Multipath networks allow each source to send packets from it to its destination over multiple paths, which increases the available bandwidth and throughput for source-destination pairs. Recently, a variety of flow control schemes have been presented for multipath networks to achieve optimal resource allocation. Unfortunately, much of the investigation focused on elastic traffic with controllable packet injection rates. Networks have witnessed an increase in real-time traffic (voice and video), which are inelastic. We consider resource allocation for heterogeneous traffic in multipath networks and formulate an optimization problem, which is intrinsically difficult nonconvex. In order to address the aforementioned issue and obtain the optimum, we approximate an equivalent problem of the original optimization problem to a strictly convex problem and present a primal-dual resource allocation algorithm for the approximation problem, which converges to an optimal solution satisfying the Karush-Kuhn-Tucker conditions of the original problem. We evaluate its convergence performance through theoretical analysis and illustrate it with numerical examples.OPTIMAL RESOURCE ALLOCATION FOR HETEROGENEOUS TRAFFIC 85 a significant drop in the QoS. The resource allocation on these inelastic traffic has received much attention recently in single-path networks (e.g., [12][13][14]) but very little in multipath networks.Meanwhile, the coexistence of elastic and inelastic traffic has been widely investigated in singlepath wired networks [13][14][15][16] and interesting schemes for resource allocation have been presented. Furthermore, the integration of both elastic and inelastic traffic is also studied in single-hop wireless systems in [17][18][19]; however, with the restriction of every traffic having a single route. As using multipath could aggregate the bandwidth of the transmission paths between the communicating endpoints, multipath networks become a novel approach to improve the performance of increasingly bandwidth-hungry applications, such as real-time inelastic traffic [3]. Thus, it is very significant to study the coexistence of inelastic and elastic traffic in multipath networks and investigate optimal resource allocation for these traffic, so as to satisfy the QoS requirements of real-time traffic while achieving the objective of utility maximization.In this paper, we consider the integration of elastic and inelastic traffic in multipath networks, and investigate the optimal resource allocation for heterogeneous traffic based on the idea of multipath network utility maximization, which applies utility-based method from economics into the area of bandwidth allocation in multipath networks. We first formulate the resource allocation model for heterogeneous traffic that incorporates both elastic and inelastic traffic in multipath networks, which is an intrinsically difficult problem of nonconvex optimization. In order to obtain the optimum, we approximate an equivalent problem of the original optimization problem to a strictly ...