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Performance analysis of polling systems with retrials and glue periods

Author

Listed:
  • Murtuza Ali Abidini

    (Eindhoven University of Technology)

  • Onno Boxma

    (Eindhoven University of Technology)

  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

  • Jacques Resing

    (Eindhoven University of Technology)

Abstract

We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:87:y:2017:i:3:d:10.1007_s11134-017-9545-y
    DOI: 10.1007/s11134-017-9545-y
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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. 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.
    3. 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.
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    Cited by:

    1. 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.

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