Diffusion approximation of a special bandwidth sharing model via infinitesimal generators with a lifting-projection method

We consider a proposed unsolved conjecture of a special bandwidth-sharing model integrating streamings and file transfers as initiated in Kumar and Massoulié (2007). Using the infinitesimal generator approach, we demonstrate its diffusion approximation with a special time-scale separation parameter. To this end, we introduce a lifting-projection method, and exhibit a novel function to show the generator of a joint process converges to that of a univariate limiting file-transfer process, where the streaming flows are averaged out in heavy traffic.