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.

Queues, infinite-server systems, Markov modulation, large deviations
Life Sciences (theme 5)
Operations Research Letters
Life Sciences and Health

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