This study proposed a new framework to solve the 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. The proposed framework couples and solves 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 allocating evacuees to shelters in a system optimal manner. The system determines the best shelters for evacuees, and evacuees tend to reach their shelters as fast as possible. Therefore, the DTA model is formulated for the user equilibrium. It means that all evacuees minimize their own travel time. We validate our methodology on the real network of Luxembourg and evaluate its performance in front of an advanced method that solves the SAP and DTA separately, i.e., the SAP is completely solved before the evacuation process. The results show that computing dynamic shelter allocation can improve mean evacuation time and significantly reduce the network clearance time compared to the methods with fixed shelter allocation plans. This means that considering the network state in the SAP can provide a more effective evacuation plan. Moreover, we perform a complete analysis for the computation time of the framework and show that solving the dynamic SAP is not computationally expensive compared to the profit providing for the evacuation problem.