Journal articles: 'Traffic flow Mathematical models'

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McCartney, M. "Comparing mathematical models of traffic flow." Teaching Mathematics and its Applications 19, no. 4 (December 1, 2000): 183–87. http://dx.doi.org/10.1093/teamat/19.4.183.

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Junevičius, Raimundas, and Marijonas Bogdevičius. "MATHEMATICAL MODELLING OF NETWORK TRAFFIC FLOW." TRANSPORT 24, no. 4 (December 31, 2009): 333–38. http://dx.doi.org/10.3846/1648-4142.2009.24.333-338.

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The article describes mathematical models of traffic flows to initiate different traffic flow processes. Separate elements of traffic flow models are made in a way to be connected together to get a single complex model. A model of straight road with different boundary conditions is presented as a separate part of the network traffic flow model. First testing is conducted in case the final point of the whole modelled traffic line is closed and no output from that point is possible. The second test is performed when a constant value of traffic flow speed and traffic flow rate is entered. Mathematical simulation is carried out and the obtained results are listed.

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Takači, Arpad. "Mathematical and simulation models of traffic flow." PAMM 5, no. 1 (December 2005): 633–34. http://dx.doi.org/10.1002/pamm.200510293.

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Junevičius, Raimundas, Marijonas Bogdevičius, and Ádám Török. "MODELLING OF INTERNAL COMBUSTION ENGINES’ EMISSION THROUGH THE USE OF TRAFFIC FLOW MATHEMATICAL MODELS." TRANSPORT 26, no. 3 (October 5, 2011): 271–78. http://dx.doi.org/10.3846/16484142.2011.621978.

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Road traffic flows on a straight road segment are modelled in this article. The mathematical model of traffic flows has been constructed by using the method of lumped parameters. CO2, CO, CH, NOx, PM regression equations of internal combustion engines’ (ICE) emission has been developed. The accuracy of regression equations is 0.98÷0.99. The article presents assumptions for constructing the mathematical model, description of the mathematical model and gives simulation results. Traffic flow parameters, such as traffic flow concentration and traffic flow speed are presented as modelling results. ICE emission depending on the concentration and traffic flow speed are presented as well.

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Otegen, Diana Assankhankyzy. "MODELS OF TRAFFIC FLOW DYNAMICS ON HIGHWAYS." Вестник КазАТК 116, no. 1 (March 15, 2021): 236–41. http://dx.doi.org/10.52167/1609-1817-2021-116-1-236-241.

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The paper is an analytical review of the currently existing methods of traffic flows modeling. The movement of vehicles on the road can be modeled in different ways. Mathematical models as tools that allow us to study complex processes in the real world, including transport infrastructure, without capital expenditures, are a popular tool for solving many problems in various spheres of the national economy. There are several approaches to mathematical modeling of traffic flows. In microscopic models, the law of motion of each car is set, depending on its current position, speed, characteristics of the movement of neighboring cars, and other factors. Microscopic models, in turn, can be divided into models that are continuous in space and time, and into models that are discrete in space and time, the so-called cellular automata. In macroscopic models, the transport flow is considered as a fluid flow with special properties. The equations of the macroscopic model establish the relationship between the flow, density, speed of movement, possibly acceleration, and so on. Macroscopic models can also be continuous or discrete. In continuous models, the change in the state of a road section without branches and intersections is usually described by partial differential equations. Modeling traffic flows is necessary because active experiments in the existing transport network are fraught with unpredictable consequences, and in many cases are not feasible at all. The work presents a description and analysis of the models, and of their advantages and disadvantages.

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Guseynov, Sharif E., and Alexander V. Berezhnoy. "MODELLING OF URBAN TRAFFIC FLOW." Environment. Technology. Resources. Proceedings of the International Scientific and Practical Conference 1 (June 15, 2017): 109. http://dx.doi.org/10.17770/etr2017vol1.2632.

