Bandwidth-sharing networks in overload

In the present talk we focus on α-fair bandwidth-sharing networks where the load on one or several of the links exceeds the capacity. In order to characterize the overload behavior, we examine the fluid limit, which emerges from a suitably scaled version of the number of flows of the various classes. We prove that the fluid limit is a linear function of time, and derive a fixed-point equation for the corresponding asymptotic growth rates. It is further shown that the fixed-point solution is also a solution to a related strictly concave optimization problem, and hence unique. We use the fixed-point equation to investigate the impact of the traffic intensities and the variability of the flow sizes on the asymptotic growth rates.