Network-on-Chip (NoC) has been proposed as an attractive alternative to traditional dedicated busses in order to achieve modularity and high performance in the future System-on-Chip (SoC) designs. Recently, endto-end congestion control has gained popularity in the design process of network-on-chip based SoCs. This paper addresses a congestion control scenario under traffic mixture which is comprised of Best Effort (BE) traffic or elastic flow and Guaranteed Service (GS) traffic or inelastic flow. We model the desired BE source rates as the solution to a rate-sum maximization problem which is constrained with link capacities while preserving GS traffic services requirements at the desired level. We proposed an iterative algorithm as the solution to the maximization problem which has the advantage of low complexity and fast convergence. The proposed algorithm may be implemented by a centralized controller with low computation and communication overhead.