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A discrete-time queueing system with optional LCFS discipline

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  • I. Atencia
  • A. Pechinkin

Abstract

We consider a discrete-time queueing system in which the arriving customers decide with a certain probability to be served under a LCFS-PR discipline and with complementary probability to join the queue. The arrivals are assumed to be geometrical and the service times are arbitrarily distributed. The service times of the expelled customers are independent of their previous ones. We carry out an extensive analysis of the system developing recursive formulae and generating functions for the steady-state distribution of the number of customers in the system and obtaining also recursive formulae and generating functions for the stationary distribution of the busy period and sojourn time as well as some performance measures. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • I. Atencia & A. Pechinkin, 2013. "A discrete-time queueing system with optional LCFS discipline," Annals of Operations Research, Springer, vol. 202(1), pages 3-17, January.
    • Handle: RePEc:spr:annopr:v:202:y:2013:i:1:p:3-17:10.1007/s10479-012-1097-2
    DOI: 10.1007/s10479-012-1097-2
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    References listed on IDEAS

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    1. Özgecan Ulusçu & Tayfur Altıok, 2009. "Waiting time approximation in single-class queueing systems with multiple types of interruptions: modeling congestion at waterways entrances," Annals of Operations Research, Springer, vol. 172(1), pages 291-313, November.
    2. Torben Meisling, 1958. "Discrete-Time Queuing Theory," Operations Research, INFORMS, vol. 6(1), pages 96-105, February.
    3. Dieter Fiems & Bart Steyaert & Herwig Bruneel, 2002. "Randomly Interrupted GI-G-1 Queues: Service Strategies and Stability Issues," Annals of Operations Research, Springer, vol. 112(1), pages 171-183, April.
    4. Wanda Rosa-Hatko & Eldon Gunn, 1997. "Queues with switchover - A review and critique," Annals of Operations Research, Springer, vol. 69(0), pages 299-322, January.
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    Cited by:

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    2. Atencia-Mc.Killop, Ivan & Galán-García, José L. & Aguilera-Venegas, Gabriel & Rodríguez-Cielos, Pedro & Galán-García, MÁngeles, 2018. "A Geo[X]/G[X]/1 retrial queueing system with removal work and total renewal discipline," Applied Mathematics and Computation, Elsevier, vol. 319(C), pages 245-253.

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