In maritime transportation, networks are often interconnected to ensure efficient operations and connectivity across various routes and ports. Understanding the dynamics of traffic flow in such interconnected networks is crucial for optimizing maritime logistics and minimizing congestion. While the majority of conducted studies on the field of interconnected networks focus on the developed concept of interconnected networks and on the other hand, on finding the optimal coupling to avoid traffic congestion in interconnected networks. Inspired by many different routing algorithm strategies used in isolated networks, this paper shifts focuses on the impact of routing schemes on traffic dynamics within interconnected maritime networks. Our study aims to analyze how different border routing schemes affect traffic dynamics and overall network performance in interconnected maritime environments. Simulation results show that our proposed method Border Administrative Authority (BAA) yields superior outcomes without extra cost and load of traffic to overcome the congestion problem in traffic dynamics in interconnected maritime networks.