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为了解决不同属性用户路径选择相互影响的混合交通均衡分配问题,利用变分不等式描述了混合网络中用户平衡UE、系统最优SO、古诺-纳什均衡CN这3类用户的路径选择行为。分别采用基于路段的对角化算法和基于路径的双重投影算法对混合网络均衡模型进行求解,以Sioux Falls网络为例,从计算效率、收敛精度2个方面对其进行对比分析。分析结果表明:对角化算法前期收敛较快,但拖尾严重,很难通过多次迭代达到较高的精度;双重投影算法即使经过上千次迭代,精度仍可提高。在多种混合比例下,SO、CN用户控制流量比越大,系统总阻抗越小,而SO用户流量比低于0.5时,系统总阻抗下降很快,随着流量比增大,下降速度随之变缓。
In order to solve the problem of balanced traffic assignment among users with different attributes, the path selection behaviors of user-balanced UEs, system optimal SOs and Cournot-Nash equilibrium CNs in hybrid networks are described using variational inequalities. Based on the diagonalization algorithm based on link and the dual projection algorithm based on path, the hybrid network equilibrium model is solved respectively. Taking Sioux Falls network as an example, comparative analysis is made from two aspects of computational efficiency and convergence precision. The analysis results show that the algorithm of diagonalization converges fast in the early stage, but the trailing is severe, which makes it difficult to achieve high precision through multiple iterations. The double projection algorithm can improve the accuracy even after thousands of iterations. Under various mixing ratios, the total system impedance decreases with the increase of SO / CN user control flow rate, while the total system impedance decreases rapidly with SO user flow ratio lower than 0.5. With the increase of flow rate ratio, Slower.