چكيده به لاتين
One of the traditional ways to improve the condition of networks is to build new roads, which are no longer a desirable option today, especially in crowded urban areas, due to the high cost of construction. traffic management methods are one of the effective options in this regard. the issue of traffic assignment, especially dynamic traffic assignment, is one of the important tools and components in the traffic management discussion by providing a platform for examining the status of the network under study and also creating a traffic flow pattern. in this study, first, a computational theory for dynamic user equilibrium in large-scale networks is introduced; then, using a dynamic network loading method based on the LWR network expansion model, the dynamic network loading problem is formulated as a system of differential algebraic equations. the resulting dynamic network loading model is capable of forming, propagating, and dissipating physical queues. to facilitate this, the system of differential algebraic equations is discretized. dynamic user equilibrium calculation is facilitated by equivalent mathematical formulations such as variable inequality, differential variable inequality, fixed point problem, and nonlinear complement problem. this research uses an algorithm based on the fixed-point formulation to solve dynamic user equilibrium problems. the innovation of this research is to create a software package in C++ language to implement both systems of differential algebraic equations and fixed-point algorithm, taking into account queue regression. the program is developed in such a way that it can be used to solve dynamic user equilibrium problems and dynamic network loading on any large-scale network. the mentioned c++ program was implemented for testing for the Chicago metropolitan area with 86,179 origin-destination pairs and 250,000 routes, and after 69 repetitions, the convergence with the threshold of 0.001 was reached and the results were evaluated. the results show that the flow departure rate assumes non-negative values only when the effective delay is minimized and equalized, which indicates the establishment of the concept of dynamic user equilibrium and accuracy of research.
