Multi-Turn LLM Conversations under the Least-Recently-Used Policy: Mean-Field Asymptotics and Hit Ratio Approximation

The major workloads in modern large language model (LLM) serving systems have shifted from single-shot LLM calls to multi-turn conversations, where new responses are generated based on the whole conversation history across all previous turns. The hit ratio, i.e., the average fraction of KV caches ac