arXiv:2508.00234v1 Announce Type: cross Abstract: Large Language Models (LLMs) have demonstrated remarkable capabilities, leading to a significant increase in user demand for LLM services. However, cloud-based LLM services often suffer from high latency, unstable responsiveness, and privacy concerns. Therefore, multiple LLMs are usually deployed at the network edge to boost real-time responsiveness and protect data privacy, particularly for many emerging smart mobile and IoT applications. Given the varying response quality and latency of LLM services, a critical issue is how to route user requests from mobile and IoT devices to an appropriate LLM service (i.e., edge LLM expert) to ensure acceptable quality-of-service (QoS). Existing routing algorithms fail to simultaneously address the heterogeneity of LLM services, the interference among requests, and the dynamic workloads necessary for maintaining long-term stable QoS. To meet these challenges, in this paper we propose a novel deep reinforcement learning (DRL)-based QoS-aware LLM routing framework for sustained high-quality LLM services. Due to the dynamic nature of the global state, we propose a dynamic state abstraction technique to compactly represent global state features with a heterogeneous graph attention network (HAN). Additionally, we introduce an action impact estimator and a tailored reward function to guide the DRL agent in maximizing QoS and preventing latency violations. Extensive experiments on both Poisson and real-world workloads demonstrate that our proposed algorithm significantly improves average QoS and computing resource efficiency compared to existing baselines.