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In mobile networks, the traffic fluctuation is unpredictable due to mobility and varying resource requirement of multimedia applications. Hence, it is essential to maintain traffic within the network capacity to provide service guarantees to running applications. This paper proposes an admission control (AC) scheme in a mobile cellular environment supporting hand-off and new application traffic. In the case of multimedia applications, each applications has its own distinct range of acceptable quality of service (QoS) requirements. The network provides the service by maintaining the application specified QoS range. We propose a linear programming resource reduction (LP-RR) principle for admission control by maintaining QoS guarantees to existing applications and to increase the percentage of admission to hand-off and new applications. Artificial neural networks are used to solve the linear programming problem, which facilitates in real time admission control decision in the practical systems. We present an analytical model and results for the proposed AC scheme with resource reduction principle and a simulation study of the AC for performance evaluation. The simulation results demonstrate that the proposed AC scheme performs well in terms of increasing the number of admitted applications and maintains higher percentage of resource utilization. The suggested principle also shown that it is appropriate for the fair resource allocation with improved resource utilization.