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In this paper non-deterministic motion of urban traffic is studied under certain assumptions. Based on those assumptions discrete and continuous mathematical models are developed: continuous model is written as the Cauchy initial-value problem for the integro-differential equation, whence among other things it is obtained the Fokker-Planck equation. Besides, the sufficient condition ensuring the mathematical legitimacy of the developed continuous model is formulated.

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Tyagi, V., S. Darbha, and K. R. Rajagopal. "A review of the mathematical models for traffic flow." International Journal of Advances in Engineering Sciences and Applied Mathematics 1, no. 1 (July 2009): 53–68. http://dx.doi.org/10.1007/s12572-009-0005-8.

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POSPELOV, PAVEL I., ALEXANDER G. TATASHEV, ALEXEY V. TERENTYEV, MARIA Yu KARELINA, and MARINA V. YASHINA. "BARTLETT FLOWS AND MATHEMATICAL DESCRIPTION OF MOTOR TRAFFIC FLOWS." H&ES Research 13, no. 6 (2021): 34–41. http://dx.doi.org/10.36724/2409-5419-2021-13-6-34-41.

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Introduction: The class of mathematical traffic models is based on the theory of queuing. In these models, the application entering the service system corresponds to the vehicle. When developing a traffic model formulated in terms of queuing, it is necessary to specify a random flow that is incoming to the queuing system. The purpose of the study: Traditional queuing systems with recurrent incoming flow under appropriate conditions do not reflect the specific features of real traffic flows. Under certain conditions, for example, it may be appropriate to use a Markov-type flow in the model, the intensity of which depends on the state of a mathematical object called the control device. In the general case, such a flow can be specified as non-uniform, and with such a task, each request is assigned a type that also depends on the state of the control device. Setting the qualitative structure and parameters of a random flow depends on the assessment of the speed characteristics of the vehicles that form the flow, and, therefore, is related to the issues of studying the speed characteristics of real vehicles. Practical significance: At a sufficiently low density of the traffic flow, the incoming flow is close to the Poisson one. As traffic increases and road conditions worsen, the risk of overtaking increases and clusters are formed, consisting of a slow car moving in front and a group of fast cars that cannot overtake a slow one. In such cases, we can assume that the incoming flow is a Bartlett flow, which has the following form: clusters form a Poisson flow, and the cluster length distribution is a two-parameter Bartlett distribution. One of the parameters of this distribution is the probability of having a group of fast cars, and the second parameter characterizes the distribution of the number of cars in this group. Discussion: In this paper, we study the questions of setting a qualitative probabilistic structure and quantitative parameters of random flows, which are elements of queuing systems used as traffic models.

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Bazaras, Jonas, Janina Jablonskytė, and Eglė Jotautienė. "INTERDEPENDENCE OF NOISE AND TRAFFIC FLOW." TRANSPORT 23, no. 1 (March 31, 2008): 67–72. http://dx.doi.org/10.3846/1648-4142.2008.23.67-72.

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Traffic flows in cities, especially in city centres, are intensive and uneven, moreover, registered noise levels exceed allowable limits. Noise levels have been measured at K. Mindaugo ave. and Birštono street crossing in Kaunas and data of automated traffic flow registration equipment have been used. A constant reduction of noise level from the beginning till the end of the green light has been identified ‐ “hot starts” generated noise dominates. To make estimates of noise and traffic flow interdependency, mathematical statistical models have been applied. Parameter distribution patterns have been analysed, prediction models have been composed.

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Oleg Fyodorovich Danilov, Victor Ivanovich Kolesov, Denis Alexandrovich Sorokin, and Maxim Leonidovich Gulaev. "Study on the Vehicle Linear Dynamic Interval in a Traffic Flow." Communications - Scientific letters of the University of Zilina 23, no. 1 (January 4, 2021): E11—E22. http://dx.doi.org/10.26552/com.c.2021.1.e11-e22.

