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Analysis of the waiting time distribution for polling systems with retrials and glue periods

Author

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  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

Abstract

We consider a single-server multi-station polling system with retrials and glue periods. Just before the server arrives at a station, there is a deterministic glue period. During a glue period, arriving customers (either newly arriving customers or retrying customers) at the station stick in the queue of that station and will be served during the following service period of that station. Whereas during any other period, arriving customers at the station join the orbit of that station and will retry after an exponentially distributed time. In this paper, we derive the Laplace–Stieltjes transform of the waiting time distribution of an arbitrary customer. This transform allows us to obtain the mean and variance of the waiting time.

Suggested Citation

  • Bara Kim & Jeongsim Kim, 2019. "Analysis of the waiting time distribution for polling systems with retrials and glue periods," Annals of Operations Research, Springer, vol. 277(2), pages 197-212, June.
    • Handle: RePEc:spr:annopr:v:277:y:2019:i:2:d:10.1007_s10479-018-2800-8
    DOI: 10.1007/s10479-018-2800-8
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    References listed on IDEAS

    as
    1. Christos Langaris, 1999. "Markovian polling systems with mixed service disciplines and retrial customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 305-322, December.
    2. 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.
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    Cited by:

    1. Vladimir Vishnevsky & Olga Semenova, 2021. "Polling Systems and Their Application to Telecommunication Networks," Mathematics, MDPI, vol. 9(2), pages 1-30, January.

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    1. 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.

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