Network Stability Under Alpha Fair Bandwidth Allocation With General File Size Distribution

Abstract—Rate allocation among a fixed set of end-to-end con-nections in the Internet is carried out by congestion control, which has a well established model: it optimizes a concave network utility, a particular case of which is the alpha-fair bandwidth allocation. This paper studies the slower dynamics of connections themselves, that arrive randomly in the network and are served at the allo-cated rate. It has been shown that under the condition that the mean offered load at each link is less than its capacity, the resulting queueing system is stochastically stable, for the case of exponen-tially distributed file-sizes. The conjecture that the result holds for general file-size distributions has remained open, and is very rel-evant since heavy-tailed distributions are often the best models of Internet file sizes. In this paper, building on existing fluid models of the system, we use a partial differential equation to characterize the dynamics. The equation keeps track of residual file size an