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In mobile networks the traffic fluctuation is unpredictable dueto mobility and varying resource requirements of multimedia applications.Henceit is essential to maintain the traffic within the network capacity to providethe service guarantees to running applications. Thispaper proposes an Admission Control (AC) scheme in a single mobile cellularenvironment supporting real-time and non-real-time application traffic. In thecase of a real-time and non-real-time multimedia applications, eachapplication has its own distinct range of acceptable Quality of Service (QoS)requirements(e.g., packet loss, delay, jitter, etc.). The network provides the service bymaintaining the application specified QoS range. We propose a LinearProgrammingResource Reduction (LP-RR) principle for admission control by maintainingQoSguarantees to existing applications and to increase the percentage ofadmissionto real-time and non-real-time applications. Artificial Neural Networks (ANNs)are used to solve linear programming problem, which facilitates an on-lineadmissioncontrol decision in the practical systems.The simulation results demonstrate that the proposed AC schemeperforms well in terms of admitted applications and maintains lower percentageof rejection to hand-off and new applications of different traffic classes.The suggested principle also shown that it is appropriate for the fairresourceallocation with improved resource utilization.