- A Central Limit Theorem for Markov-Modulated Infinite-Server Queues
- Lecture Notes in Computer Science
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
This paper 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 λ i by a factor N and the rate q ij of the background process by a factor N α , with α ∈ ℝ + , we establish a central limit theorem as N tends to ∞. We find different scaling regimes, based on the value of α. Remarkably, for α < 1, we find a central limit theorem with a non-square-root scaling but rather with N α/2; in the expression for the variance deviation matrices appear.
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- Proceedings title: Analytical and Stochastic Modeling Techniques and Applications: 20th International Conference, ASMTA 2013,
Ghent, Belgium, July 8-10, 2013, Proceedings
Place of publication: Berlin
Editors: A. Dudin, K. De Turck
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