Call admission protocol (CAC) is a very important process in the provision of good Quality of Service (QoS) in cellular mobile networks. With micro/Pico cellular architectures that are now used to provide higher capacity, the cell size decreases with a drastic increase in the handoff rate. In this paper, we present modeling and simulation results to help in better understanding of the performance and efficiency of CAC in cellular networks. Handoff prioritization is a common characteristic, which is achieved through the threshold bandwidth reservation policy framework. Combined with this framework, we use pre-emptive call admission scheme and elastic bandwidth allocation for data calls in order to gain a near optimal QoS. In this paper, we also use a Genetic Algorithm (GA) based approach to optimize the fitness function, which we obtained by calculating the mean square error of predicted rejection values and the actual ones. The predicted values are calculated using a linear model, which relates the rejection ratios with different threshold values.