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A large deviations principle for infinite-server queues in a random environment

(2016) QUEUEING SYSTEMS. 82(1-2). p.199-235
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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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Please use this url to cite or link to this publication:

MLA
Jansen, Hermanus Marinus et al. “A Large Deviations Principle for Infinite-server Queues in a Random Environment.” QUEUEING SYSTEMS 82.1-2 (2016): 199–235. Print.
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.
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.
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.
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. Springer Nature; 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://dx.doi.org/10.1007/s11134-015-9470-x},
  volume       = {82},
  year         = {2016},
}

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