Future cellular systems are envisioned to support mixed traffic, and ultimately multimedia services. However, a mixture of voice and data requires novel service mechanisms that can guarantee quality of service. In order to transfer high-speed data, multislot channel allocation is seen as a favoured solution to the present systems with the least compromise to circuit- switched services. This paper evaluates the performance of narrowband voice calls and multislot data packet transmission in such integrated systems by using a matrix-analytic approach. This method achieves quadratic convergence compared to the conventional spectral methods. Mobility is also considered in a prioritized cellular environment where frequent handoff has the potential of degrading data performance. The voice call distribution, data packets throughput, delay and waiting time distribution are derived. Moreover, a new multiple priority-based distributed control algorithm and a voice rate control scheme are enforced to mitigate the queuing congestion of data packets. The numerical results derived from this study show that larger data packets incur longer latency and the use of these flexible schemes can improve the overall performance.