The proportionality condition is a standard approach to dealing with the non-uniqueness issue in the user equilibrium (UE) traffic assignment problems (TAP). Although the proportionality condition can reduce the degree of arbitrariness, it remains unclear how much arbitrariness remains and whether it can meaningfully affect model outcomes and relevant decisions that depend on them. The answers to these questions are impeded by the lack of an efficient algorithm that can find the exact maximum entropy UE path flow solution for networks of practical size. In this paper, we fill this gap by developing a high-performance augmented Lagrangian algorithm that effectively exploits the special problem structure. Our numerical results reveal that there are a considerable number of links with non-negligible arbitrariness in the solution generated by the proportionality condition, and that this problem becomes worse if the level of congestion increases in the network. Since about a decade ago, many practitioners have relied on state-of-the-art traffic assignment tools based on the proportionality condition to perform select link analysis, among other applications. The results reported herein are a reminder that their toolbox may need reevaluation and perhaps an upgrade.

中文翻译：

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2 阶比例是否足够好来近似用户均衡流量分配中最可能的路径流？


比例条件是处理用户均衡（UE）流量分配问题（TAP）中非唯一性问题的标准方法。尽管比例条件可以降低任意性程度，但仍不清楚任意性仍然存在多少，以及它是否能够对模型结果和依赖于它们的相关决策产生有意义的影响。由于缺乏有效的算法来为实际规模的网络找到准确的最大熵 UE 路径流解决方案，这些问题的答案受到阻碍。在本文中，我们通过开发一种有效利用特殊问题结构的高性能增强拉格朗日算法来填补这一空白。我们的数值结果表明，比例条件生成的解中存在相当多的具有不可忽略的任意性的链接，并且如果网络中的拥塞程度增加，这个问题就会变得更糟。自大约十年前以来，许多从业者依赖基于比例条件的最先进的流量分配工具来执行选择链接分析以及其他应用。本文报告的结果提醒人们，他们的工具箱可能需要重新评估，甚至可能需要升级。