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This paper proposes a call admission control (CAC) policy for a cellular system supporting voice and data services, and providing a higher priority to handoff calls than to new calls. A procedure for searching the optimal admission region is given. The traffic flow is characterized by a three-dimensional (3-D) birth-death model, which captures the complex interaction between the on/off voice and best-effort data traffic sharing the total resources without partition. To reduce complexity, the 3-D model is simplified to an exact (approximate) 2-D model for voice (data). The mathematical expressions are then derived for the performance measures and for the minimal amount of resources required for quality-of-service (QoS) provisioning. Numerical results demonstrate that: 1) the proposed CAC policy performs well in terms of QoS satisfaction and resource utilization; 2) the approximate 2-D model for data traffic can achieve a high accuracy in the traffic flow characterization; and 3) the admission regions obtained by the proposed search method agree very well with those obtained by numerically solving the mathematical equations. Furthermore, computer simulation results demonstrate that the impact of lognormal distributed data file size is not significant, and may be compensated by conservatively applying the Markovian analysis results.