Application of Density and Queue Length Functions in Mesoscopic Dynamic Traffic Assignment

One of the traditional ways to improve the condition of the networks is the construction of new roads, which is not a desirable option today, especially in crowded urban areas due to the high cost of construction. One of the effective options in this regard is traffic management methods. The issue of traffic assignment, especially dynamic traffic assignment by providing a platform for examining the status of the network under study by providing a traffic flow model is one of the important tools and components in the discussion of traffic management. In this study, using a complete and general dynamic network loading method based on LWR network expansion model, the dynamic network loading problem is formulated as a system of differential algebraic equations that the resulting dynamic network loading model is able to form, propagate and lose physical queue. In this research, an algorithm based on the fixed point formula has been used to solve dynamic user equilibrium problems. Then the software package algorithm in C ++ language is defined to implement both systems of differential algebraic equations and the fixed point algorithm by considering the queue spillback. The program is developed in such a way that it can be used to solve dynamic user balance problems and load dynamic network in any large-scale network defined by the user. The C ++ program was implemented for the Chicago metropolitan area network with 86,179 origin-destination pairs and 250,000 routes, and after 69 repetitions, the convergence threshold was reached and the results were evaluated. Finally, the results of this study are evaluated and the accuracy of the results is shown.