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 $\lambda_i$ by a factor $N$, tail probabilities are examined when letting $N$ tend to $\infty$; non-standard large deviations results are obtained. An importance-sampling based estimation algorithm is proposed, that is proven to be logarithmically efficient.

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Operations Research Letters
Evolutionary Intelligence

Blom, J., & Mandjes, M. (2013). A large-deviations analysis of Markov-modulated infinite-server queues. Operations Research Letters, 41(3), 220–225.