This article 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 $N$ and the rates $\nu_{ij}$ of the background process by $N^{1+\vareps}$ (for some $\vareps > 0$), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that $N$ tends to $\infty$. In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean.

inifinite-server systems, large deviations, Markov modulation, queues
Queueing theory (msc 60K25)
Life Sciences (theme 5)
Taylor&Francis
dx.doi.org/10.1080/15326349.2013.838511
Stochastic Models
Life Sciences and Health

Blom, J.G, de Turck, K, & Mandjes, M.R.H. (2013). Rare event analysis of Markov-modulated infinite-server queues: A Poisson limit. Stochastic Models, 29(4), 463–474. doi:10.1080/15326349.2013.838511