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

Rosario Delgado

Stochastic Processes and their Applications, 2007, vol. 117, issue 2, 188-201

Abstract: 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.

Keywords: Reflected; fractional; Brownian; motion; Fluid; model; Queueing; network; Workload; process; On-off; sources; Heavy; traffic (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (9)

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