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math.PR2016★ 1 cited
Refined large deviations asymptotics for Markov-modulated infinite-server systems
Joke Blom, Koen De Turck, Michel Mandjes
Many networking-related settings can be modeled by Markov-modulated infinite-server systems. In such models, the customers' arrival rates and service rates are modulated by a Marko…
math.PR2016
Functional central limit theorems for Markov-modulated infinite-server systems
Joke Blom, Koen de Turck, Michel Mandjes
In this paper we study the Markov-modulated M/M/ queue, with a focus on the correlation structure of the number of jobs in the system. The main results describe the system'…
math.PR2014★ 19 cited
Analysis of Markov-modulated infinite-server queues in the central-limit regime
Joke Blom, Koen De Turck, Michel Mandjes
This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1…