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A new Channel Allocation (CA) policy by employing a hysteresis mechanism and guard channel scheme is considered for use in Low Earth Orbit (LEO) satellite networks. The aim is to provide for handoff call with priority attempts over new call attempts so as to avoid the forced call terminations due to handover failures without unduly affecting the performance seen by new call attempts. In addition, the algorithm improves resource utilization efficiently in LEO satellite networks. A Markovian modeling approach is used to analyze the performance, and its results have been validated through simulations.