We study an original scheme based on distributed feedforward neural networks, aimed at modelling several queueing systems in cascade fed with bursty traffic. For each queueing 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 neural network along the path. The potential of this method is successfully illustrated on several single server FIFO (First In, First Out) queues and on small queueing networks made up from a combination of queues in tandem and in parallel fed by a superposition of ideal sources. Our long-term goal is the design of preventive control strategy in a multiservice communication network.