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Distributed model predictive control (DMPC) advocates the distribution of sensing and decision making to operate large, geographically distributed systems such as the power grid and traffic networks. This paper presents a distributed optimization framework for DMPC of linear dynamic networks with constraints on each network node. A linear dynamic network can be thought of as a directed graph, whose nodes have local dynamics that depend on the local and upstream control signals and are subject to constraints on state and control variables. The distributed algorithm is based on interior-point methods and can be shown to converge to a globally optimal solution. Some theoretical results are stated and a preliminary application to green-time control in urban traffic networks is described.