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In this paper, an analytical method for the design of a congestion control scheme in store-and-forward networks is presented. The control architecture is rate based with a local feedback controller associated with each switching node. The controller itself is a generalization of the standard PD controller with the only difference that extra D terms are involved to accommodate the delay present in high speed networks. It is shown that, under a specific priority discipline introduced, there exists a set of control gains that result in asymptotic stability of the linearized network model. A method for calculating these gains is given. In addition, it is shown that the resulting steady state rate allocation possesses the so-called max-min fairness property. The theoretical results are illustrated by a simulation example where it is shown that the controller designed using the methods developed works well for both the priority scheme introduced in this paper and for the standard first-come-first serve scheme.