Radroach infestation occur randomly or after a failed Rush attempt. Radroaches will start appearing in nearby rooms if not contained immediately. Dwellers in the room where the infestation started will deal with the infestation automatically but for empty rooms like Living Quarters or storage rooms, you have to drag any available dweller. You have to watch out for your dwellers health since they can die if you don't give them stimpacks in time. The best way to deal with radroaches is equipping Weapons to your dwellers. Take note that the number of dwellers that can enter the room will depend on the room's capacity.