Beyond normality: A cross moment-stochastic user equilibrium model
Beyond normality: A cross moment-stochastic user equilibrium model
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DOI：
10.1016/j.trb.2015.01.005
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发表时间：
2015-11
影响因子：
6.8
通讯作者：
S. Ahipaşaoğlu;Rudabeh Meskarian;T. Magnanti;K. Natarajan
中科院分区：
文献类型：
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作者：
S. Ahipaşaoğlu;Rudabeh Meskarian;T. Magnanti;K. Natarajan
随机用户平衡（SUE）模型预测交通平衡流假设用户选择他们的感知最大效用路径（或感知最短路径），同时考虑到由于用户共享链接而产生的拥堵的影响。最近的工作分布鲁棒优化，特别是交叉矩（CMM）的选择模型的启发，我们开发了一个新的SUE模型，使用路径效用的均值和协方差信息，但不承担特定形式的分布。在这个模型中，通过最小化具有固定两个矩的所有分布的最坏情况下的预期成本，获得了对分布假设的鲁棒性。我们证明了在温和的条件下，CMM-SUE（交叉矩随机用户平衡）的存在性和唯一性。通过结合一个简单的投影梯度上升方法来评估路径选择概率与梯度下降方法找到流量，我们表明CMM-SUE是有效的可计算。CMM-SUE提供了建模灵活性和计算优势，例如众所周知的MNP-SUE（多项概率-随机用户均衡）模型，该模型需要分布（正态）假设来模拟重叠路径的相关性效应。特别是，它避免了使用模拟方法在基于分布的MNP-SUE模型的计算。初步的计算结果表明，CMM-SUE提供了一个实用的分布鲁棒替代MNP-SUE。
The Stochastic User Equilibrium (SUE) model predicts traffic equilibrium flow assuming that users choose their perceived maximum utility paths (or perceived shortest paths) while accounting for the effects of congestion that arise due to users sharing links. Inspired by recent work on distributionally robust optimization, specifically a Cross Moment (CMM) choice model, we develop a new SUE model that uses the mean and covariance information on path utilities but does not assume the particular form of the distribution. Robustness to distributional assumptions is obtained in this model by minimizing the worst-case expected cost over all distributions with fixed two moments. We show that under mild conditions, the CMM-SUE (Cross Moment-Stochastic User Equilibrium) exists and is unique. By combining a simple projected gradient ascent method to evaluate path choice probabilities with a gradient descent method to find flows, we show that the CMM-SUE is efficiently computable. CMM-SUE provides both modeling flexibility and computational advantages over approaches such as the well-known MNP-SUE (Multinomial Probit-Stochastic User Equilibrium) model that require distributional (normality) assumptions to model correlation effects from overlapping paths. In particular, it avoids the use of simulation methods employed in computations for the distribution-based MNP-SUE model. Preliminary computational results indicate that CMM-SUE provides a practical distributionally robust alternative to MNP-SUE.