Economics and Mathematical MethodsEconomics and Mathematical MethodsЭкономика и математические методы0424-73883034-6177The Russian Academy of Sciences65330510.31857/S0424738824020091Mathematical analysis of economic modelsМатематический анализ экономических моделейResearch ArticleDynamic and agent-based models of intelligent transportation systemsДинамические и агентные модели интеллектуальных транспортных системBeklaryanL. A.БекларянЛ. А.
Russian Federation
beklar@cemi.rssi.ruBeklaryanG. L.БекларянГ. Л.
Russian Federation
glbeklaryan@gmail.comAkopovA. S.АкоповА. С.
Russian Federation
akopovas@umail.ruKhachatryanN. K.ХачатрянН. К.
Russian Federation
nerses-khachatryan@yandex.ruCentral Economics and Mathematics Institute, Russian Academy of Sciences (CEMI RAS)ЦЭМИ РАН0409202460210512203022025Copyright ©; 2024, Russian Academy of SciencesCopyright ©; 2024, Российская академия наук2024Russian Academy of SciencesРоссийская академия наукhttps://journals.eco-vector.com/0424-7388/article/view/653305

The authors present mathematical and simulation models of intelligent transportation systems (ITS). The models of two types are considered: the dynamic model of cargo transportation and agent-based model of the ITS — the ‘Manhattan grid’ type. The problem of rational railway planning related to research of cargo transportation models and corresponding cargo flows within the dynamic system is studied. The process of cargo transportation was modelled considering the mechanism of interactions with major railway infrastructure elements. The variation ranges of parameters at which cargo transportation system can be consistently active are defined. Possibilities of simulation modelling transportation and pedestrian flows at the micro-level considering complex interactions between heterogeneous agents, in particular, vehicles-to-pedestrians (V2P), vehicles-to-vehicles (V2V), vehicles-to- infrastructure elements (traffic lights) (V2I) etc. using the case study as the ITS belonging to the “Manhattan grid” type studied. As a result, it is shown that ITS with partially controlled pedestrian crossings have advantage by the level of the total traffic in comparison to the ITS with uncontrolled crossings, especially with low-intensity and high-speed traffic. The two types of models are united by the unity of their tool-making description. For models of the first type, all processes at the micro-level are strictly regulated. Therefore, such systems are well characterized by established macro-indicators — states of the soliton solutions class (i. e. the solutions of travelling wave type). In models of the second type, there are large fluctuations at the micro-level that affect the safety of road users (e. g., traffic jams, accidents, etc.). This explains the use of agent-based models that consider processes at the micro-level. At the same time, macro-indicators are the most important characteristics for checking the adequacy of agent-based models.

В статье представлены разработанные авторами математические и имитационные модели интеллектуальных транспортных систем (ИТС) — динамическая модель грузоперевозок и агентная модель ИТС «Манхэттенская решетка». Изучена проблема рационального железнодорожного планирования, относящаяся к исследованию режимов грузоперевозок и соответствующих им грузопотоков в рамках динамической системы. Выполнено моделирование процесса грузоперевозок с учетом механизма взаимодействия основных элементов железнодорожной инфраструктуры. Определены диапазоны изменения параметров, при которых система грузоперевозок может бесперебойно функционировать. На примере ИТС «Манхэттенская решетка» изучены возможности имитационного моделирования транспортных и пешеходных потоков на микроуровне с учетом сложных взаимодействий между гетерогенными агентами, в частности транспортными средствами (ТС) и пешеходами (V2P), ТС и ТС (V2V), ТС и инфраструктурными элементами (светофорами) (V2I) и т. д. Показано, что ИТС с частично регулируемыми пешеходными переходами имеет преимущество по уровню суммарного трафика по сравнению с нерегулируемыми переходами, особенно при малоинтенсивном и высокоскоростном движении. Приведенные в статье модели объединяет единство их инструментального описания. Для моделей первого типа все действия на микроуровне строго регламентированы. Поэтому такие системы хорошо характеризуют установившиеся макропоказатели — состояния класса солитонных (решений типа бегущей волны). В моделях второго типа на микроуровне существуют большие флуктуации, которые влияют на безопасность участников движения (образование пробок, аварии и т. д.). Этим объясняется и применение агентных моделей, учитывающих процессы на микроуровне. Макропоказатели являются важнейшими характеристиками для проверки адекватности агентных моделей.