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The transportation industry of a modern city involves the effective systems for the road traffic management. To manage any object is impossible without understanding its specifics. The tasks of road traffic management are based on mathematical models of traffic flows. The “following the leader” model based on the linear dynamic interval of vehicles has become widely accepted in the model analysis. The paper discusses the mathematical model of the linear dynamic interval of vehicles; the model is identified structurally and parametrically. Coefficients of the model are analyzed in detail; a generalized assessment of the dynamic performance of the traffic flow, evolved in various road conditions, is given. The study has resulted in the proposed basic models for traffic flows that can be used for algorithmic support of the model analysis of traffic flows and the road traffic management.

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De Angelis, E. "Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems." Mathematical and Computer Modelling 29, no. 7 (April 1999): 83–95. http://dx.doi.org/10.1016/s0895-7177(99)00064-3.

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Twarock, Reidun. "Quadratic algebras in traffic flow models." Reports on Mathematical Physics 51, no. 2-3 (April 2003): 381–89. http://dx.doi.org/10.1016/s0034-4877(03)80030-7.

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Karelina, Maria Yu, Pavel I. Pospelov, Yuri V. Trofimenko, Alexey V. Terentyev, Alexander G. Tatashev, and Marina V. Yashina. "Mathematical models for traffic flows on highways with intersections and junctions." T-Comm 15, no. 11 (2021): 61–68. http://dx.doi.org/10.36724/2072-8735-2021-15-11-61-68.

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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.

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Schadschneider, A., and M. Schreckenberg. "Cellular automation models and traffic flow." Journal of Physics A: Mathematical and General 26, no. 15 (August 7, 1993): L679—L683. http://dx.doi.org/10.1088/0305-4470/26/15/011.

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Shevtsova, Anastasiya, Marina Yablonovskaya, and Alexey Borovskoy. "Origin-Destination Matrix as a Way to Create a Basic Algorithm for Simulation a Load of Transport Network." Applied Mechanics and Materials 725-726 (January 2015): 1218–23. http://dx.doi.org/10.4028/www.scientific.net/amm.725-726.1218.

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Article is devoted to studying of traffic flows using the origin-destination matrix. The first paragraph of this article deals with the possibility of applying the origin-destination matrix when modeling load of transport network. The types of transportations, the factors that affect the loading of the transport network are described. The concept of a generalized path cost, interdistrict transportations and some others are considered. There are proposed several steps to create a origin-destination matrix. In the second paragraph of the paper is proposed the classification of mathematical models that can be applied in the simulation of traffic flow, as well as their features are marked. This will help in the processing of data for selection of a mathematical model that satisfies the requirements and objectives that have set themselves researchers. The conclusions on the application of mathematical models in the study of traffic flow are made.

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Velasco, Rosa María, and Patricia Saavedra. "Macroscopic Models in Traffic Flow." Qualitative Theory of Dynamical Systems 7, no. 1 (July 9, 2008): 237–52. http://dx.doi.org/10.1007/s12346-008-0014-1.

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Abrahamowicz, Ewa, and Przemysław Orłowski. "Mathematical Model of Traffic Flow in a Macroscopic Scale." Pomiary Automatyka Robotyka 21, no. 3 (September 30, 2017): 5–10. http://dx.doi.org/10.14313/par_225/5.

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Dong, Yu Bo. "Discussion on Urban Road Traffic Congestion Algorithm for Automatically Determining." Advanced Materials Research 926-930 (May 2014): 3790–93. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.3790.

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Compared with the expressway, most of the traffic flow in urban road network can be denoted as interrupted traffic flow. Based on the current employed equipment for traffic flow collection and traffic signal control in urban roads, different types of traffic flow in urban roads are analyzed with the traffic flow arrival/departure model in transportation engineering. Mathematical models complying with traffic flow changes are utilized to match the traffic flow in both entry and exit road blocks, thus, enabled the automatic detection of traffic incident. This algorithm provides a measurement for the automatic judgment of urban road congestion and the expansion utility of intelligent transportation facilities in urban areas.

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Trapeznikova, Marina Alexandrovna, Antonina Alexandrovna Chechina, and Natalia Gennadievna Churbanova. "Traffic flow dynamics on road network fragments using two-dimensional mathematical models." Keldysh Institute Preprints, no. 93 (2016): 1–20. http://dx.doi.org/10.20948/prepr-2016-93.

