Abstract
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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References
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Blom, J., De Turck, K., Mandjes, M. (2013). A Central Limit Theorem for Markov-Modulated Infinite-Server Queues. In: Dudin, A., De Turck, K. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2013. Lecture Notes in Computer Science, vol 7984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39408-9_7
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DOI: https://doi.org/10.1007/978-3-642-39408-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39407-2
Online ISBN: 978-3-642-39408-9
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