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The aim of this paper was to provide a methodological framework for estimating the amount of driving data that should be collected for each driver in order to acquire a clear picture regarding their driving behavior. We examined whether there is a specific discrete time point for each driver, in the form of total driving duration and/or the number of trips, beyond which the characteristics of driving behavior are stabilized over time. Various mathematical and statistical methods were employed to process the data collected and determine the time point at which behavior converges. Detailed data collected from smartphone sensors are used to test the proposed methodology. The driving metrics used in the analysis are the number of harsh acceleration and braking events, the duration of mobile usage while driving and the percentage of time driving over the speed limits. Convergence was tested in terms of both the magnitude and volatility of each metric for different trips and analysis is performed for several trip durations. Results indicated that there is no specific time point or number of trips after which driving behavior stabilizes for all drivers and/or all metrics examined. The driving behavior stabilization is mostly affected by the duration of the trips examined and the aggressiveness of the driver.