Modern AI services rely on vast, expensive computational resources and processing power, all sustained by a global network of data centers. A key operational challenge is ensuring these systems remain responsive by efficiently routing requests. This talk introduces the Greatest Marginal Service Rate (GMSR) policy, a novel policy that routes each request to the data center where it will have the highest marginal impact on the current service rate. GMSR is designed to be fully distributed, with routers in different geographic regions making decisions independently using only local information. This design makes the system scalable and resilient while eliminating the need for complex coordination. We prove that, despite its distributed design, the GMSR policy converges to the globally optimal solution that a central coordinator would choose to minimize system-wide latency. Furthermore, the policy is robust: even when the system is overloaded, it maximizes throughput and minimizes latency for all completed requests. This work provides a practical and provably optimal load balancer for building the next generation of scalable and responsive AI systems.