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 $\varepsilon$-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.

翻译：本文研究了带边约束的动态交通分配问题。首先，针对经典边延迟模型中容量约束交通模型动态均衡存在性的一个关键文献结果，我们给出了一个反例。该反例表明可行流空间不必是凸的，并进一步揭示了经典无限维变分不等式不适用于定义带边约束的动态均衡。基于流粒子在时空上可行ε偏离的概念，我们提出了一种新的带边约束动态均衡框架。在自然假设下，我们分别通过拟变分不等式和变分不等式来刻画由此产生的均衡。最后，针对容量约束的非凸情形，我们建立了带边约束动态均衡的首个存在性结果。