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In modern satellite communication systems, the quality of service (QoS) management has became a crucial topic due to the increasing interest in multimedia traffic. The actual trends consider the satellite networks as an integrated part of the terrestrial data networks. In IP networks, the differentiated service (DiffServ) approach seems to be the best that satisfies the QoS constraints, due to its end-to-end philosophy. Actual trend considers the satellite on-board switching capabilities for managing multibeam inputs and outputs. In particular this paper deals with the proposal of a new cellular neural network (CNN) for the on-board switching problem to reduce the computational complexity; several traffic classes, according to the DiffServ approach, have been considered and the switch takes into account their priority, queue length and time spent inside queues. Numerical results have shown that the performance is similar to the optimal switching solution of the flexible cellular neural network. Simulation results have been driven with a memoryless distribution and heavy-tailed distribution for several input buffer size and switch dimension.