Asymptotics of waiting time distributions in the accumulating priority queue
- Author
- Joris Walraevens (UGent) , Thomas Van Giel (UGent) , Stijn De Vuyst (UGent) and Sabine Wittevrongel (UGent)
- Organization
- Abstract
- We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by Kleinrock in the 60s-he coined it time-dependent priority-to diversify waiting time objectives of different classes in a paramaterized way. It also avoids the typical starvation problem of regular priority queues. All customers build up priority linearly while waiting in the queue but at a class-dependent rate. At a service opportunity epoch, the customer with highest priority present is served. Stanford and colleagues recently calculated the Laplace-Stieltjes Transform (LST) of the waiting time distributions of the different classes, but only invert these LSTs numerically. In this paper, we analytically calculate the asymptotics of the corresponding distributions from these LSTs. We show that different singularities of the LST can play a role in the asymptotics, depending on the magnitude of service differentiation between both classes.
- Keywords
- Accumulating priority, Dominant singularity analysis, TASKS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-01H2B065EVJPC5VVW447CJEFGT
- MLA
- Walraevens, Joris, et al. “Asymptotics of Waiting Time Distributions in the Accumulating Priority Queue.” QUEUEING SYSTEMS, vol. 101, no. 3–4, 2022, pp. 221–44, doi:10.1007/s11134-022-09839-7.
- APA
- Walraevens, J., Van Giel, T., De Vuyst, S., & Wittevrongel, S. (2022). Asymptotics of waiting time distributions in the accumulating priority queue. QUEUEING SYSTEMS, 101(3–4), 221–244. https://doi.org/10.1007/s11134-022-09839-7
- Chicago author-date
- Walraevens, Joris, Thomas Van Giel, Stijn De Vuyst, and Sabine Wittevrongel. 2022. “Asymptotics of Waiting Time Distributions in the Accumulating Priority Queue.” QUEUEING SYSTEMS 101 (3–4): 221–44. https://doi.org/10.1007/s11134-022-09839-7.
- Chicago author-date (all authors)
- Walraevens, Joris, Thomas Van Giel, Stijn De Vuyst, and Sabine Wittevrongel. 2022. “Asymptotics of Waiting Time Distributions in the Accumulating Priority Queue.” QUEUEING SYSTEMS 101 (3–4): 221–244. doi:10.1007/s11134-022-09839-7.
- Vancouver
- 1.Walraevens J, Van Giel T, De Vuyst S, Wittevrongel S. Asymptotics of waiting time distributions in the accumulating priority queue. QUEUEING SYSTEMS. 2022;101(3–4):221–44.
- IEEE
- [1]J. Walraevens, T. Van Giel, S. De Vuyst, and S. Wittevrongel, “Asymptotics of waiting time distributions in the accumulating priority queue,” QUEUEING SYSTEMS, vol. 101, no. 3–4, pp. 221–244, 2022.
@article{01H2B065EVJPC5VVW447CJEFGT,
abstract = {{We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by Kleinrock in the 60s-he coined it time-dependent priority-to diversify waiting time objectives of different classes in a paramaterized way. It also avoids the typical starvation problem of regular priority queues. All customers build up priority linearly while waiting in the queue but at a class-dependent rate. At a service opportunity epoch, the customer with highest priority present is served. Stanford and colleagues recently calculated the Laplace-Stieltjes Transform (LST) of the waiting time distributions of the different classes, but only invert these LSTs numerically. In this paper, we analytically calculate the asymptotics of the corresponding distributions from these LSTs. We show that different singularities of the LST can play a role in the asymptotics, depending on the magnitude of service differentiation between both classes.}},
author = {{Walraevens, Joris and Van Giel, Thomas and De Vuyst, Stijn and Wittevrongel, Sabine}},
issn = {{0257-0130}},
journal = {{QUEUEING SYSTEMS}},
keywords = {{Accumulating priority,Dominant singularity analysis,TASKS}},
language = {{eng}},
number = {{3-4}},
pages = {{221--244}},
title = {{Asymptotics of waiting time distributions in the accumulating priority queue}},
url = {{http://doi.org/10.1007/s11134-022-09839-7}},
volume = {{101}},
year = {{2022}},
}
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