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Analysis of Discrete-Time Queues with Branching Arrivals

Author

Listed:
  • Dieter Fiems

    (Department Telin, Ghent University, B-9000 Gent, Belgium
    These authors contributed equally to this work.)

  • Koen De Turck

    (Department Telin, Ghent University, B-9000 Gent, Belgium
    These authors contributed equally to this work.)

Abstract

We consider a discrete-time single server queueing system, where arrivals stem from a multi-type Galton–Watson branching process with migration. This branching-type arrival process exhibits intricate correlation, and the performance of the corresponding queueing process can be assessed analytically. We find closed-form expressions for various moments of both the queue content and packet delay. Close inspection of the arrival process at hand, however, reveals that sample paths consist of large independent bursts of arrivals followed by geometrically distributed periods without arrivals. Allowing for non-geometric periods without arrivals, and correlated bursts, we apply π -thinning on the arrival process. As no closed-form expressions can be obtained for the performance of the corresponding queueing system, we focus on approximations of the main performance measures in the light and heavy traffic regimes.

Suggested Citation

  • Dieter Fiems & Koen De Turck, 2023. "Analysis of Discrete-Time Queues with Branching Arrivals," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1020-:d:1071340
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    References listed on IDEAS

    as
    1. S. Pradhan & U. C. Gupta, 2019. "Analysis of an infinite-buffer batch-size-dependent service queue with Markovian arrival process," Annals of Operations Research, Springer, vol. 277(2), pages 161-196, June.
    2. Philip A. Ernst & Søren Asmussen & John J. Hasenbein, 2018. "Stability and busy periods in a multiclass queue with state-dependent arrival rates," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 207-224, December.
    3. Dharmaraja Selvamuthu & Paola Tardelli, 2022. "Infinite-server systems with Hawkes arrivals and Hawkes services," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 329-351, August.
    4. Kevei, Péter & Wiandt, Péter, 2021. "Moments of the stationary distribution of subcritical multitype Galton–Watson processes with immigration," Statistics & Probability Letters, Elsevier, vol. 173(C).
    5. Dieter Fiems & Eitan Altman, 2012. "Gated polling with stationary ergodic walking times, Markovian routing and random feedback," Annals of Operations Research, Springer, vol. 198(1), pages 145-164, September.
    Full references (including those not matched with items on IDEAS)

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