Publication:
Steady state solution of a single-server queue with linear repeated requests

dc.contributor.authorArtalejo Rodríguez, Jesús Manuel
dc.contributor.authorGómez-Corral, Antonio
dc.date.accessioned2023-06-20T16:55:15Z
dc.date.available2023-06-20T16:55:15Z
dc.date.issued1997
dc.description.abstractQueueing systems with repeated requests have many useful applications in communications and computer systems modeling. In the majority of previous work the repeat requests are made individually by each unsatisfied customer. However, there is in the literature another type of queueing situation, in which the time between two successive repeated attempts is independent of the number of customers applying for service. This paper deals with the M/G/1 queue with repeated orders in its most general setting, allowing the simultaneous presence of both types of repeat requests. We first study the steady state distribution and the partial generating functions. When the service time distribution is exponential we show that the performance characteristics can be expressed in terms of hypergeometric functions.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipDGICYT
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/15889
dc.identifier.citationABRAMOWITZ, M. AND STEGUN, I.A. (1972) Handbook of Mathematical Functions. Dover, New York. ARTALEJO, J.R. (1993) Explicit formulae for the characteristics of the M/H2/1 retrial queue. J Operat. Res. Soc. 44, 309-313. ARTALEJO, J.R. AND FALIN,G.I. (1994) Stochastic decomposition for retrial queues. Top 2, 329-342. BAILEYW, N. (1972) Generalized Hypergeometric Series. Hafner, New York. COOPER, R.B. (1981) Introduction to Queueing Theory. Elsevier, Amsterdam. FALIN, G.I. (1980) An M/M/1 queue with repeated calls in the presence of persistence function. Paper #1606-80. All-Union Institute for Scientific and Technical Information, Moscow. FALIN, G.I. (1984) Double-channel queueing system with repeated calls. Paper #4221-84. All-Union Institute for Scientific and Technical Information, Moscow. FALIN, G.I. (1990) A survey of retrial queues. QUESTA 7, 127-168. FARAHMAND, K. (1990) Single line queue with repeated demands. QUESTA 6, 223-228. FAYOLLE, G. (1986) A simple telephone exchange with delayed feedbacks. In Teletraffic Analysis and Computer Performance Evaluation. ed. O.J. Boxma, J. W. Cohen and H. C. Tijms. Elsevier, Amsterdam. FUHRMANNS, W. AND COOPER, R.B. (1985) Stochastic decomposition in the M/G/1 queue with generalized vacations. Operat. Res. 33, 1117-1129. HANSCHKE, T. (1987) Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts. J Appl. Prob. 24, 486-494. JONIN, G.L. AND SEDOLJ, J. (1970) Telephone systems with repeated calls. Proc. 6th Int. Teletraffic Congress 435/1-435/5. MARTIN, M. AND ARTALEJO, J. R. (1995) Analysis of an M/G/1 queue with two types of impatient units. Adv. Appl. Prob. 27, 840-861. PEARCE, C. (1989) Extended continued fractions, recurrence relations and two-dimensional Markov processes. Adv. Appl. Prob. 21, 357-375. SENNOTT L.I., HUMBLET, P.A. AND TWEEDIE, R.L. (1983) Mean drifts and the non-ergodicity of Markov chains. Operat. Res. 31, 783-789. YANG,T. AND TEMPLETON, J.G.C. (1987) A survey on retrial queues. QUESTA 2, 201-233.
dc.identifier.issn0021-9002
dc.identifier.officialurlhttp://www.jstor.org/stable/3215189
dc.identifier.relatedurlhttp://www.jstor.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57427
dc.issue.number1
dc.journal.titleJournal of Applied Probability
dc.language.isoeng
dc.page.final233
dc.page.initial223
dc.publisherApplied Probability Trust
dc.relation.projectIDPB95-0416
dc.rights.accessRightsrestricted access
dc.subject.cdu519.216
dc.subject.keywordQueues with repeated requests
dc.subject.keywordhypergeometric functions
dc.subject.ucmProcesos estocásticos
dc.subject.unesco1208.08 Procesos Estocásticos
dc.titleSteady state solution of a single-server queue with linear repeated requests
dc.typejournal article
dc.volume.number34
dspace.entity.typePublication
relation.isAuthorOfPublicationdb4b8a04-44b0-48e9-8b2c-c80ffae94799
relation.isAuthorOfPublication.latestForDiscoverydb4b8a04-44b0-48e9-8b2c-c80ffae94799
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