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Overflow asymptotics for an infinite-server queue in different random environments

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Abstract
In this talk, we will consider an infinite-server queue in two different random environments. A random environment is represented by a stochastic background process, which modulates both the arrival process and the service process of the queue. The two different background processes that we will consider are a continuous-time Markov chain and a reflected Brownian motion. We will look at a queue that has to divide its attention between allowing customers to enter and serving the customers. The background process determines how much attention goes to either task. We will study the probability that the number of jobs in the system becomes unusually large, i.e. we will study overflow. Scaling the arrival process and using large deviations techniques, we compute the rate functions that describe the exponential rate of convergence of the overflow probabilities in the respective random environments. Surprisingly, the rate functions turn out to be the same for both random environments. Apparently, two very different modulating processes may lead to the same large deviations principle.
Keywords
overflow, infinite-server systems, queues, random environment, large deviations

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Citation

Please use this url to cite or link to this publication:

MLA
Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, et al. “Overflow Asymptotics for an Infinite-server Queue in Different Random Environments.” 8th Young European Queueing Theorists Workshop, Book of Abstracts. 2014. Print.
APA
Jansen, H. M., Mandjes, M., De Turck, K., & Wittevrongel, S. (2014). Overflow asymptotics for an infinite-server queue in different random environments. 8th Young European Queueing Theorists workshop, Book of Abstracts. Presented at the 8th Young European Queueing Theorists workshop.
Chicago author-date
Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, and Sabine Wittevrongel. 2014. “Overflow Asymptotics for an Infinite-server Queue in Different Random Environments.” In 8th Young European Queueing Theorists Workshop, Book of Abstracts.
Chicago author-date (all authors)
Jansen, Hermanus Marinus, Michel Mandjes, Koen De Turck, and Sabine Wittevrongel. 2014. “Overflow Asymptotics for an Infinite-server Queue in Different Random Environments.” In 8th Young European Queueing Theorists Workshop, Book of Abstracts.
Vancouver
1.
Jansen HM, Mandjes M, De Turck K, Wittevrongel S. Overflow asymptotics for an infinite-server queue in different random environments. 8th Young European Queueing Theorists workshop, Book of Abstracts. 2014.
IEEE
[1]
H. M. Jansen, M. Mandjes, K. De Turck, and S. Wittevrongel, “Overflow asymptotics for an infinite-server queue in different random environments,” in 8th Young European Queueing Theorists workshop, Book of Abstracts, Eindhoven, the Netherlands, 2014.
@inproceedings{6848650,
  abstract     = {In this talk, we will consider an infinite-server queue in two different random environments. A random environment is represented by a stochastic background process, which modulates both the arrival process and the service process of the queue. The two different background processes that we will consider are a continuous-time Markov chain and a reflected Brownian motion. We will look at a queue that has to divide its attention between allowing customers to enter and serving the customers. The background process determines how much attention goes to either task. We will study the probability that the number of jobs in the system becomes unusually large, i.e. we will study overflow. Scaling the arrival process and using large deviations techniques, we compute the rate functions that describe the exponential rate of convergence of the overflow probabilities in the respective random environments. Surprisingly, the rate functions turn out to be the same for both random environments. Apparently, two very different modulating processes may lead to the same large deviations principle.},
  author       = {Jansen, Hermanus Marinus and Mandjes, Michel and De Turck, Koen and Wittevrongel, Sabine},
  booktitle    = {8th Young European Queueing Theorists workshop, Book of Abstracts},
  keywords     = {overflow,infinite-server systems,queues,random environment,large deviations},
  language     = {eng},
  location     = {Eindhoven, the Netherlands},
  title        = {Overflow asymptotics for an infinite-server queue in different random environments},
  year         = {2014},
}