A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue

Abstract : The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distribu-tional properties of M , the number of molecules, under specific time-scaling; the background process is sped up by N α , the arrival rates are scaled by N , for N large. A functional central limit theorem is derived for M , which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on α is observed. For α ≤ 1 the parameters of the limiting process contain the deviation matrix associated with the background process.
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https://hal.archives-ouvertes.fr/hal-01426312
Contributor : Koen de Turck <>
Submitted on : Wednesday, January 4, 2017 - 1:23:33 PM
Last modification on : Thursday, April 5, 2018 - 12:30:05 PM
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D Anderson, J Blom, M Mandjes, H Thorsdottir, K de Turck. A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue. Methodology and Computing in Applied Probability, Springer Verlag, 2016, 18, pp.153 - 168. ⟨10.1007/s11009-014-9405-8⟩. ⟨hal-01426312⟩

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