论文标题
侧限制的动态交通平衡
Side-Constrained Dynamic Traffic Equilibria
论文作者
论文摘要
我们研究动态的交通分配。我们首先对文献中的关键结果进行反示例，内容涉及在经典边缘 - 延迟模型中为体积受限的流量模型存在动态平衡。我们的反示例表明，可行的流动空间不必是凸，它进一步揭示了经典的无限尺寸变分不等式不适合定义侧面构成的动态平衡。我们基于空间和时间上流动粒子的可行$γ$降低的概念，为侧面约束动态平衡提出了一个新的框架。在自然假设下，我们分别通过准差异和变异不等式来表征所得的平衡。最后，我们为非凸构设置的侧面约束动态平衡建立了第一个存在结果。
We study dynamic traffic assignment with side-constraints. We first give a counter-example to a key result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical edge-delay model. Our counter-example shows that the feasible flow space need not be convex and it further reveals that classical infinite dimensional variational inequalities are not suited for the definition of side-constrained dynamic equilibria. We propose a new framework for side-constrained dynamic equilibria based on the concept of feasible $γ$-deviations of flow particles in space and time. Under natural assumptions, we characterize the resulting equilibria by means of quasi-variational and variational inequalities, respectively. Finally, we establish first existence results for side-constrained dynamic equilibria for the non-convex setting of volume-constraints.
