Workshop on Mathematical Modeling and Analysis of Computer Networks

"Bandwidth-Sharing Networks in Overload"

Sem Borst
Alcatel-Lucent Bell Labs & Eindhoven University of Technology

Bandwidth-sharing networks as considered by Massoulie & Roberts provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Under mild assumptions, it has been established that a wide family of so-called alpha-fair bandwidth-sharing strategies achieve stability in such networks provided that no individual link is overloaded. In the talk we focus on alpha-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. The convergence of the scaled number of flows to the fluid limit is empirically validated through simulation experiments. 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. The results are illustrated for linear topologies and star networks as two important special cases. Finally, we briefly discuss extensions to models with user impatience.

Note: +Based on joint work with Regina Egorova (CWI & Eindhoven University of Technology) and Bert Zwart (Georgia Tech)