The disclosed embodiments provide a system that prevents oscillatory load behavior for a multi-node distributed system. During operation, the system uses a load-balancing policy to distribute requests to nodes of the distributed system. The system determines operational characteristics for the nodes as they process a set of requests, and then uses these operational characteristics to compute machine queuing models that describe the machine state of each node. The system then uses this machine state for the nodes to determine whether the load-balancing policy and the distributed system are susceptible to oscillatory load behavior.