Modern deep neural network (DNN) and large language model (LLM) applications integrate multiple models into inference pipelines with stringent latency requirements for customized tasks. To mitigate extensive request timeouts caused by accumulation, systems for inference pipelines commonly drop a subset of requests so the remaining ones can satisfy latency constraints. Since it is commonly believed that request dropping adversely affects goodput, existing systems only drop requests when they have to, which we call reactive dropping. However, this reactive policy can not maintain high goodput, as it neither makes timely dropping decisions nor identifies the proper set of requests to drop, leading to issues of dropping requests too late or dropping the wrong set of requests.