Математическая модель транспортного поведения на основе теории транспортных макросистем

Continuing the study, the purpose of which was to develop a new approach to determining the transport behaviour of residents of urban agglomerations, to outline the main ways of its development, a new description of transport behaviour is proposed based on various scientific disciplines and the theory of macrosystems.This, according to the authors, will make contribution to laying the foundation for creation of a currently missing theory of transport behaviour.A developed mathematical model of transport behaviour based on the provisions of academician Yu. S. Popkov’s theory of macrosystems, uses the entropy approach to determine the equilibrium state of the transport system. At the same time, the model identifies an initial list of parameters responsible for describing the «transport behaviour». The latter is considered as a collective phenomenon that creates a deterministic representation resulting from interaction of many stochastically acting elements (road users). A compiled preliminary scheme can be used to solve the problem of finding unknowns in the system of equations and inequalities within the model.В продолжение исследования, целью которого была разработка нового подхода к определению транспортного поведения жителей городских агломераций, наметить главные пути его развития, предложено новое описание транспортного поведения с позиций самых разных научных дисциплин и теории макросистем.Это, по мнению авторов, закладывает базис для создания теории транспортного поведения, которая в настоящее время отсутствует.Разработана математическая модель транспортного поведения, которая основана на положениях теории макросистем академика Ю. С. Попкова, с использованием энтропийного подхода при определении равновесного состояния транспортной системы. При этом в модели определён первоначальный список параметров, отвечающих за описание «транспортного поведения». Последнее рассматривается как коллективный феномен, создающий детерминированное представление, возникающее в результате взаимодействия множества стохастически действующих элементов (участников дорожного движения).Составлена предварительная схема решения задачи о поиске неизвестных системы уравнений и неравенств в модели

Taking into account the complexity in the tasks of transport demand

The article describes the theoretical basis for taking into account the complexity in solving problems of transport demand, the analysis of the concept of “self-organized criticality” is carried out. The problems of describing complex conduct in transport systems are solved, the prerequisites or causes of complex behavior are indicated, the traditional definitions of a “complex transport system” are formalized. Examples of some models demonstrating complex behavior in transport systems are given. Objective: formulation of research directions in the theory of transport systems, which should be developed with the help of conceptual and mathematical devices of individual sciences, such as complexity theory, nonlinear dynamics, to solve problems of transport demand, accompanied by flows of various events and elements in transport macrosystems, to take into account the complexity of problems in the theory of transport systems in modeling the dynamics of transport demand. Approaches used: development of mathematical models of nonlinear transport systems demonstrating complex behavior, including models with power-law distribution of system characteristics within the framework of self-organized criticality, as well as models demonstrating bifurcations. Methods and (or) methodological apparatus of research: methods of the theory of self-organized criticality and synergetics, allowing to take into account the properties of a complex system. The scientific novelty lies in the use of methods and approaches of the theory of self-organized criticality and complexity theory for a wide class of models of transport systems used in problems of transport demand and based on traffic flow models. Directions for further research, recommendations: it is required to analyze real statistics of the behavior of transport systems that correspond to various states of the transport system, including complex behavior, as well as the formulation and solution of problems of the theory of transport macrosystems