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Network utility maximization (NUM) provides an important perspective to conduct rate allocation where optimal performance, in terms of maximal aggregate bandwidth utility, is generally achieved such that each source adaptively adjusts its transmission rate. Behind most of the recent literature on NUM, common assumptions are that traffic flows are elastic and that their utility functions are strictly concave. This provides design simplicity but, in practice, limits the applicability of resulting protocols, in that severe QoS problems may be encountered when bandwidth is shared by inelastic flows. This paper investigates the problem of distributively allocating data transmission rates to multiclass services, both elastic and inelastic, and overcomes the restrictive and often unrealistic assumptions. The proposed method is based on the Lagrangian Relaxation for a dual formulation that decomposes the higher dimension NUM into a number of subproblems. We use a novel Surrogate Subgradient based stochastic method to solve the dual problem. Unlike the ordinary subgradient methods, surrogate subgradient can compute optimal prices without the need to solve all the subproblems. For the lower dimension, nonlinear and nonconvex subproblems we use a hybrid particle swarm optimization (PSO) and sequential quadratic programming (SQP) method, where the objective is to achieve fast convergence as well as accuracy. We demonstrate the efficiency of the proposed rate allocation algorithm, in terms maintaining QoS for multiclass services, and validate its scalability and accuracy for large scale flows.