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Projected dynamical systems modeling and computation of spatial network equilibria

In this paper, we consider the price formulation-rather than the quantity formulation ― of spatial network equilibria and introduce a projected dynamical system, whose set of stationary points corresponds to the set of solutions of the governing variational inequality problem. We then interpret the dynamical system as a tatonnement process in which the commodity prices and shipments are updated simultaneously. We propose an Euler-type method for the computation of the commodity prices and trade patterns, provide convergence results, and demonstrate that the algorithm can be implemented on massively parallel architectures. The notable feature of the algorithm is that the prices and shipments can be computed independently and in closed form. Finally, we illustrate the performance of the implemented algorithm on the Thinking Machine's CM-2 and CM-5 architectures.