Rare Event Analysis of Markov-Modulated Infinite-Server Queues: A Poisson Limit

Author: Blom Joke   De Turck Koen   Mandjes Michel  

Publisher: Taylor & Francis Ltd

ISSN: 1532-6349

Source: Stochastic Models, Vol.29, Iss.4, 2013-10, pp. : 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+ (for some > 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.