This study proposes a new framework to solve the road network evacuation problem, considering a dynamic allocation of evacuees to shelters. Although many studies have been performed on this problem with static settings, there are few studies in the literature that address this problem in a dynamic context. We couple and solve the dynamic traffic assignment (DTA) and dynamic shelter allocation problem (SAP) using agent-based dynamic simulation. The model for the SAP aims to satisfy system operator interests by determining the best shelters for evacuees, and evacuees tend to reach their shelters as fast as possible. We validate our methodology on the real network of Luxembourg City and evaluate its performance in front of one of the advanced methods in the literature. The results show that calculating dynamic shelter allocation improves mean evacuation time and significantly reduces the network clearance time compared to the methods with fixed shelter allocation plans.