Load analysis of packet switched networks in control systems

Analysis and design of switched networks in control systems often comes in close connection with the load analysis problem. Given the volume and pattern of traffic among the network end nodes, the problem can be defined as computing the amount of traffic or load on the network internal nodes, corresponding to network switch devices. We discuss a systematic solution to this problem using the graph model of the network coupled with a compact representation of the network traffic in the form of a traffic matrix. In particular, we present an iterative solution for a special class of switched networks, namely, networks with free topology. Beginning with the graph model and the traffic matrix of the original network, the loads on end nodes of the network are computed through simple matrix operations. The graph model is then trimmed by removing a group of end nodes and an equivalent traffic matrix is computed for the new graph. The procedure is repeated until the network is reduced to a single node, which typically happens to be the backbone switch of the network.