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A queueing model with two classes of retrial customers and paired services

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  • Ioannis Dimitriou

Abstract

We mathematically investigate a single server system accepting two types of retrial customers and paired service. If upon arrival a customer finds the server busy, it is routed to an infinite capacity orbit queue according to each type. Upon a service completion epoch, if at least one orbit queue is non-empty, the server seeks to find customers from the orbits. If both orbit queues are non-empty, the seeking process will bring to the service area a pair of customers, one from each orbit. If there is only one non-empty, then a single customer from this orbit queue will be brought to the service area. However, if a primary customer arrives during the seeking process it will occupy the server immediately. It is shown that the joint stationary orbit queue length distribution at service completion epochs is determined by solving a Riemann boundary value problem. Stability condition is investigated, while generalizations of the main model are also discussed. A simple numerical example is obtained and yields insight into the behavior of the system. Copyright Springer Science+Business Media New York 2016

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  • Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:p:123-143:10.1007/s10479-015-2059-2
    DOI: 10.1007/s10479-015-2059-2
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    References listed on IDEAS

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    1. Langaris, Christos & Dimitriou, Ioannis, 2010. "A queueing system with n-phases of service and (n-1)-types of retrial customers," European Journal of Operational Research, Elsevier, vol. 205(3), pages 638-649, September.
    2. B. Kumar & J Raja, 2006. "On multiserver feedback retrial queues with balking and control retrial rate," Annals of Operations Research, Springer, vol. 141(1), pages 211-232, January.
    3. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    4. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
    5. Anastasia Winkler, 2013. "Dynamic scheduling of a single-server two-class queue with constant retrial policy," Annals of Operations Research, Springer, vol. 202(1), pages 197-210, January.
    6. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.
    7. B. Kumar & A. Vijayakumar & D. Arivudainambi, 2002. "An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume," Annals of Operations Research, Springer, vol. 113(1), pages 61-79, July.
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    Cited by:

    1. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2022. "Approximations for the performance evaluation of a discrete-time two-class queue with an alternating service discipline," Annals of Operations Research, Springer, vol. 310(2), pages 477-503, March.
    2. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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