In an access node to a hybrid-switching network (e.g., a base station handling the downlink in a cellular wireless network), the output link bandwidth is dynamically shared between isochronous (guaranteed bandwidth) and asynchronous traffic types. The bandwidth allocation is effected by an admission controller, whose goal is to minimize the refusal rate of connection requests as well as the loss probability of packets queued in a finite buffer. Optimal admission control strategies are approximated by means of backpropagation feedforward neural networks, acting on the embedded Markov chain of the connection dynamics. The case of unknown, slowly varying, input rates is explicitly considered. Numerical results are presented, comparing the approximation with the optimal solution obtained by dynamic programming.