Operating large language models (LLMs) at scale in real-world scenarios necessitates multiple backend replicas. The inter-replica load balancing algorithm greatly influences overall system performance by impacting the caching dynamics inherent in modern inference engines. In this study, we explore the application of the Consistent Hashing with Bounded Loads (CHWBL) algorithm in the domain of LLM inference. We simulate real-world load patterns on Kubernetes, the industry's most widely adopted deployment platform. Our results demonstrate a 95% reduction in Time To First Token (TTFT) and a 127% increase in overall throughput compared to the baseline strategy.