## A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic.(English)Zbl 1108.60074

Summary: 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 an rfBm.

### MSC:

 60K25 Queueing theory (aspects of probability theory) 60G15 Gaussian processes 90B22 Queues and service in operations research
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### References:

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