×

Files d’attente à rejet différé. (Queues with rejection). (French) Zbl 0616.60092

The author considers a queueing model with rejection. A customer is rejected, when the server is busy. The rejected customer turns the queue with the next customer and is served together with him when the server is free or rejected once more but less than k times. In an extended probability space a stationary solution is evaluated with J. Neveu’s method [Cours de Zurich. (Février 1983). Théorie Ergodique et Processus Ponctuels Stationnaires. Application aux files d’attente.] Some properties of the queue are derived.
Reviewer: W.Schlee-Kössler

MSC:

60K25 Queueing theory (aspects of probability theory)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
90B22 Queues and service in operations research
PDF BibTeX XML Cite
Full Text: Numdam EuDML

References:

[1] A.A. Borovkov : Stochastic processes in queuing theory . Springer 1976 . MR 391297 | Zbl 0319.60057 · Zbl 0319.60057
[2] J.W. Cohen : The simple server queue . North Holland . Amsterdam 1969 . Zbl 0183.49204 · Zbl 0183.49204
[3] M.R. Jaïbi : Evolution d’une file d’attente avec priorité . Annales de l’I.H.P. , Section B, Vol. XVI n^\circ 3 . Numdam | Zbl 0445.60074 · Zbl 0445.60074
[4] R. Loynes : The stability of a queue with non-independent inter-arrival and service-times . Proc. Cambridge Philo-Soci. 58 ( 1962 ). MR 141170 | Zbl 0203.22303 · Zbl 0203.22303
[5] J. Neveu [1] : Cours de Zurich. (Février 83). Théorie Ergodique et Processus Ponctuels Stationnaires. Application aux files d’attente .
[6] : Introduction aux processus aléatoires . Cours de 3ème Cycle . Université Paris VI . · Zbl 0212.49201
[7] : Processus Ponctuels. Ecole d’Eté de Probabilités de St-Flour VI ( 1976 . Lecture Notes . Springer Verlag ( 1977 ). MR 474493
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.