A Heavy-Traffic Limit of a Two-Station Fluid Model with Heavy-Tailed On/Off Sources, Feedback and Flexible Servers

Abstract: We consider a two-station fluid model that can be approximated under heavy-traffic by a reflected fractional Browian motion (rfBm) process on a convex polyhedron. Specifically, we prove a heavy-traffic limit theorem for a two single-server workstation fluid model with feedback and flexible servers. Flexibility here means that one of the servers is capable to help the other. The non-deterministic arrival process is generated by a large enough number of heavy-tailed 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.