In order to maintain consistent quality of service, computer network engineers face the task of monitoring the traffic fluctuations on the individual links making up the network. However, due to resource constraints and limited access, it is not possible to directly measure all the links. Starting with a physically interpretable probabilistic model of networkwide traffic, we demonstrate how an expensively obtained set of measurements may be used to develop a network-specific model of the traffic across the network. This model may then be used in conjunction with easily obtainable measurements to provide more accurate prediction than is possible with only the inexpensive measurements. We show that the model, once learned may be used for the same network for many different periods of traffic. Finally, we show an application of the prediction technique to create relevant control charts for detection and isolation of shifts in network traffic.The rows of the matrix A correspond to the L links and the columns to the J routes. In the Internet2 network, for example, the route j from Chicago to Kansas City involves only one link, and thus the j-th column of A has a single '1' on corresponding to the link connecting the two nodes; similarly, the k-hop routes correspond to columns of A with precisely k 1's. We are interested in the statistical modeling of the traffic on the entire network. Let X(t) = (X j (t)) 1≤j≤J be the vector of the traffic flows at time t on all J routes, i.e. between all source-destination pairs. That is, X j (t), t =