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Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit

Joke Blom, Koen De Turck (UGent) and Michel Mandjes
(2013) STOCHASTIC MODELS. 29(4). p.463-474
Author
Organization
Abstract
This article studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates (i) by a factor N and the rates (ij) of the background process by N1+E (for some E>0), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that N tends to . In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean.
Keywords
Infinite-server systems, Large deviations, Markov modulation, Queues, 60K25, MODELS, RANDOM ENVIRONMENT

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MLA
Blom, Joke, et al. “Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit.” STOCHASTIC MODELS, vol. 29, no. 4, 2013, pp. 463–74, doi:10.1080/15326349.2013.838511.
APA
Blom, J., De Turck, K., & Mandjes, M. (2013). Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit. STOCHASTIC MODELS, 29(4), 463–474. https://doi.org/10.1080/15326349.2013.838511
Chicago author-date
Blom, Joke, Koen De Turck, and Michel Mandjes. 2013. “Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit.” STOCHASTIC MODELS 29 (4): 463–74. https://doi.org/10.1080/15326349.2013.838511.
Chicago author-date (all authors)
Blom, Joke, Koen De Turck, and Michel Mandjes. 2013. “Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit.” STOCHASTIC MODELS 29 (4): 463–474. doi:10.1080/15326349.2013.838511.
Vancouver
1.
Blom J, De Turck K, Mandjes M. Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit. STOCHASTIC MODELS. 2013;29(4):463–74.
IEEE
[1]
J. Blom, K. De Turck, and M. Mandjes, “Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit,” STOCHASTIC MODELS, vol. 29, no. 4, pp. 463–474, 2013.
@article{5651784,
  abstract     = {{This article studies an infinite-server queue in a Markov environment, that is, an infinite-server queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates (i) by a factor N and the rates (ij) of the background process by N1+E (for some E>0), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that N tends to . In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean.}},
  author       = {{Blom, Joke and De Turck, Koen and Mandjes, Michel}},
  issn         = {{1532-6349}},
  journal      = {{STOCHASTIC MODELS}},
  keywords     = {{Infinite-server systems,Large deviations,Markov modulation,Queues,60K25,MODELS,RANDOM ENVIRONMENT}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{463--474}},
  title        = {{Rare event analysis of Markov-modulated infinite-server queues: a Poisson limit}},
  url          = {{http://doi.org/10.1080/15326349.2013.838511}},
  volume       = {{29}},
  year         = {{2013}},
}
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