intelligent transportation systemscargo transportation models‘Manhattan grid’agent-based modelling of transportation systemstraffic simulationdynamic transportation systemsmanagement of railway transport‘smart’ traffic lightsинтеллектуальные транспортные системымодели грузоперевозокМанхэттенская решеткаагентное моделирование транспортных системмоделирование дорожного движениядинамические транспортные системыуправление железнодорожным транспортомумные светофорыАкопов A. C., Бекларян Л. А. (2022). Моделирование динамики дорожно-транспортных происшествий с участием беспилотных автомобилей в транспортной системе «умного города» // Бизнес-информатика. Т. 16. № 4. С. 19–35. [Akopov A. S., Beklaryan L. A. (2022). Simulation of rates of traffic accidents involving unmanned ground vehicles within a transportation system for the ‘smart city’. Business Informatics, 16 (4), 19–35 (in Russian).]Акопов А. С., Бекларян Л. А. (2015). Агентная модель поведения толпы при чрезвычайных ситуациях // Автоматика и телемеханика. № 10. С. 131–143. [Akopov A. S., Beklaryan L. A. (2015). An agent model of crowd behaviour in emergencies. Automation and Remote Control, 76 (10), 1817–1827 (in Russian).]Бекларян А. Л., Бекларян Л. А., Акопов А. С. (2023). Имитационная модель интеллектуальной транспортной системы «умного города» с адаптивным управлением светофорами на основе нечёткой кластеризации // Бизнес-информатика. Т. 17. № 3. С. 70–86. DOI: 10.17323/2587-814X.2023.3.70.86 [Beklaryan A. L., Beklaryan L. A., Akopov A. S. (2023). Simulation model of an intelligent transportation system for the ‘smart city’ with adaptive control of traffic lights based on fuzzy clustering. Business Informatics, 17, 3, 70–86 (in Russian).]Бекларян Л. А. Хачатрян Н. К. (2013). Об одном классе динамических моделей грузоперевозок // Журнал вычислительной математики и математической физики. Т. 53. № 10. С. 1649–1667. [Beklaryan L. A., Khachatryan N. K. (2013). On one class of dynamic transportation models. Computational Mathematics and Mathematical Physics, 53 (10), 1466–1482 (in Russian).]Гасников А. В., Кленов С. Л., Нурминский Е. А., Холодов Я. А., Шамрай Н. Б. (2013). Введение в математическое моделирование транспортных потоков. А. В. Гасников (ред.). М.: МЦНМО. [Gasnikov A. V., Klenov S. L., Nurminsky E. A., Kholodov Ya.A., Shamray N. B. (2013). Introduction to mathematical modeling of traffic flows. A. V. Gasnikov (ed.). Moscow: Moscow Center for Continuous Mathematical Education (in Russian).]Лазарев А. А., Мусатова Е. Г., Гафаров Е. Р., Кварацхелия А. Г. (2012). Теория расписаний. Задачи железнодорожного планирования. М.: ИПУ РАН. 92 с. [Lazarev A. A., Musatova E. G., Gafarov E. R., Kvaratskhelia A. G. (2012). Schedule theory. Problems of railway planning. Moscow: Trapeznikov Institute of Control Sciences RAS. 92 p. (in Russian).]Лазарев А. А., Садыков Р. Р. (2014). Задача управления парком грузовых железнодорожных вагонов. В сб.: «XII Всероссийское совещание по проблемам управления (ВСПУ 2014)». Москва, ИПУ РАН, 16–19 июня 2014. С. 5083–5093. [Lazarev A. A., Sadykov R. R. (2014). The task of managing the fleet of freight railway cars. In: XII All-Russian Conference on Management Problems (VSPU2014). Moscow: Trapeznikov Institute of Control Sciences RAS, June 16–19, 2014, 5083–5093 (in Russian).]Хачатрян Н. К. (2013). Динамическая модель организации грузоперевозок при ограниченности емкостей перегонных путей // Бизнес-информатика. № 4 (26). С. 62–68. [Khachatryan N. K. (2013). Dynamic model of organization of cargo transportation with a limited capacity of the distillation ways. Business Informatics, 4 (26), 62–68 (in Russian).]