A large-deviations analysis of Markov-modulated infinite-server queues

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