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This paper addresses the challenge of optimizing cloudlet resource allocation in a code evaluation system. The study models the relationship between system load and response time when users submit code to an an online code evaluation platform called LambdaChecker that operates a cloudlet-based processing pipeline. The pipeline includes code correctness checks, static analysis, and design-pattern detection using a local Large Language Model (LLM). To optimize the system we develop a mathematical model and apply it to LambdaChecker resource management. The proposed approach is assessed using both simulations and real contest data, focusing on improvements in average response time, resource-utilization efficiency, and user satisfaction. The results indicate that adaptive scheduling and workload prediction effectively reduce waiting times without substantially increasing operational costs. Overall, the study suggests that systematic cloudlet optimization can enhance the educational value of automated code evaluation systems by improving responsiveness while preserving sustainable resource usage.