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In this paper, novel call admission control (CAC) algorithms are developed based on cellular neural networks. These algorithms can achieve high network utilization by performing CAC in real-time, which is imperative in supporting quality of service (QoS) communication over packet-switched networks. The proposed solutions are of basic significance in access technology where a subscriber population (connected to the Internet via an access module) needs to receive services. In this case, QoS can only be preserved by admitting those user configurations which will not overload the access module. The paper treats CAC as a set separation problem where the separation surface is approximated based on a training set. This casts CAC as an image processing task in which a complex admission pattern is to be recognized from a couple of initial points belonging to the training set. Since CNNs can implement any propagation models to explore complex patterns, CAC can then be carried out by a CNN. The major challenge is to find the proper template matrix which yields high network utilization. On the other hand, the proposed method is also capable of handling three-dimensional separation surfaces, as in a typical access scenario there are three traffic classes (e.g., two type of Internet access and one voice over asymmetric digital subscriber line.