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A phenomenal growth is witnessed in the development and deployment of wireless services. Wireless bandwidth is a scarce resource in a cellular mobile network and hence must be effectively utilized. This paper introduces two intelligent schemes to investigate the bandwidth allocation in cellular mobile networks namely Back Propagation Neural Network (BPN) and Particle Swarm Optimization (PSO). The performance objective is to maximize the bandwidth utilization while minimizing the bandwidth allocation for individual users. PSO and BPN methods are compared with the conventional Random Allocation and Linear Programming based Resource Reduction methods. Simulation results prove that the PSO method performs better than the BPN method.