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A dual price-based congestion control (DPCC) mechanism for optical burst switching (OBS) networks is proposed in this paper, which can achieve an optimal rate-reliability tradeoff by allocating proper network traffic and resources based on the idea of network utility maximization (NUM). The DPCC uses the congestion and reliability prices and feedback information to dynamically adjust the users' data sending rate and the end-to-end data transmission reliability in an OBS network. The performance of DPCC is evaluated and analyzed through simulations. Results verify that DPCC works very well in terms of its convergence and optimality. Moreover, compared with TCP, DPCC can achieve a maximum network utility, a parameter which can be used to reflect the overall user satisfaction degree in a network. DPCC is scalable due to its distributed nature.