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The MAGIC and LST-1 telescopes, located at the Roque de los Muchachos Observatory on La Palma, operate dedicated On-Site Analysis (OSA) pipelines that provide rapid, automated processing of observational data. These systems produce high-level data products just a few hours after observations are completed, enabling quick-look analyses, next-day data quality assessments, and rapid-response science such as flare detection and Target of Opportunity follow-ups. OSA pipelines have been in continuous operation since 2012 for MAGIC and since 2021 for LST-1, automatically processing nightly data using the standard analysis chain. The experience gained from both systems provides essential lessons for the development of Cherenkov Telescope Array Observatory’s (CTAO’s) on-site analysis, demonstrating the practical and scientific benefits of fast data processing in Cherenkov telescopes.