Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue

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dc.contributor.authorGómez-Corral, Antonio
dc.contributor.authorArtalejo Rodríguez, Jesús Manuel
dc.date.accessioned2023-06-20T19:17:37Z
dc.date.available2023-06-20T19:17:37Z
dc.date.issued1996
dc.description.abstractThis paper is concerned with the stochastic analysis of the departure and quasi-input processes of a Markovian single-server queue with negative exponential arrivals and repeated attempts. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins an orbit of unsatisfied customers. The orbiting customers form a queue such that only a customer selected according to a certain rule can reapply for service. The intervals separating two successive repeated attempts are exponentially distributed with rate α+jμ, when the orbit size is j≥1. Negative arrivals have the effect of killing some customer in the orbit, if one is present, and they have no effect otherwise. Since customers can leave the system without service, the structural form of type M/G/1 is not preserved. We study the Markov chain with transitions occurring at epochs of service completions or negative arrivals. Then we investigate the departure and quasi-input processes.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/29639
dc.identifier.citationArtalejo, J.R. and Gomez-Corral, A., Quasi-birth and death processes with applications to queues with repeated attempts, (in preparation) 1995. Conolly, B.W. and Langaris, C., On a new formula for the transient state probabilities for M/M/1 queues and computational implications, J. Appl. Probab. 30 (1993), 237-246. Cooper, R.B., Introduction to Queueing Theory, Edward Arnold, London 1981. Falin, G.I., A survey of retrial queues, Queueing Syst. 7 (1990), 127-168. Farahmand, K., Single line queue with repeated attempts, Queueing Syst. 6 (1990), 223-228. Harrison, P.G. and Pitel, E., Sojourn times in single-server queues with negative customers, J. Appl. Probab. 31} (1993), 943-963. Martin, M. and Artalejo, J.R., Analysis of an M/G/1 queue with two types of impatient units, Adv. Appl. Probab. 27 (1995), 840-861. Stidham, Jr., S., Regenerative processes in the theory of queues, with applications to the alternating-priority queue, Adv. Appl. Probab. 4 (1972), 542-577.
dc.identifier.doi10.1155/S1048953396000172
dc.identifier.issn1048-9533
dc.identifier.officialurlhttp://www.hindawi.com/journals/ijsa/1996/579834/abs/
dc.identifier.relatedurlhttp://www.hindawi.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/59490
dc.issue.number2
dc.journal.titleJournal of Applied Mathematics and Stochastic Analysis
dc.language.isoeng
dc.page.final183
dc.page.initial171
dc.publisherHindawi Publishing Corporation
dc.rights.accessRightsopen access
dc.subject.cdu519.21
dc.subject.keywordQueueing
dc.subject.keywordRepeated Attempts
dc.subject.keywordNegative Arrivals
dc.subject.keywordRegenerative Processes
dc.subject.keywordGeneralized Hypergeometric Functions.
dc.subject.ucmProbabilidades (Matemáticas)
dc.titleStochastic analysis of the departure and quasi-input processes in a versatile single-server queue
dc.typejournal article
dc.volume.number9
dspace.entity.typePublication
relation.isAuthorOfPublicationdb4b8a04-44b0-48e9-8b2c-c80ffae94799
relation.isAuthorOfPublication.latestForDiscoverydb4b8a04-44b0-48e9-8b2c-c80ffae94799
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