  This paper considers the optimization-based traffic allocation problem among
multiple end points in connectionless networks. The network utility function is
modeled as a non-concave function, since it is the best description of the
quality of service perceived by users with inelastic applications, such as
video and audio streaming. However, the resulting non-convex optimization
problem, is challenging and requires new analysis and solution techniques. To
overcome these challenges, we first propose a hierarchy of problems whose
optimal value converges to the optimal value of the non-convex optimization
problem as the number of moments tends to infinity. From this hierarchy of
problems, we obtain a convex relaxation of the original non-convex optimization
problem by considering truncated moment sequences. For solving the convex
relaxation, we propose a fully distributed iterative algorithm, which enables
each node to adjust its date allocation/ rate adaption among any given set of
next hops solely based on information from the neighboring nodes. Moreover, the
proposed traffic allocation algorithm converges to the optimal value of the
convex relaxation at a $O(1/K)$ rate, where $K$ is the iteration counter, with
a bounded optimality. At the end of this paper, we perform numerical
simulations to demonstrate the soundness of the developed algorithm.
