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ABSTRACT We consider a twostation fluid model that can be approximated under heavytraffic by a reflected fractional Browian motion (rfBm) process on a convex polyhedron. Specifically, we prove a heavytraffic limit theorem for a two singleserver workstation fluid model with feedback and flexible servers. Flexibility here means that one of the servers is capable to help the other. The nondeterministic arrival process is generated by a large enough number of heavytailed On/Off sources, N. We introduce the adequate definition of workload, and scaling conveniently by a factor r and by N, and letting N and r approach infinity (in this order), we prove that the scaled workload process converges to a rfBm on a convex polyhedron. 
KEYWORDS fluid network, flexible servers, reflected fractional Brownian motion, convex polyhedron, On/Off sources, workload process, heavytraffic limit, Skorokhod problem 
REFERENCES [1] R. Delgado, A reflected fBm limit for fluid models with ON/OFF sources under heavytraffic, Stochastic Processes and Their Applications 117, 2007, pp. 188201. [1] R. Delgado, A reflected fBm limit for fluid models with ON/OFF sources under heavytraffic, Stochastic Processes and Their Applications 117, 2007, pp. 188201. 
Cite this paper Rosario Delgado. (2016) A HeavyTraffic Limit of a TwoStation Fluid Model with HeavyTailed On/Off Sources, Feedback and Flexible Servers. International Journal of Mathematical and Computational Methods, 1, 149158 
