- Author
- Dieter Fiems (UGent)
- Organization
- Abstract
- We consider the M/D/1 retrial queueing system with constant retrial times, which makes up a natural abstraction for optical fibre delay line buffers. Drawing on a time-discretisation approach and on an equivalence with polling systems, we find explicit expressions for the distribution of the number of retrials, and the probability generating function of the number of customers in orbit. While the state space of the queueing system at hand is complicated, the results are strikingly simple. The number of retrials follows a geometric distribution, while the orbit size decomposes into two independent random variables: the system content of the M/D/1 queue at departure times and the orbit size of the M/D/1 retrial queue when the server is idle. We finally obtain explicit expressions for the retrial rate after a departure and for the distribution of the time until the nth retrial after a departure.
- Keywords
- APPROXIMATION METHOD, STABILITY, BEHAVIOR, SYSTEM, Retrial queue, Polling system, Probability generating function
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01H3YGPQWQPCQHQG7BV610GCDQ
- MLA
- Fiems, Dieter. “Retrial Queues with Constant Retrial Times.” QUEUEING SYSTEMS, vol. 103, no. 3–4, 2023, pp. 347–65, doi:10.1007/s11134-022-09866-4.
- APA
- Fiems, D. (2023). Retrial queues with constant retrial times. QUEUEING SYSTEMS, 103(3–4), 347–365. https://doi.org/10.1007/s11134-022-09866-4
- Chicago author-date
- Fiems, Dieter. 2023. “Retrial Queues with Constant Retrial Times.” QUEUEING SYSTEMS 103 (3–4): 347–65. https://doi.org/10.1007/s11134-022-09866-4.
- Chicago author-date (all authors)
- Fiems, Dieter. 2023. “Retrial Queues with Constant Retrial Times.” QUEUEING SYSTEMS 103 (3–4): 347–365. doi:10.1007/s11134-022-09866-4.
- Vancouver
- 1.Fiems D. Retrial queues with constant retrial times. QUEUEING SYSTEMS. 2023;103(3–4):347–65.
- IEEE
- [1]D. Fiems, “Retrial queues with constant retrial times,” QUEUEING SYSTEMS, vol. 103, no. 3–4, pp. 347–365, 2023.
@article{01H3YGPQWQPCQHQG7BV610GCDQ,
abstract = {{We consider the M/D/1 retrial queueing system with constant retrial times, which makes up a natural abstraction for optical fibre delay line buffers. Drawing on a time-discretisation approach and on an equivalence with polling systems, we find explicit expressions for the distribution of the number of retrials, and the probability generating function of the number of customers in orbit. While the state space of the queueing system at hand is complicated, the results are strikingly simple. The number of retrials follows a geometric distribution, while the orbit size decomposes into two independent random variables: the system content of the M/D/1 queue at departure times and the orbit size of the M/D/1 retrial queue when the server is idle. We finally obtain explicit expressions for the retrial rate after a departure and for the distribution of the time until the nth retrial after a departure.}},
author = {{Fiems, Dieter}},
issn = {{0257-0130}},
journal = {{QUEUEING SYSTEMS}},
keywords = {{APPROXIMATION METHOD,STABILITY,BEHAVIOR,SYSTEM,Retrial queue,Polling system,Probability generating function}},
language = {{eng}},
number = {{3-4}},
pages = {{347--365}},
title = {{Retrial queues with constant retrial times}},
url = {{http://doi.org/10.1007/s11134-022-09866-4}},
volume = {{103}},
year = {{2023}},
}
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