Single server retrial queues with two way communication
| dc.contributor.author | Artalejo Rodríguez, Jesús Manuel | |
| dc.contributor.author | Phung-Duc, T. | |
| dc.date.accessioned | 2023-06-19T13:21:24Z | |
| dc.date.available | 2023-06-19T13:21:24Z | |
| dc.date.issued | 2013-02 | |
| dc.description.abstract | The main aim of this paper is to study the steady state behavior of an M/G/1-type retrial queue in which there are two flows of arrivals namely ingoing calls made by regular customers and outgoing calls made by the server when it is idle. We carry out an extensive stationary analysis of the system, including stability condition, embedded Markov chain, steady state joint distribution of the server state and the number of customers in the orbit (i.e., the retrial group) and calculation of the first moments. We also obtain light-tailed asymptotic results for the number of customers in the orbit. We further formulate a more complicate but realistic model where the arrivals and the service time distributions are modeled in terms of the Markovian arrival process (MAP) and the phase (PH) type distribution. | |
| dc.description.department | Depto. de Estadística e Investigación Operativa | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Government of Spain (Ministry of Science and Innovation) | |
| dc.description.sponsorship | European Commission | |
| dc.description.sponsorship | Japan Society for the Promotion of Science | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20330 | |
| dc.identifier.doi | 10.1016/j.apm.2012.04.022 | |
| dc.identifier.issn | 0307-904X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0307904X12002533 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/33269 | |
| dc.issue.number | 4 | |
| dc.journal.title | Applied Mathematical Modelling | |
| dc.language.iso | eng | |
| dc.page.final | 1822 | |
| dc.page.initial | 1811 | |
| dc.publisher | Elsevier Science Inc | |
| dc.relation.projectID | MTM2011-23864 | |
| dc.relation.projectID | 22.470 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 519.2 | |
| dc.subject.keyword | Retrial queues | |
| dc.subject.keyword | Two Way communication | |
| dc.subject.keyword | Stationary distribution | |
| dc.subject.keyword | Light-tailed behavior | |
| dc.subject.keyword | Bernoulli vacation schedule | |
| dc.subject.keyword | feedback | |
| dc.subject.keyword | customers | |
| dc.subject.keyword | model | |
| dc.subject.ucm | Estadística matemática (Matemáticas) | |
| dc.subject.unesco | 1209 Estadística | |
| dc.title | Single server retrial queues with two way communication | |
| dc.type | journal article | |
| dc.volume.number | 37 | |
| dcterms.references | J.R. Artalejo, A. Gomez-Corral, Retrial Queueing Systems: A Computational Approach, Springer, Berlin, 2008. G.I. Falin, J.G.C. Templeton, Retrial Queues, Chapman and Hall, London, 1997. J.R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model. 30 (1999) 1–6. J.R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000–2009, Math. Comput. Model. 51 (2010) 1071–1081. A. Gomez-Corral, A bibliographical guide to the analysis of retrial queues through matrix analytic techniques, Ann. Operat. Res. 141 (2006) 163–191. J.R. Artalejo, M.J. Lopez-Herrero, On the distribution of the number of retrials, Appl. Math. Model. 31 (2007) 478–489. G. Choudhury, Steady state analysis of an M=G=1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule, Appl. Math. Model. 32 (2008) 2480–2489. G. Choudhury, J.-C. Ke, A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delaying repair, Appl. Math. Model. 36 (2012) 255–269. T.V. Do, An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity, Appl. Math. Model. 34 (2010) 2272–2278. B. Krishna Kumar, R. Rukmani, V. Thangaraj, On multiserver feedback retrial queue with finite buffer, Appl. Math. Model. 33 (2009) 2062–2083. Y.W. Shin, T.S. Choo, M=M=s queue with impatient customers and retrials, Appl. Math. Model. 33 (2009) 2596–2606. J. Wu, Z. Liu, G. Yang, Analysis of the finite source MAP=PH=N retrial G-queue operating in a random environment, Appl. Math. Model. 35 (2011) 1184–1193. G.I. Falin, Model of coupled switching in presence of recurrent calls, Eng. Cybernet. Rev. 17 (1979) 53–59. J.R. Artalejo, J.A.C. Resing, Mean value analysis of single server retrial queues, Asia-Pacific J. Operat. Res. 27 (2010) 335–345. J.R. Artalejo, T. Phung-Duc, Markovian single server retrial queues with two way communication, in: Proceedings of the 6th International Conference on Queueing Theory and Network Applications, Seoul, 2011, pp. 1–7. J.R. Artalejo, A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated request, J. Appl. Prob. 34 (1997) 223–233. B.D. Choi, Y.C. Kim, Y.W. Lee, The M=M=c retrial queue with geometric loss and feedback, Comput. Math. Appl. 36 (1998) 41–52. T. Hanschke, Explicit formulas for the characteristics of the M=M=2=2 queue with repeated attempts, J. Appl. Prob. 24 (1987) 486–494. J. Kim, Retrial queueing system with collision and impatience, Commun. Korean Math. Soc. 25 (2010) 647–653. A. Krishnamoorthy, T.G. Deepak, V.C. Joshua, An M=G=1 retrial queue with nonpersistent customers and orbital search, Stoch. Anal. Appl. 23 (2005) 975–997. T. Phung-Duc, H. Masuyama, S. Kasahara, Y. Takahashi, State-dependent M=M=c=c þ r retrial queues with Bernoulli abandonment, J. Ind. Manag. Optim. 6 (2010) 517–540. J. Kim, B. Kim, S.-S. Ko, Tail asymptotics for the queue size distribution in an M=G=1 retrial queue, J. Appl. Prob. 44 (2007) 1111–1118. L.I. Sennott, P.A. Humblet, R.L. Tweedie, Mean drifts and the non-ergodicity of Markov chains, Operat. Res. 31 (1983) 783–789. E. Çinlar, Introduction to Stochastic Processes, Prentince-Hall, Englewood Cliffs, New Jersey, 1975. R.W. Wolff, Poisson arrivals see time averages, Operat. Res. 30 (1982) 223–231. R.B. Cooper, Introduction to Queueing Theory, Elsevier, Amsterdam, 1981. P. Flajolet, A. Odlyzko, Singularity analysis of generating functions, SIAM J. Disc. Math. 3 (1990) 216–240. J.R. Artalejo, M. Pozo, Numerical calculation of the stationary distribution of the main multiserver retrial queue, Ann. Operat. Res. 116 (2002) 41–56. M.F. Neuts, B.M. Rao, Numerical investigation of a multiserver retrial model, Queue. Syst. 7 (1990) 169–190. T. Phung-Duc, H. Masuyama, S. Kasahara, Y. Takahashi, A simple algorithm for the rate matrices of level-dependent QBD processes, in: Proceedings of the 5th International Conference on Queueing Theory and Network Applications, Beijing, 2010b, pp. 46–52. S. Bhulai, G. Koole, A queueing model for call blending in call centers, IEEE Trans. Automat. Control 48 (2003) 1434–1438. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | db4b8a04-44b0-48e9-8b2c-c80ffae94799 | |
| relation.isAuthorOfPublication.latestForDiscovery | db4b8a04-44b0-48e9-8b2c-c80ffae94799 |
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