A heuristic technique for traffic assignment with variable step size and number of iterations

Abstract

The prediction of traffic flows on network links is an essential issue in urban transportation modeling and planning. Although manual assignment methods are possible for tiny networks, the networks involved in practical-size problems usually require complex calculations with large amounts of data. In the traditional incremental traffic assignment technique (TITAT), the O-D matrix is divided into N equal portions and assigned to the network at each iteration. Travel times are then updated, based on which the next portion of the O-D matrix is loaded onto the network. In this paper, the assumption of equal step size in all iterations is relaxed, and variable step size for the different iterations is proposed to increase the efficiency of this technique. It is shown that an intelligent choice of step size can cause more efficiency. To implement this concept quantitatively for a real-size problem, Mashhad, as the second-largest city of Iran with about 4.5 million trips per year, is used as the case study to analyze and evaluate the proposed technique and compare the results with those of TITAT. Results suggest that regarding the reliability of the outcomes and computational efficacy, the proposed algorithm is as good as other methods. Unlike other methods, there is no additional parameter to be calibrated, and the convergence behavior of the algorithm is promising. It is observed in this particular case, that there is an inverse linear relationship between the number of iterations and the initial step size; and that for a specified number of iterations, the best results are obtained for equal step sizes for all but the first iteration. The main advantage of this technique is that it can provide a simple and economical method for traffic assignment as compared with user equilibrium for which goodness-of-fit measure of predicted-observed flows on selected links equals 0.57.In contrast, this measure for the proposed incremental traffic assignment technique (PITAT) equals 0.52. The main shortcoming of the method is the fact that it is a heuristic method. Despite showing promising results, the convergence of the algorithm has yet to be practically proved. Considering the order of calculations, PITAT seems very attractive and can be applied as a substitute in situations similar to the case of this paper.