The paper addresses the problem of estimating the traffic demand between any pair of nodes in a circuitswitched network on the basis of trunk group measurements (canied load and blocking probability on a link) and the routing plan. Two methodsa closed form one based on the use of the pseudo-inverse matrix and an iterative oneare examined in network scenarios of varied size and connectivity under different congestion levels. In addition, a criterion based on a Bayesian approach is proposed for initializing the iterative method. It is shown that the iterative method is affected by lower estimation errors than the pseudo-inverse method, and that the iterative method's performance is further enhanced by the employment of the Bayesian initialization criterion. Some tentative relationships are provided between the estimation accuracy and the network size and connectivity. The improvement in the estimation accuracy is accompanied by an even more pronounced reduction in the computational load. The use of the iterative method with Bayesian initialization requires in fact running times even two orders of magnitude lower than those needed by the pseudo-inverse method, the gap being larger the larger the network and the higher the connectivity.