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Retrial Queues: Scaling Limits
1
Department of Policy and Planning Sciences, Institute of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan
2
Center for Artificial Intelligence Research (C-AIR), Tsukuba Institute for Advanced Research (TIAR), University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan
* Corresponding Author:
Tuan Phung-Duc,
[email protected]
Volume 1, Issue 2
2026
Received: 22 December 2025
Accepted: 28 April 2026
Published: 30 April 2026
Article Information
Abstract
Retrial queues arise in various applications such as call centers, services, and computer networks. The study of retrial queues is an important research branch of Queueing Theory. Retrial queues are characterized by the feature that customers who cannot receive service upon arrival do not queue but retry to enter the server after some random time. This makes the analysis of retrial queues more difficult than that of corresponding models without retrials. While the latter can be considered the limit of the former as the retrial time tends to infinity, some scaling limits are needed to obtain a scaled version of the number of retrial customers as the retrial time tends to zero, because the number of retrial customers explodes under this limiting regime. In this paper, a brief survey is provided on the major scaling limits of these models, and open problems are discussed. These limits can be used as approximations of complex systems with retrials.
Graphical Abstract
Keywords
scaling limits
fluid limit
diffusion limit
heavy traffic
retrial queues
networks
Data Availability Statement
Not applicable.
Funding
This work was supported by the Kayamori Foundation of Informational Science Advancement.
Conflicts of Interest
The author declares no conflicts of interest.
AI Use Statement
The author declares that no generative AI was used in the preparation of this manuscript.
Ethical Approval and Consent to Participate
Not applicable.
References
- Falin, G. I. and Templeton, J.G.C. (1997). Retrial Queues (First ed.). Chapman & Hall, London. https://books.google.com/books?hl=zh-CN&lr=&id=OsKoEAAAQBAJ&oi=fnd&pg=PR9&ots=h7b4U_DApG&sig=IBtE-ICC_nFb-ybEZPEJWVH48qw#v=onepage&q&f=false
[Google Scholar] - Moiseev, A., Nazarov, A., & Paul, S. (2020). Asymptotic diffusion analysis of multi-server retrial queue with hyper-exponential service. Mathematics, 8(4), 531.
[CrossRef] [Google Scholar] - Atar, R., & Lev-Ari, A. (2018). Optimizing buffer size for the retrial queue: two state space collapse results in heavy traffic. Queueing Systems, 90(3), 225-255.
[CrossRef] [Google Scholar] - Mandelbaum, A., Massey, W. A., Reiman, M. I., Stolyar, A., & Rider, B. (2002). Queue lengths and waiting times for multiserver queues with abandonment and retrials. Telecommunication Systems, 21(2), 149-171.
[CrossRef] [Google Scholar] - Nazarov, A., Phung-Duc, T., & Izmailova, Y. (2020, September). Multidimensional central limit theorem of the multiclass M/M/1/1 retrial queue. In International Conference on Distributed Computer and Communication Networks (pp. 298-310). Cham: Springer International Publishing.
[CrossRef] [Google Scholar] - Nazarov, A. A., & Fedorova, E. A. (2025). Method of the Marginal Asymptotic-Diffusion Analysis for Multiclass Retrial Queue Mn/GIn. AUTOMATION AND REMOTE CONTROL, 86(3), 235-248.
[Google Scholar]
Cite This Article
APA Style
Phung-Duc, T. (2026). Retrial Queues: Scaling Limits. Journal of Systems Scalability, 1(2), 39-42. https://doi.org/10.62762/JSS.2025.500072
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TY - JOUR AU - Phung-Duc, Tuan PY - 2026 DA - 2026/04/30 TI - Retrial Queues: Scaling Limits JO - Journal of Systems Scalability T2 - Journal of Systems Scalability JF - Journal of Systems Scalability VL - 1 IS - 2 SP - 39 EP - 42 DO - 10.62762/JSS.2025.500072 UR - https://www.icck.org/article/abs/JSS.2025.500072 KW - scaling limits KW - fluid limit KW - diffusion limit KW - heavy traffic KW - retrial queues KW - networks AB - Retrial queues arise in various applications such as call centers, services, and computer networks. The study of retrial queues is an important research branch of Queueing Theory. Retrial queues are characterized by the feature that customers who cannot receive service upon arrival do not queue but retry to enter the server after some random time. This makes the analysis of retrial queues more difficult than that of corresponding models without retrials. While the latter can be considered the limit of the former as the retrial time tends to infinity, some scaling limits are needed to obtain a scaled version of the number of retrial customers as the retrial time tends to zero, because the number of retrial customers explodes under this limiting regime. In this paper, a brief survey is provided on the major scaling limits of these models, and open problems are discussed. These limits can be used as approximations of complex systems with retrials. SN - 3142-7855 PB - Institute of Central Computation and Knowledge LA - English ER -
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@article{PhungDuc2026Retrial,
author = {Tuan Phung-Duc},
title = {Retrial Queues: Scaling Limits},
journal = {Journal of Systems Scalability},
year = {2026},
volume = {1},
number = {2},
pages = {39-42},
doi = {10.62762/JSS.2025.500072},
url = {https://www.icck.org/article/abs/JSS.2025.500072},
abstract = {Retrial queues arise in various applications such as call centers, services, and computer networks. The study of retrial queues is an important research branch of Queueing Theory. Retrial queues are characterized by the feature that customers who cannot receive service upon arrival do not queue but retry to enter the server after some random time. This makes the analysis of retrial queues more difficult than that of corresponding models without retrials. While the latter can be considered the limit of the former as the retrial time tends to infinity, some scaling limits are needed to obtain a scaled version of the number of retrial customers as the retrial time tends to zero, because the number of retrial customers explodes under this limiting regime. In this paper, a brief survey is provided on the major scaling limits of these models, and open problems are discussed. These limits can be used as approximations of complex systems with retrials.},
keywords = {scaling limits, fluid limit, diffusion limit, heavy traffic, retrial queues, networks},
issn = {3142-7855},
publisher = {Institute of Central Computation and Knowledge}
}
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