This paper considers optimal rate control and routing schemes for multipath networks which can be formulated as multipath network utility maximization problems. In these schemes, maximizing the aggregated user utility over the network with multipath routes under the link capacity constraints is the objective of utility maximization problems. By adopting the Lagrangian method, sub-problems for users and paths are deduced and interpreted from an economic point of view. In order to obtain the optimal rate allocation, a novel distributed primal-dual algorithm is proposed, and the performance is evaluated through simulations under two different fairness concepts. Moreover, window-based flow control scheme is also presented since it is more convenient to realize in practical end-to-end implementation than the rate control scheme
