A large deviations principle for infinite-server queues in a random environment
- Author
- Hermanus Marinus Jansen (UGent) , Michel Mandjes, Koen De Turck (UGent) and Sabine Wittevrongel (UGent)
- Organization
- Abstract
- This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements, and the server work rate are modulated by a general càdlàg stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.
- Keywords
- infinite-server queue, random environment, modulation, large deviations principle
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8507348
- MLA
- Jansen, Hermanus Marinus, et al. “A Large Deviations Principle for Infinite-Server Queues in a Random Environment.” QUEUEING SYSTEMS, vol. 82, no. 1–2, Springer Nature, 2016, pp. 199–235, doi:10.1007/s11134-015-9470-x.
- APA
- Jansen, H. M., Mandjes, M., De Turck, K., & Wittevrongel, S. (2016). A large deviations principle for infinite-server queues in a random environment. QUEUEING SYSTEMS, 82(1–2), 199–235. https://doi.org/10.1007/s11134-015-9470-x
- Chicago author-date
- Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, and Sabine Wittevrongel. 2016. “A Large Deviations Principle for Infinite-Server Queues in a Random Environment.” QUEUEING SYSTEMS 82 (1–2): 199–235. https://doi.org/10.1007/s11134-015-9470-x.
- Chicago author-date (all authors)
- Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, and Sabine Wittevrongel. 2016. “A Large Deviations Principle for Infinite-Server Queues in a Random Environment.” QUEUEING SYSTEMS 82 (1–2): 199–235. doi:10.1007/s11134-015-9470-x.
- Vancouver
- 1.Jansen HM, Mandjes M, De Turck K, Wittevrongel S. A large deviations principle for infinite-server queues in a random environment. QUEUEING SYSTEMS. 2016;82(1–2):199–235.
- IEEE
- [1]H. M. Jansen, M. Mandjes, K. De Turck, and S. Wittevrongel, “A large deviations principle for infinite-server queues in a random environment,” QUEUEING SYSTEMS, vol. 82, no. 1–2, pp. 199–235, 2016.
@article{8507348,
abstract = {{This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements, and the server work rate are modulated by a general càdlàg stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.}},
author = {{Jansen, Hermanus Marinus and Mandjes, Michel and De Turck, Koen and Wittevrongel, Sabine}},
issn = {{0257-0130}},
journal = {{QUEUEING SYSTEMS}},
keywords = {{infinite-server queue,random environment,modulation,large deviations principle}},
language = {{eng}},
number = {{1-2}},
pages = {{199--235}},
publisher = {{Springer Nature}},
title = {{A large deviations principle for infinite-server queues in a random environment}},
url = {{http://doi.org/10.1007/s11134-015-9470-x}},
volume = {{82}},
year = {{2016}},
}
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