| Abstract |
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 λ i by a factor N and the rates ν ij of the background process by N 1+ϵ (for some ϵ > 0), the focus is on the tail probabilities of the number of customers in the system, in the asymptotic regime that N tends to ∞. In particular, it is shown that the logarithmic asymptotics correspond to those of a Poisson distribution with an appropriate mean.
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