The purpose of this study is twofold. First the study illustrates the utility of applying sparse matrix methods to packet network models. Secondly, these methods are used to give new results about the control of store and forward congestion in packet networks. Store and forward congestion (node to node blocking) reduces the effective traffic carrying capacity of the network by unnecessarily idling network resources. This study shows how store and forward congestion can be controlled by a combination of buffer reservation and processor capacity allocation. The scheme presented is analyzed using a Markovian state-space model of two coupled packet switches. The model contains more detail than previous analytic models. It is therefore solved using numerical sparse matrix methods. The results show that the combination of buffer reservation and processor capacity allocation gives strictly nondecreasing network output as a function of increasing network input load, i.e., undesirable store and forward congestion effects are eliminated.