A Queueing-Theoretic Framework for Stability Analysis of LLM Inference with KV Cache Memory Constraints

Researchers introduce a queueing-theoretic framework that models LLM inference stability by accounting for both computational and GPU memory constraints from KV caching. The framework derives conditions for service stability and enables operators to calculate optimal cluster sizes for efficient GPU provisioning, with experimental validation showing predictions within 10% accuracy.

This research addresses a critical infrastructure challenge facing LLM deployment at scale. The key innovation lies in formalizing the interaction between two competing resource constraints—compute and memory—that have previously been analyzed separately. KV caching significantly accelerates inference decoding but creates a memory bottleneck that often becomes the limiting factor before computational capacity is exhausted. By bridging queueing theory with LLM-specific resource dynamics, the framework provides operators with a principled method for capacity planning.

The problem emerged as organizations scaled LLM inference services and discovered that traditional performance models failed to account for the unique memory-computation trade-off. Most existing approaches either ignore memory constraints entirely or treat them as afterthoughts in performance analysis. This research formalizes the problem mathematically, deriving rigorous stability conditions that predict when queue backlogs grow unboundedly versus remaining manageable.

The practical implications are substantial. GPU resources represent one of the largest capital expenditures for AI infrastructure providers. Over-provisioning wastes billions in unnecessary spending, while under-provisioning degrades service quality and damages user experience. The framework enables data-driven cluster sizing decisions by combining arrival rate estimates with derived stable service rates. The reported 10% prediction accuracy suggests the model captures real-world dynamics effectively.

For the broader LLM inference ecosystem, this establishes a foundation for optimized resource allocation. Future work likely extends this to heterogeneous hardware, dynamic batching strategies, and multi-model serving scenarios. As LLM inference becomes increasingly cost-sensitive and competitive, optimization frameworks like this determine economic viability for cloud providers and startups alike.

• →Queueing theory framework explicitly models both computation and KV cache memory constraints in LLM inference stability analysis.
• →Derived stability conditions enable accurate calculation of minimum GPU cluster sizes needed to meet service demand without queue growth.
• →Experimental validation confirms theoretical predictions with typical deviations within 10% across real GPU production environments.
• →Framework addresses critical GPU provisioning challenge affecting both capital efficiency and service performance for LLM inference operators.
• →Formalizes the memory-computation trade-off unique to LLM inference, previously analyzed ad-hoc or separately.