A Central Limit Theorem for Markov-Modulated Infinite-Server Queues
نویسندگان
چکیده
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 λi by a factor N and the rate qij of the background process by a factor N, 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; in the expression for the variance deviation matrices appear.
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