Before revision: We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network , and we study weighted proportionally fair sharing policies where the weights represent the relative importance of flows on different routes. We are interested in characterizing performance in the heavy-traffic regime. Existing work on this problem has focused on diffusion approximations, which were first studied by Kang et al. (2009). However, except for the case where the weights of all the routes are equal, the steady-state distribution of the limiting diffusion process is unknown and thus there are no explicit-form characterizations, even when exponential file size distributions are assumed.
After revision: We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network , and we study weighted proportionally fair sharing policies and establish explicit-form characterizations, even when exponential file size distributions are assumed.