Mobile users such as airplanes or ships will constitute an important segment of the future satellite communications market. Operators are now able to leverage digital payloads that allow flexible resource allocation policies that are robust against dynamic user bases. One of the key problems is managing the frequency spectrum efficiently, which has not been sufficiently explored for mobile users. To address this gap, we propose a dynamic frequency management algorithm based on linear programming that assigns resources in scenarios with both fixed and mobile users by combining long-term planning with real-time operation. We propose different strategies divided into proactive strategies, which stem from robust optimization practices, and reactive strategies, which exploit a high degree of real-time control. This represents a tradeoff between how conservative long-time planning should be and how much real-time reconfiguration is needed. To assess the performance of our method and to determine which proactive and reactive strategies work better under which context, we simulate operational use cases of non-geostationary constellations with different levels of dimensionality and uncertainty, showing that our method is able to serve over 99.97\% of the fixed and mobile users in scenarios with more than 900 beams. Finally, we discuss the trade-offs between the studied strategies in terms of the number of served users, power consumption, and number of changes that need to happen during operations.
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