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.


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