AI 中文总结
研究大规模交通分配均衡模型，提出扰动效用马尔可夫均衡框架，开发扰动效用马尔可夫选择模型，将均衡表述为变分不等式问题，给出改进策略迭代等计算方法，实验证明框架可扩展且稳健。
AI 中文摘要
大规模交通分配需要行为合理且计算易处理的均衡模型。本文提出扰动效用马尔可夫均衡（PUME）框架，保留基于链路的马尔可夫交通均衡模型的可扩展性，扩展其在边界选择概率、无折扣网络负荷和一般链路交互设置中的适用性。首先开发扰动效用马尔可夫选择模型（PUMCM）作为行为基础，其通过凸盈余函数定义贝尔曼最优算子，推广现有加性随机效用（ARUM）马尔可夫选择模型，允许内部和边界选择概率。建立相应马尔可夫决策问题适定且产生恰当需求映射的条件。然后将均衡表述为对偶成本空间上的变分不等式（VI）问题，建立其存在性和唯一性。对于计算，开发用于网络负荷的改进策略迭代方法和用于计算均衡的保障加速元算法，二者全局收敛且数值性能良好。基准和合成网络实验表明该框架高度可扩展且对多种供需设置稳健。
英文摘要
Large-scale traffic assignment requires equilibrium models that are both behaviorally plausible and computationally tractable. This paper develops a perturbed utility Markovian equilibrium (PUME) framework that preserves the scalability of link-based Markovian traffic equilibrium models and extends their applicability to settings with boundary choice probabilities, undiscounted network loading, and general link interactions. As the behavioral basis of PUME, we first develop the perturbed utility Markovian choice model (PUMCM) in which the Bellman optimality operator is defined through a convex surplus function whose gradient directly yields the optimal policy. The model generalizes existing additive random utility (ARUM) Markovian choice models and admits both interior and boundary choice probabilities. Accordingly, unattractive links can receive zero flow without imposing ex ante choice-set restrictions as in existing ARUM models. We establish conditions under which the corresponding Markov decision problem is well posed and yields a proper demand mapping. We then formulate the equilibrium as a variational inequality (VI) problem on the dual cost space and establish its existence and uniqueness. Particularly, the VI formulation of PUME accommodates non-separable and asymmetric cost structures and thus offers a more flexible modeling framework than existing Markovian traffic equilibrium (MTE) models. For computation, we develop a modified policy iteration method for network loading and a safeguarded accelerated meta-algorithm for computing equilibrium. Both algorithms are proven to be globally convergent and have demonstrated satisfactory numerical performances. Experiments on benchmark and synthetic networks further show that the proposed framework is highly scalable and robust towards a wide variety of demand-supply settings.
