Vehicle route control is a promising approach for addressing traffic congestion caused by temporary changes in road capacity, such as traffic accidents and road construction. Several studies have proposed to guide vehicles to bypass congestion and thus alleviate it. However, this method stops route control immediately after the congestion disappears, resulting in the reoccurrence of congestion and road instability. To overcome this problem, we propose a method called congestion management based on in- and outflow volumes (COMIO), which stabilizes traffic by controlling the detour traffic volume until congestion is truly resolved. Our method works in tandem with a conventional route guidance method, where the conventional method detects congestion and computes detour paths and COMIO gradually controls the detour traffic volume over time until the congestion disappears. The key strategy of our method is to manage the balance of the inflow and outflow of the congested road. By maintaining the inflow volume a certain amount smaller than the outflow volume, congestion is gradually reduced without rapid traffic changes and finally disappears without its reoccurrence. COMIO offers stable traffic control during traffic congestion resolution, resulting in more efficient traffic control for the entire road network.