A Queueing-Theoretic Framework for Stability Analysis of LLM Inference with KV Cache Memory Constraints
This provides a tool for GPU provisioning in LLM inference services, addressing the challenge of balancing cost and performance.
The paper introduces a queueing-theoretic framework for LLM inference that accounts for both computation and KV cache memory constraints, deriving stability conditions to prevent unbounded queue growth. Experiments show predicted stability conditions are accurate within 10%.
The rapid adoption of large language models (LLMs) has created significant challenges for efficient inference at scale. Unlike traditional workloads, LLM inference is constrained by both computation and the memory overhead of key-value (KV) caching, which accelerates decoding but quickly exhausts GPU memory. In this paper, we introduce the first queueing-theoretic framework that explicitly incorporates both computation and GPU memory constraints into the analysis of LLM inference. Based on this framework, we derive rigorous stability and instability conditions that determine whether an LLM inference service can sustain incoming demand without unbounded queue growth. This result offers a powerful tool for system deployment, potentially addressing the core challenge of GPU provisioning. By combining an estimated request arrival rate with our derived stable service rate, operators can calculate the necessary cluster size to avoid both costly over-purchasing and performance-violating under-provisioning. We further validate our theoretical predictions through extensive experiments in real GPU production environments. Our results show that the predicted stability conditions are highly accurate, with deviations typically within 10%.