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This paper considers the problem of call admission control (CAC) in a wireless ATM network. It proposes a mechanism, which is threshold-based to privilege handover requests over new call requests, to decide the admission of calls using the available bit rate (ABR) mode already standardized for wired ATM networks. A call can be accepted only if the network can guarantee the minimum requirements, that is the minimum cell rate (MCR). If, on the other hand, there are free channels, they are assigned, according to a fair strategy, to calls that were previously transmitting with fewer than the peak call rate (PCR) channels. In order to assess the effectiveness of the proposed CAC strategy, a Markov-based approach is introduced and the performance provided to each user by the network are evaluated.