A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic

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We consider a family of non-deterministic fluid models that can be approximated under heavy traffic conditions by a multidimensional reflected fractional Brownian motion (rfBm). Specifically, we prove a heavy traffic limit theorem for multi-station fluid models with feedback and non-deterministic arrival process generated by a large enough number of heavy tailed ON/OFF sources, say N. Scaling in time by a factor r and in state space conveniently, and letting N and r approach infinity (in this order) we prove that the scaled immediate workload process converges in some sense to a rfBm. © 2006 Elsevier Ltd. All rights reserved.
Idioma originalEnglish
Pàgines (de-a)188-201
RevistaStochastic Processes and their Applications
Volum117
DOIs
Estat de la publicacióPublicada - 1 de febr. 2007

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