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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.
60K25Queueing theory
60G15Gaussian processes
90B22Queues and service (optimization)