Моделирование транспортных потоков методом системной динамики

Abstract

The article discusses the application of the system dynamics methodology for simulation of controlled traffic flows. In the classical formulation, system dynamics models represent a system of finite-difference equations, which is an approximation of the Cauchy problem by the Euler method. The implementation of finite-difference equations in system dynamics by J. Forrester is carried out by the DYNAMO specialized graphical tools. It is proposed that the Cauchy problem be implemented using structural diagrams in which a one-to-one correspondence of specific structural links to system dynamics paradigms is established. As a result of the research, it was shown that an aperiodic link with a typical nonlinear “saturation” function identifies with a sufficient accuracy the basic paradigms of system dynamics, such as rates, levels and delays. It is shown that the resulting system of ordinary differential equations, when imposing control conditions, has discontinuities of the first kind in derivatives and requires integration methods with a variable step and variable order for effective solution. The proposed approach to modeling traffic flows, in contrast to the classical one, allows the use of modern modeling tools with a graphical language of structural diagrams and a library of methods for numerical analysis of complex dynamic processes. The implementation of a specific test scenario for modeling traffic flows was carried out in the SimInTech software package. The efficiency metrics of integration methods are obtained. A comparative analysis of the effectiveness of integration methods in solving this problem was carried out. It is shown that the most effective in solving problems of the considered class are the explicit adaptive integration methods ARK21, AM61 with a variable step from the SimInTech library, which are much more effective than the explicit Euler method in classical system dynamics.