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This paper introduces a queueing-theoretic model for LLM inference that explicitly accounts for both computational and KV cache memory constraints on GPUs. The authors derive stability and instability conditions that determine whether an LLM inference service can handle incoming requests without unbounded queue growth. Empirical validation in production GPU environments demonstrates high accuracy (within 10%) of the predicted stability conditions.
Forget heuristics: this queueing theory framework precisely predicts LLM inference stability under KV cache constraints, letting you right-size your GPU cluster.
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%.