Хачатрян Н. К., Бекларян Л. А. (2021). Исследование динамики потока в модели организации грузоперевозок по круговой цепочке станций // Экономика и математические методы. Т. 57. № 1. С. 83– 91. [Khachatryan N. K., Beklaryan L. A. (2021). Study of flow dynamics in the model of cargo transportation organization along a circular chain of stations. Economics and Mathematical Methods, 57 (1), 83–91 (in Russian).]Швецов В. И. (2003). Математическое моделирование транспортных потоков // Автоматика и телемеханика. № 11. С. 3–46. [Shvetsov V. I. (2003). Mathematical modelling of traffic flows. Automation and Remote Control, 64 (11), 1651–1689 (in Russian).]Akopov A. S., Beklaryan L. A., Beklaryan A. L. (2020). Simulation-based optimization for autonomous transportation systems using a parallel real-coded genetic algorithm with scalable nonuniform mutation. Cybernetics and Information Technologies, 21 (3), 127–144.Akopov A. S., Beklaryan L. A., Thakur M. (2022). Improvement of maneuverability within a multiagent fuzzy transportation system with the use of parallel bi-objective real-coded genetic algorithm. IEEE Transactions on Intelligent Transportation Systems, 23 (8), 12648–12664.Akopov A. S., Beklaryan L. A. (2024). Traffic improvement in Manhattan road networks with the use of parallel hybrid biobjective genetic algorithm. IEEE Access, 12, 19532–19552.Andersen J., Christiansen M. (2009). Designing new European rail freight services. Journal of the Operational Research Society, 60, 348–360.Bando M., Hasebe K., Nakanishi K., Nakayama A. (1998). Analysis of optimal velocity model with explicit delay. Physical Review. E, 58, 5429–5435.Bar-Gera H. (2002). Origin-based algorithm for the traffic assignment problem. Transportation Science, 36, 4, 398–417.Beklaryan L. A., Khachatryan N. K. (2006). Traveling wave type solutions in dynamic transport models. Functional Differential Equations, 13, 2, 125–155.Beklaryan L. A., Khachatryan N. K., Akopov A. S. (2019). Model for organization cargo transportation at resource restrictions. International Journal of Applied Mathematics, 32, 4, 627–640.Brackstone M., McDonald M. (2000). Car following: A historical review. Transportation Research. F, 2, 181–196.Brassil J., Choudhury A. K., Maxemchuk N. F. (1994). The Manhattan street network: A high performance, highly reliable metropolitan area network. Computer Networks and ISDN Systems, 26, 6–8, 841–858.Buchel B., Spanninger T., Corman F. (2020). Empirical dynamics of railway delay propagation identified during the large-scale Rastatt disruption. Scientific Reports, 10, 1. DOI: 10.1038/s41598-020-75538-zCacchiani V., Caprara A., Toth P. (2010). Scheduling extra freight trains on railway networks. Transportation Research. B, 44, 2, 215–231.Campetella M., Lulli G., Pietropaoli U., Ricciardi N. (2006). Fright service design for the Italian railways company. In: Proceedings of the 6th Workshop on Algorithmic Approach for Transportation Modelling, Optimization, and Systems (ATMOS2006). Zurich, Switzerland, 14 September 2006, 1–13.Carrothers G. A.P. (1956). An historical review of the gravity and potential concepts of human interaction. Journal of the American Institute of Planners, 22, 94–102.Cassidy M. J., Jang K., Daganzo C. F. (2011). Macroscopic fundamental diagrams for freeway networks: Theory and observation. Transportation Research Record Journal of the Transportation Research Board, 2260, 8–15.Ceselli A., Gatto M., Lübbecke M., Nunkesser M., Schilling H. (2008). Optimizing the cargo express service of Swiss Federal Railways. Transportation Science, 42, 4, 450–465.Chowdhury D., Santen L., Schadschneider