Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit
| Authors |
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| Publication date | 2013 |
| Journal | Stochastic Models |
| Volume | Issue number | 29 | 4 |
| Pages (from-to) | 463-474 |
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| 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. |
| Document type | Article |
| Language | English |
| Published at |
https://doi.org/10.1080/15326349.2013.838511
(Final published version)
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