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The CAC algorithm of a mobile network is responsible for reducing the handoff drop ratio (HDR) to an acceptable low level as well as achieving a high acceptance ratio for locally generated calls. Algorithms based on dynamic resource reservation depend on complex measurement, calculation and information exchange between cells. Recently, an adaptive service has been proposed to protect the QoS of mobile users and increase the capacity of a mobile network. We introduce a new sliding window based CAC algorithm especially designed for the adaptive service. This algorithm can avoid the complex estimation of the handoff probability in the dynamic algorithm, and simulation results show that this algorithm can reduce the HDR to nearly zero and can also get a higher acceptance ratio than the dynamic algorithm.