The Random Neural Network (RNN) is a recurrent neural network in which neurons interact with each other by exchanging excitatory and inhibitory spiking signals. The stochastic excitatory and inhibitory interactions in the network make the RNN an excellent modeling tool for various interacting entities. It has been applied in a number of applications such as optimization, image processing, communication systems, simulation pattern recognition and classification. In this paper, we briefly describe the RNN model and some learning algorithms for RNN. We discuss how the RNN with reinforcement learning was successfully applied to Cognitive Packet Network (CPN) architecture so as to offer users QoS driven packet delivery services. The experiments conducted on a 26-node testbed clearly demonstrated the learning capability of the RNNs in CPN.