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Computing the steady-state probabilities of the number of customers in the system of a tandem queueing system, a Machine Learning approach

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  • Sherzer, Eliran

Abstract

Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume that the arrival process for the first station is governed by a general renewal process, which implies that arrivals at subsequent stations will likely deviate from a renewal pattern.

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  • Sherzer, Eliran, 2025. "Computing the steady-state probabilities of the number of customers in the system of a tandem queueing system, a Machine Learning approach," European Journal of Operational Research, Elsevier, vol. 326(1), pages 141-156.
  • Handle: RePEc:eee:ejores:v:326:y:2025:i:1:p:141-156
    DOI: 10.1016/j.ejor.2025.04.040
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    References listed on IDEAS

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    1. Ward Whitt, 1995. "Variability Functions for Parametric-Decomposition Approximations of Queueing Networks," Management Science, INFORMS, vol. 41(10), pages 1704-1715, October.
    2. Ward Whitt & Wei You, 2018. "Using Robust Queueing to Expose the Impact of Dependence in Single-Server Queues," Operations Research, INFORMS, vol. 66(1), pages 184-199, January.
    3. Chaithanya Bandi & Dimitris Bertsimas & Nataly Youssef, 2015. "Robust Queueing Theory," Operations Research, INFORMS, vol. 63(3), pages 676-700, June.
    4. Weimin Dai & Jian-Qiang Hu, 2022. "Correlated queues with service times depending on inter-arrival times," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 41-60, February.
    5. Gabriel R. Bitran & Devanath Tirupati, 1988. "Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference," Management Science, INFORMS, vol. 34(1), pages 75-100, January.
    6. A. B. Dieker & S. Ghosh & M. S. Squillante, 2017. "Optimal Resource Capacity Management for Stochastic Networks," Operations Research, INFORMS, vol. 65(1), pages 221-241, February.
    7. Qixin Wang & Jian-Qiang Hu, 2024. "Queues with correlated inter-arrival and service times," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 1-30, October.
    8. Sunkyo Kim, 2011. "Modeling Cross Correlation in Three-Moment Four-Parameter Decomposition Approximation of Queueing Networks," Operations Research, INFORMS, vol. 59(2), pages 480-497, April.
    9. Opher Baron & Dmitry Krass & Arik Senderovich & Eliran Sherzer, 2024. "Supervised ML for Solving the GI / GI /1 Queue," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 766-786, May.
    10. Civelek, Ismail & Biller, Bahar & Scheller-Wolf, Alan, 2021. "Impact of dependence on single-server queueing systems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1031-1045.
    11. Sherzer, Eliran & Baron, Opher & Krass, Dmitry & Resheff, Yehezkel, 2025. "Approximating G(t)/GI/1 queues with deep learning," European Journal of Operational Research, Elsevier, vol. 322(3), pages 889-907.
    12. A. B. Dieker & S. Ghosh & M. S. Squillante, 2017. "Optimal Resource Capacity Management for Stochastic Networks," Operations Research, INFORMS, vol. 65(1), pages 221-241, February.
    13. Ruth Sagron & Uri Yechiali, 2024. "Inter-Departure Time Correlations in PH / G /1 Queues," Mathematics, MDPI, vol. 12(9), pages 1-23, April.
    14. Barış Tan & Siamak Khayyati, 2022. "Supervised learning-based approximation method for single-server open queueing networks with correlated interarrival and service times," International Journal of Production Research, Taylor & Francis Journals, vol. 60(22), pages 6822-6847, November.
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