Heavy-Traffic Insensitive Bounds for Weighted Proportionally Fair Bandwidth Sharing Policies

We consider a connection-level model proposed by Massoulié and Roberts for bandwidth sharing among file transfer flows in communication network. study weighted proportionally fair policies establish explicit-form bounds on the sum of expected numbers different routes heavy traffic. The are linear number critically loaded links network, they hold class phase-type file-size distributions; that is, heavy-traffic insensitive to distributions this class. Our approach is Lyapunov drift based, which from widely used diffusion approximation approach. A key technique we develop construct novel inner product state space, then allows us obtain multiplicative type state-space collapse steady state. Furthermore, result implies interchange limits as byproduct unweighted policy under distributions, demonstrating insensitivity stationary distribution.