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Infinite-server systems with Hawkes arrivals and Hawkes services

Author

Listed:
  • Dharmaraja Selvamuthu

    (Indian Institute of Technology Delhi)

  • Paola Tardelli

    (University of L’Aquila)

Abstract

This paper is devoted to the study of the number of customers in infinite-server systems driven by Hawkes processes. In these systems, the self-exciting arrival process is assumed to be represented by a Hawkes process and the self-exciting service process by a state-dependent Hawkes process (sdHawkes process). Under some suitable conditions, for the $$\mathrm{Hawkes/sdHawkes/\infty }$$ Hawkes / sdHawkes / ∞ system, the Markov property of the system is derived. The joint time-dependent distribution of the number of customers in the system, the arrival intensity and the server intensity is characterized by a system of differential equations. Then, the time-dependent results are also deduced for the $$\mathrm{M/sdHawkes/\infty }$$ M / sdHawkes / ∞ system.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:101:y:2022:i:3:d:10.1007_s11134-022-09813-3
    DOI: 10.1007/s11134-022-09813-3
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    References listed on IDEAS

    as
    1. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    2. Dassios, Angelos & Zhao, Hongbiao, 2013. "Exact simulation of Hawkes process with exponentially decaying intensity," LSE Research Online Documents on Economics 51370, London School of Economics and Political Science, LSE Library.
    3. Zhongping Li & Lirong Cui, 2020. "Numerical method for means of linear Hawkes processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(15), pages 3681-3697, August.
    4. Tomasz R. Bielecki & Monique Jeanblanc & Marek Rutkowski, 2006. "Hedging of Credit Derivatives in Models with Totally Unexpected Default," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 2, pages 35-100, World Scientific Publishing Co. Pte. Ltd..
    5. Chiang, Wen-Hao & Liu, Xueying & Mohler, George, 2022. "Hawkes process modeling of COVID-19 with mobility leading indicators and spatial covariates," International Journal of Forecasting, Elsevier, vol. 38(2), pages 505-520.
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    Cited by:

    1. Dieter Fiems & Koen De Turck, 2023. "Analysis of Discrete-Time Queues with Branching Arrivals," Mathematics, MDPI, vol. 11(4), pages 1-13, February.

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