Heavy-traffic limit for a feed-forward fluid model with heterogeneous heavy-tailed On/Off sources

We consider a multi-station fluid model with arrivals generated by a large number of non-homogeneous heavy-tailed On/Off sources. If the model is feed-forward in the sense that fluid cannot flow from one station to other with lighter tail distributions, we prove that under heavy-traffic, the scaled workload converges in distribution to a reflected fractional Brownian motion process with a multi-dimensional Hurst parameter. As an application, we analyze the impact of having independent streams with variable parameters in high-speed telecommunication networks, on the asymptotic behavior of the maximum queue length.