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A queueing system with n-phases of service and (n-1)-types of retrial customers

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  • Langaris, Christos
  • Dimitriou, Ioannis

Abstract

A queueing system with a single server providing n-phases of service in succession is considered. Every customer receives service in all phases. Arriving customers join a single ordinary queue, waiting to start the service procedure. When a customer completes his service in the ith phase he decides either to proceed to the next phase or to join the Ki retrial box (i=1,2,...,n-1), from where he repeats the demand for the (i+1)th phase of service after a random amount of time and independently to the other customers in the system. Every customer can join during his service procedure a number of retrial boxes before departs from the system. When at the moment that a customer, either departs from the system or joins a retrial box and so releases the server, there are no other customers waiting in the ordinary queue, then the server departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service times are arbitrarily distributed. For such a system, the mean number of customers in the ordinary queue and in each retrial box separately are obtained, and used to investigate numerically system performance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:205:y:2010:i:3:p:638-649
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    References listed on IDEAS

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    1. 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.
    2. 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. K. Avrachenkov & E. Morozov & B. Steyaert, 2016. "Sufficient stability conditions for multi-class constant retrial rate systems," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 149-171, February.
    2. 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.
    3. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    4. Murtuza Ali Abidini & Onno Boxma & Bara Kim & Jeongsim Kim & Jacques Resing, 2017. "Performance analysis of polling systems with retrials and glue periods," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 293-324, December.
    5. 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.
    6. Dieter Fiems & Tuan Phung-Duc, 2019. "Light-traffic analysis of random access systems without collisions," Annals of Operations Research, Springer, vol. 277(2), pages 311-327, June.

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