A. (2000). Statistical physics of vehicular traffic and some related systems. Physics Reports, 329, 199–329.Cremer M., Ludwig J. (1986). A fast simulation model for traffic flow on the basis of Boolean operations. Mathematics and Computers in Simulation, 28, 297–303.Daganzo C. F. (1995). The cell transmission model. Part II: Network traffic. Transportation Research. B, 29, 79–93.Daganzo C. F. (2008). An analytical approximation for the macroscopic fundamental diagram of urban traffic. Transportation Research. B, 42, 9, 771–781.Dekker M., Medvedev A., Rombouts J., Siudem G., Tupikina L. (2022). Modelling railway delay propagation as diffusion-like spreading. EPJ Data Science, 11, 44. DOI: 10.1140/epjds/s13688-022-00359-1Dekker M. M., Panja D. (2021). Cascading dominates large-scale disruptions in transport over complex networks. PLoS ONE, 16, 1, 1–17.Ferreira L., Murray M. H. (1997). Modelling rail track deterioration and maintenance: Current practices and future needs. Transport Reviews, 17, 3, 207–221.Fotheringham A. S. (1986). Modelling hierarchical destination choice. Environment and Planning. A, 18, 401–418.Fukasawa R., Arago M. P., Porto O., Uchoa E. (2002). Solving the freight car flow problem to optimality. Electronic Notes in Theoretical Computer Science, 66, 6, 42–52.Gambardella L. M., Rizzoli A. E., Funk P. (2002). Agent-based planning and simulation of combined rail/road transport. Simulation, 78, 5, 293–303.Gazis D. C., Herman R., Rothery R. W. (1961). Nonlinear follow the leader models of traffic flow. Operations Research, 9, 4, 545–567.Geroliminis N., Sun J. (2011). Properties of a well-defined macroscopic fundamental diagram for urban traffic. Transportation Research. B, 45, 3, 605–617.Goverde R. M.P. (2010). A delay propagation algorithm for large-scale railway traffic networks. Transportation Research. C, 18, 3, 269–287.Harris B., Wilson A. G. (1978). Equilibrium values and dynamics of attractiveness terms in production-constrained spatial-interaction models. Environment and Planning. A, 10, 371–388.Harrod S., Cerreto F., Nielsen O. A. (2019). A closed form railway line delay propagation model. Transportation Research. C, 102, 189–209.Helbing D., Treiber M. (1998). Gas-kinetic-based traffic model explaining observed hysteretic phase transition. Physical Review Letters, 81, 3042–3045.Heywood P., Richmond P., Maddock S. (2015). Road network simulation using FLAME GPU. In: Euro-Par 2015: Parallel Processing Workshops. Euro-Par 2015 International Workshops, 24–25 Aug 2015, 2015. Vienna (Austria). Lecture Notes in Computer Science, 9523. Springer (Cham.), 430–441. ISBN: 978-3-319-27307-5.Higgins A., Ferreira L., Kozan E. (1995). Modeling single-line train operations. Transportation Research Record, 1489, 9–16.Jeong S.-J., Lee C.-G., Bookbinder J. (2007). The European freight railway system as a hub-and-spoke network. Transportation Research. A, 41, 6, 523–536.Kerner B. S. (2009). Introduction to modern traffic flow theory and control: The long road to three-phase traffic theory. Berlin: Springer.Khachatryan N. (2022). Bifurcation in the model of cargo transportation organization. Advances in Systems Science and Applications, 22, 4, 79–91.Khachatryan N. K. (2020). Study of flow dynamics in the model of cargo transportation organization between node stations. International Journal of Applied Mathematics, 33, 5, 937–949.Khachatryan N. K. (2021). Modeling the process of cargo transportation between node stations. International Journal of Applied Mathematics, 34, 6, 1223–1235.Khachatryan N. K., Akopov A. S. (2017). Model for organizing cargo transportation with