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T-Comm_Article 8_11_2021

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MATHEMATICAL MODELS FOR TRAFFIC FLOWS ON HIGHWAYS WITH INTERSECTIONS AND JUNCTIONS

Maria Yu. Karelina,  Moscow Automobile and Road Construction State Technical University, Moscow, Russia, karelina@madi.ru
Pavel I. Pospelov, Moscow Automobile and Road Construction State Technical University, Moscow, Russia, pospelov@madi.ru
Yuri V. Trofimenko, Moscow Automobile and Road Construction State Technical University, Moscow, Russia
Alexey V. Terentyev, Moscow Automobile and Road Construction State Technical University, Moscow, Russia
Alexander G. Tatashev, Moscow Automobile and Road Construction State Technical University, Moscow, Russia, a-tatashev@yandex.ru
Marina V. Yashina, Moscow Automobile and Road Construction State Technical University, Moscow, Russia, yash-marina@yandex.ru

Abstract
Mathematical models of motor traffic flow on highway sections on highway sections near intersections or flow segregation sections are considered. In these models, the particles corresponding to motor vehicles move according to probabilistic rules along a cellular field that moves at a constant speed in the direction coinciding with the direction of movement of the particles. A cell field consists of sequences of cells. Each such sequence corresponds to a lane on the highway. The time scale in the model is discrete or continuous. The model is a dynamic system with a discrete state space and discrete or continuous time. The mathematical description of the model can also be presented in terms of a cellular automaton or a random process with prohibitions. At any given time, there is no more than one particle in each cell. With each movement, the particle either moves one cell in the direction of movement, or moves to the next lane, or remains in place. The speed of the traffic flow on the highway section corresponds to the sum of the set speed of the cell field and the average speed of the particles relative to the field. The studied characteristics are the speed of the traffic flow, its intensity and the probability of successful rebuilding of the vehicle on the considered section of the highway. When setting the parameters of the model, data from measurements of the characteristics of traffic flows on highways are used. Analytical approaches have been developed to evaluate the studied characteristics. Computer programs have been created to implement the developed calculation algorithms. The results of calculations are given.

Keywords:mathematical models of traffic, characteristics of motor traffic, multi-lane traffic, cellular automata, random processes with prohibitions

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Information about authors:

Maria Yu. Karelina, Doctor of Technical Sciences, Professor, Moscow Automobile and Road Construction State Technical University, Moscow, Russia
Pavel I. Pospelov, Doctor of Technical Sciences, Professor, Moscow Automobile and Road Construction State Technical University, Moscow, Russia
Yuri V. Trofimenko, Moscow Automobile and Road Consstruction State Technical University, Moscow, Russia
Alexey V. Terentyev, Doctor of Technical Sciences, Docent, Moscow Automobile and Road Construction State Technical University, Moscow, Russia
Alexander G. Tatashev, Doctor of Physical and Mathematical Sciences, Professor, Moscow Automobile and Road Construction State Technical University, Moscow, Russia
Marina V. Yashina, Doctor of Technical Sciences, Professor, Moscow Automobile and Road Construction State Technical University, Moscow, Russia