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Current admission controls seeking to optimize network utilization create a bias against wideband calls. This paper proposes a BNP (buffer without preemption) model that will hold a call in a buffer rather than directly reject it when the residual bandwidth is insufficient. Such a mechanism increases the throughput since the buffer can temporarily hold a call; it also reduces the bias for wideband calls since all calls are rejected when the buffer is not empty, even when the residual bandwidth suffices for narrowband calls. The performance of the models is analyzed by solving a two-dimensional Markov chain. A modified model, BNP W, in which a waiting time threshold is added, is further offered to prevent an overlong wait for the queued call. Also, different thresholds for heterogeneous calls are set to provide equal admitting probability for them. Analytical and numerical results demonstrate that both models actually achieve fair, that is, equal or similar, admitting probability for wideband and narrowband calls.