Serving LLM adapters has gained significant attention as an effective approach to adapt general-purpose language models to diverse, task-specific use cases. However, serving a wide range of adapters introduces several and substantial overheads, leading to performance degradation and challenges in optimal placement. To address these challenges, we present an analytical, AI-driven pipeline that accurately determines the optimal allocation of adapters in single-node setups. This allocation maximizes performance, effectively using GPU resources, while preventing request starvation. Crucially, the proposed allocation is given based on current workload patterns. These insights in single-node setups can be leveraged in multi-replica deployments for overall placement, load balancing and server configuration, ultimately enhancing overall performance and improving resource efficiency. Our approach builds on an in-depth analysis of LLM adapter serving, accounting for overheads and performance variability, and includes the development of the first Digital Twin capable of replicating online LLM-adapter serving systems with matching key performance metrics. The experimental results demonstrate that the Digital Twin achieves a SMAPE difference of no more than 5.5% in throughput compared to real results, and the proposed pipeline accurately predicts the optimal placement with minimal latency.