Proof of global convergence of an efficient algorithm for predicting trip generation, trip distribution, modal split and traffic assignment simultaneously on large-scale networks

Abstract

Safwat and Magnanti have developed a combined trip generation, trip distribution, modal split and traffic assignment model that can predict demand and performance levels on large-scale transportation networks simultaneously. An efficient algorithm for predicting equilibrium on the model was suggested by the authors and applied to large-scale systems. The algorithm was found to consistently converge very rapidly in all cases. A formal proof of convergence was not available at the time of those applications. This paper provides a formal proof of global convergence of this efficient algorithm under no additional assumptions on the model. This proof should strengthen the methodology and further encourage its widespread implementation for transportation planning studies, particularly those of a large-scale nature.