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Providing multimedia services with quality of service (QoS) guarantees in next generation wireless cellular networks poses great challenges due to the scarce radio bandwidth. Effective call admission control (CAC) is important for the efficient utilization of the limited bandwidth. In this paper we present an optimal Markov decision-based call admission control (MD-CAC) policy for the multimedia services that characterize the next generation of wireless cellular networks. A Markov decision process (MDP) is used to represent the CAC policy. The MD-CAC is formulated as a linear programming problem with the objectives of maximizing the system utilization while ensuring class differentiation and providing quantitative fairness guarantees among different classes of users. Through simulation, we show that the MD-CAC policy upholds the handoff call dropping probability required by each traffic class and provides fairness for all classes while maximizing the bandwidth utilization.