, M.J., 2005. A discrete-time multiserver retrial queue: Performance analysis and simulation. In: Ermakov, S.M., Melas, V.B., Pepelyshev, A.N. (Eds.), Proceedings of the 5th Workshop on Simulation, St. Petersburg, pp. 85–90. J.R. Artalejo, M. Pozo. Numerical calculation of the stationary distribution of the main multiserver retrial queue. Annals of Operations Research, 116 (2002), pp. 41–56 J.R. Artalejo, I. Atencia, P. Moreno. A discrete-time Geo[X]/G/1 retrial queue with control of admission. Applied Mathematical Modelling, 29 (2005), pp. 1100–1120. J.R. Artalejo, A. Economou, M.J. Lopez-Herrero. Algorithmic approximations for the busy period distribution of the M/M/c retrial queue. European Journal of Operational Research, 176 (2007), pp. 1687–1702 I. Atencia, P. Moreno. A discrete-time Geo/G/1 retrial queue with general retrial times. Queueing Systems, 48 (2004), pp. 5–21 I. Atencia, P. Moreno. A discrete-time Geo/G/1 retrial queue with the server subject to starting failures. Annals of Operations Research, 141 (2006), pp. 85–107 H. Bruneel, B.G. Kim. Discrete-Time Models for Communications Systems including ATM. Kluwer Academic Publishers, Boston (1993) M.L. Chaudhry. On numerical computations of some discrete-time queues. W.K. Grassmann (Ed.),Computational Probability, Kluwer, Boston (2000) B.D. Choi, J.W. Kim. Discrete-time Geo1, Geo2/G/1 retrial queueing system with two types of calls. Computers and Mathematics with Applications, 33 (1997), pp. 79–88 G.I. Falin, J.G.C. Templeton Retrial Queues, Monographs on Statistics and Applied Probability, vol. 75Chapman and Hall, London (1997) A. Gómez-Corral. A bibliographical guide to the analysis of retrial queues through matrix analytic techniques. Annals of Operations Research, 141 (2006), pp. 163–191 J.J. Hunter. Mathematical Techniques of Applied Probability, Discrete Time Models: Basic Theory, vol. 1 Academic Press, New York (1983) G. Latouche, V. Ramaswami. Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability. SIAM, Philadelphia (1999) H. Li, T. Yang. Geo/G/1 discrete time retrial queue with Bernoulli schedule. European Journal of Operational Research, 111 (1998), pp. 629–649 H. Li, T. Yang. Steady-state queue size distribution of discrete-time PH/Geo/1 retrial queues. Mathematical and Computer Modelling, 30 (1999), pp. 51–63 M.F. Neuts. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore, Maryland (1981) M.F. Neuts, B.M. Rao. Numerical investigation of a multiserver retrial model. Queueing Systems, 7 (1990), pp. 169–190 W.J. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton University Press, New Jersey (1994) H. Takagi. Queueing Analysis: A Foundation of Performance Evaluation, Discrete-Time Systems, vol. 3North-Holland, Amsterdam (1993) M. Takahashi, H. Osawa, T. Fujisawa Geo[X]/G/1 retrial queue with non-preemptive priority. Asia-Pacific Journal of Operational Research, 16 (1999), pp. 215–234 M.E. Woodward. Communication and Computer Networks: Modelling with Discrete-Time Queues. IEEE Computer Society Press, Los Alamitos (1994) T. Yang, H. Li. On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated attempts.Queueing Systems, 21 (1995), pp. 199–215
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