- Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit
- Stochastic Models
- Volume | Issue number
- 29 | 4
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
Faculty of Science (FNWI)
- Amsterdam School of Economics Research Institute (ASE-RI)
Korteweg-de Vries Institute for Mathematics (KdVI)
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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