Convergence to multi-resource fairness under end-to-end window control

Abstract

The paper relates to multi-resource sharing between flows with heterogeneous requirements as arises in networks with wireless links or software routers implementing network function virtualization. Bottleneck max fairness (BMF) is a sharing objective in this context with good performance. The paper shows that BMF results when local fairness is imposed at each resource while flow rates are controlled by an end-to-end window. We analytically prove convergence to BMF under a fluid model when flows share a network limited to 2 resources while numerical results confirm BMF convergence for larger networks. Simulation results illustrate the impact of packetized transmission.