Flow-Controlled Scheduling for LLM Inference with Provable Stability Guarantees

Large language models (LLMs) have been widely adopted due to their great performance across a wide range of applications. ChatGPT and Gemini now serve hundreds of millions of active users and handle billions of user requests per day, which puts optimizing LLM inference into the spotlight. A key challenge in LLM inference is that decode lengths are unknown. The memory usage for each request grows with generated tokens, which may lead to overflow and cause system instability. To address this concern, we propose a simple flow-control framework that controls the rate at which prompts join the active set. We derive a necessary condition that any stable system must satisfy and establish sufficient conditions under which our algorithm provably achieves stability. Experiments show that, compared to commonly used strategies in practice, our approach achieves higher token and request throughput, lower average and tail latency, and more stable KV cache utilization.