Traffic congestion in the United States alone results in $n100 billion in lost productivity. In this paper we consider the modeling and solution of dynamic traffic models formulated as projected dynamical systems. The proposed discrete time algorithm, the Euler method, resolves the problem at each step into subproblems in path flow variables, all of which can be solved simultaneously and in closed form. Convergence results are also presented. Finally, the algorithm is implemented on the massively parallel architecture, the Thinking Machine's CM-5, and its performance compared to an implementation on the IBM SP2 on several traffic network examples.