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With the handoff occurring more and more frequently in cellular networks, an effective call admission control is increasingly urgent for optimum utility of valuable bandwidth. Recently, the dynamic call admission mechanism using stochastic control was found to be more stable and precise. But, it is still hard to get an effective dynamic call admission mechanism for multi-services. The main challenges with multiple types of traffic are that each has its own requirements of bandwidth, QoS guarantee and handoff rate, especially for data call types. In this paper, we use a buffer to regulate the data type traffic and use the proposed 1D stochastic model to compute the key parameters, such as call dropping probability and admission probability, considering fairness among multi-services. The result is decreased computational complexity. Numerical results of simulation show that the proposed scheme, named FDCA (fair dynamic call admission scheme), steadily satisfies the hard constraints on call dropping probability for multi-services while maintaining a very high channel throughput.