an initial station of departure and a final station of cargo distribution. Business Informatics, 1, 25–35.Khachatryan N. K., Akopov A. S., Belousov F. A. (2018). About quasi-solutions of traveling wave type in models for organizing cargo transportation. Business Informatics, 1, 43, 61–70.Kraay D., Barker P. T., Chen B. T. (1991). Optimal pacing of trains in freight railroads: Model formulation and solution. Operations Research, 39, 1, 82–99.Kuhne R. D. (1984). Macroscopic freeway model for dense traffic stop-start waves and incident detection. Proceedings of Ninth International Symposium on Transport and Traffic Theory. R. Hamerslag (ed.). Utrecht: VNU Science, 21–42.Liu L., Dessouky M. (2017). A decomposition based hybrid heuristic algorithm for the joint passenger and freight train scheduling problem. Computers & Operations Research, 87, 165–182.Lo H. K., Chen A. (2002). Traffic equilibrium problem with route-specific costs: Formulation and algorithms. Transportation Research. B, 34, 6, 493–513.Ludvigsen J., Klaboe R. (2014). Extreme weather impacts on freight railways in Europe. Natural Hazards, 70, 1, 767–787.Lulli G., Pietropaoli U., Ricciardi N. (2011). Service network design for freight railway transportation: the Italian case. Journal of the Operational Research Society, 62, 12, 2107–2119.Nelson P. (1995). A kinetic model of vehicular traffic and its associated bimodal equilibrium solutions. Transport Theory and Statistical Physics, 24, 383–409.Pipes L. A. (1953). An operational analysis of traffic dynamics. Journal of Applied Physics, 24, 274–281.Popkov Yu.S. (1995). Macrosystems theory and its applications. Berlin: Springer Verlag.Richmond P., Chisholm R., Heywood P., Leach M., Kabiri Chimeh M. (2021). FLAME GPU. ZENODO. Available at: https://zenodo.org/records/5465845Sadykov R., Lazarev A., Shiryaev V., Stratonnikov A. (2013). Solving a freight railcar flow problem arising in Russia. In: 13th Workshop on Algorithmic Approach for Transportation Modelling, Optimization, and Systems (ATMOS’13). Sophia Antipolis, France, 5 September 2013, 55–67.Samal S. R., Mohanty M., Santhakumar S. M. (2021). Adverse effect of congestion on economy, health and environment under mixed traffic scenario. Transportation in Developing Economies, 7, 15. DOI: 10.1007/s40890-021-00125-4Sarma S. S., Sinha K., Sub-r-pa C., Chakraborty G., Sinha B. P. (2021). Optimal distribution of traffic in Manhattan road networks for minimizing routing-time. IEEE Transactions on Intelligent Transportation Systems, 22, 11, 6799–6820.Shvetsov V. I. (2009). Algorithms for distributing traffic flows. Automation and Remote Control, 70, 10, 1728–1736.Sweet M. (2014). Traffic congestion’s economic impacts: Evidence from US metropolitan regions. Urban Studies, 51, 10, 2088–2110.Tomer E., Safonov L., Havlin S. (2000). Presence of many stable nonhomogeneous states in an inertial car-following model. Physical Review Letters, 84, 2, 382–385.Treiber M., Hennecke A., Helbing D. (2000). Congested traffic states in empirical observations and microscopic simulations. Physical Review. E, 62, 1805–1824.Weik N. (2022). Macroscopic traffic flow in railway systems — a discussion of the applicability of fundamental diagrams. Journal of Rail Transport Planning & Management, 23 (5). DOI: 10.1016/j.jrtpm.2022.100330Wilson A. G. (1971). A family of spatial interaction models and associated developments. Environment and Planning. A, 3, 255–282.Zieger S., Weik N., Niesen N. (2018). The influence of buffer time distributions in delay propagation modelling of railway networks. Journal of Rail Transport Planning & Management, 8, 3–4, 220–232.