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Zbl 1108.60074
Delgado, Rosario
A reflected fBm limit for fluid models with ON/OFF sources under heavy traffic. (English)
[J] Stochastic Processes Appl. 117, No. 2, 188-201 (2007). ISSN 0304-4149

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 2000:: *60K25 Queueing theory
60G15 Gaussian processes
90B22 Queues and service

Keywords: reflected fractional Brownian motion; queueing network; workload process

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