The congestion queuing method that uses four static queues in Cisco IOS-based routers is Custom Queuing (CQ). CQ is designed to provide a consistent level of service to different traffic types. In CQ, the router's interface is divided into multiple (up to 16) queues, and each queue is assigned a fixed amount of bandwidth. The queues are serviced in a round-robin fashion, ensuring that each queue gets a chance to send packets. This method is particularly useful when you need to guarantee a certain level of service for specific types of traffic.