Edge Computing enables low-latency processing for real-time applications but introduces challenges in power management due to the distributed nature of edge devices and their limited energy resources. This paper proposes a stochastic modeling approach using Markov Chains to analyze power state transitions in Edge Computing. By deriving steady-state probabilities and evaluating energy consumption, we demonstrate the benefits of AI-driven predictive power scaling over conventional reactive methods. Monte Carlo simulations validate the model, showing strong alignment between theoretical and empirical results. Sensitivity analysis highlights how varying transition probabilities affect power efficiency, confirming that predictive scaling minimizes unnecessary transitions and improves overall system responsiveness. Our findings suggest that AI-based power management strategies significantly enhance energy efficiency by anticipating workload demands and optimizing state transitions. Experimental results indicate that AI-based power management optimizes workload distribution across heterogeneous edge nodes, reducing energy consumption disparities between devices, improving overall efficiency, and enhancing adaptive power coordination in multi-node environments.

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