We discuss an original scheme based on distributed feedforward neural networks (NN), aimed at modeling several queuing systems in cascade fed with bursty traffic. For each queuing system, a neural network is trained to anticipate the average number of waiting packets, the packet loss rate and the coefficient of variation of the packet inter-departure time, given the mean rate, the peak rate and the coefficient of variation of the packet inter-arrival time. The latter serves for the calculation of the coefficient of variation of the cell inter-arrival time of the aggregated traffic, which is fed, as input to the next NN along the path. The potential of this method was successfully illustrated on several single server FIFO queues in [3]. We now apply this technique to model a small queuing network made up from a combination of queues in tandem and in parallel fed by a superimposition of On Off sources. Our long-term goal is the design of preventive control strategy in a multiservice communication network.