Simulation of One-way Traffic Flow Using the System Dynamics Method

The problems of simulation traffic flows arise in various areas of human activity, for example in the road industry and in the design of production lines. Various approaches are used to simulate traffic flows. One of them is the use of system dynamics methods. The use of system dynamics makes it possible to model traffic flow as a continuous system of ordinary differential equations. The presence of control algorithms in the model when using the system dynamics method leads to the appearance of additional nonlinearities with discontinuities of the first type. This leads to the fact that in certain regimes the system of differential equations becomes stiff. To solve these systems of equations, various integration methods can be used, including methods with a variable integration step. The use of methods with a variable integration step in combination with event detection methods makes it possible to perform calculations with a step significantly larger than when using discrete traffic flow models.