A linear dynamic network is a system of subsystems that approximates the dynamic model of large, geographically distributed systems such as the power grid and traffic networks. A favorite technique to operate such networks is distributed model predictive control (DMPC), which advocates the distribution of decision-making while handling constraints in a systematic way. This paper contributes to the state-of-the-art of DMPC of linear dynamic networks in two ways. First, it extends a baseline model by introducing constraints on the output of the subsystems and by letting subsystem dynamics to depend on the state besides the control signals of the subsystems in the neighborhood. With these extensions, constraints on queue lengths and delayed dynamic effects can be modeled in traffic networks. Second, this paper develops a distributed interior-point algorithm for solving DMPC optimization problems with a network of agents, one for each subsystem, which is shown to converge to an optimal solution. In a traffic network, this distributed algorithm permits the subsystem of an intersection to be reconfigured by only coordinating with the subsystems in its vicinity.