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A large deviations principle for infinite-server queues in a random environment

Author

Listed:
  • H. M. Jansen

    (University of Amsterdam
    Ghent University)

  • M. R. H. Mandjes

    (University of Amsterdam)

  • K. De Turck

    (École CentraleSupélec, Université Paris Saclay)

  • S. Wittevrongel

    (Ghent University)

Abstract

This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements, and the server work rate are modulated by a general càdlàg stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.

Suggested Citation

  • H. M. Jansen & M. R. H. Mandjes & K. De Turck & S. Wittevrongel, 2016. "A large deviations principle for infinite-server queues in a random environment," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 199-235, February.
    • Handle: RePEc:spr:queues:v:82:y:2016:i:1:d:10.1007_s11134-015-9470-x
    DOI: 10.1007/s11134-015-9470-x
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    References listed on IDEAS

    as
    1. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    2. Jansen, H.M. & Mandjes, M.R.H. & De Turck, K. & Wittevrongel, S., 2015. "On the upper bound in Varadhan’s Lemma," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 24-29.
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    Cited by:

    1. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    2. Cheung, Eric C.K. & Rabehasaina, Landy & Woo, Jae-Kyung & Xu, Ran, 2019. "Asymptotic correlation structure of discounted Incurred But Not Reported claims under fractional Poisson arrival process," European Journal of Operational Research, Elsevier, vol. 276(2), pages 582-601.
    3. Alexander Moiseev & Maria Shklennik & Evgeny Polin, 2023. "Infinite-server queueing tandem with Markovian arrival process and service depending on its state," Annals of Operations Research, Springer, vol. 326(1), pages 261-279, July.
    4. Wenwen Li & Alexander Goldenshluger, 2024. "Adaptive minimax estimation of service time distribution in the $$M_t/G/\infty $$ M t / G / ∞ queue from departure data," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 81-123, October.

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