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Kerner, B. S., and S. L. Klenov. "Deterministic microscopic three-phase traffic flow models." Journal of Physics A: Mathematical and General 39, no. 23 (May 23, 2006): 7605. http://dx.doi.org/10.1088/0305-4470/39/23/c01.

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Kerner, Boris S., and Sergey L. Klenov. "Deterministic microscopic three-phase traffic flow models." Journal of Physics A: Mathematical and General 39, no. 8 (February 8, 2006): 1775–809. http://dx.doi.org/10.1088/0305-4470/39/8/002.

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Jiang, Rui, and Qing-Song Wu. "Cellular automata models for synchronized traffic flow." Journal of Physics A: Mathematical and General 36, no. 2 (December 17, 2002): 381–90. http://dx.doi.org/10.1088/0305-4470/36/2/307.

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Elmehdi, Hussein. "Assessing traffic noise in teh City of Sharjah using prediction models." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 2 (August 1, 2021): 4520–25. http://dx.doi.org/10.3397/in-2021-2725.

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Noise originated from traffic on inner-city roads has been recognized as a major issue that has negative effects that go beyond annoyance and adverse health effects on people living near such roads. In this paper, we report the results of employing mathematical models for assessing traffic noise levels near roads in the City of Sharjah, UAE. Our field measurements indicated high noise levels near inter-city roads including roads in residential areas. To further investigate this, measured noise levels arising from principle traffic noise parameters were re-examined using published mathematical models with the objective of validating the acoustic noise levels generated by traffic noise of mixed composition, traffic flow rate and distance from the source. The main sound levels, namely the statistical equivalent sound levels (Leq): L10, L50 and L90 were used in the mathematical predictive models, to calculate the day time sound levels and correlated it with in situ measurements. We have examined 10 linear regression models, reported in the literature, five of which were found to provide strong correlation and were validated for predicting noise arising from traffic. The models are recommended for calculating mixed traffic noise levels and its effects on people living near these inter-city roads.

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Burinskienė, Marija, Denis Kapski, Valery Kasyanik, Anton Pashkevich, Aleksandra Volynets, and Oleg Kaptsevich. "Estimating Parameters for Traffic Flow Using Navigation Data on Vehicles." Baltic Journal of Road and Bridge Engineering 15, no. 4 (September 28, 2020): 1–21. http://dx.doi.org/10.7250/bjrbe.2020-15.492.

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The article describes the method for estimating transport flow parameters using the two-fluid Herman-Prigogine mathematical model developed considering the proposed method of estimating parameters for the system based on the passive processing of navigation data on the movement of vehicles. The efficiency of the suggested algorithms and mathematical models for estimating road traffic flow parameters and the system as a whole was confirmed performing tests using a set of tracks on the main highways of Belarus.

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Suleimen, A. А., G. B. Kashaganova, G. B. Issayeva, B. R. Absatarova, and M. C. Ibraev. "OPTIMIZATION OF MANAGEMENT OF URBAN LIGHTS WITH THE USE OF NEURAL NETWORKS." BULLETIN 389, no. 1 (February 10, 2021): 14–17. http://dx.doi.org/10.32014/2021.2518-1467.2.

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One of the most pressing problems of large cities is the problem of traffic management of vehicles. The reason for this problem is an imperfect way to manage traffic flows. Traffic light regulation is of particular importance in traffic management. Most modern traffic light control systems operate at set time intervals and are not able to cope with the constantly changing situation on the road. A promising direction for solving this problem is to optimize the system using artificial neural networks. The advantage of neural networks is self-learning, which allows the system to adapt to the changing situation on the road. Despite numerous attempts, it has not yet been possible to obtain a high-quality mathematical model of urban traffic management. This model should determine the functional dependence of transport flow parameters on control parameters. Nowadays, traffic flows are regulated everywhere by means of traffic lights. If we can get a fairly accurate mathematical model of traffic flows, we can determine the optimal duration of the traffic signal phases to achieve the maximum capacity of the road network node. A fairly accurate mathematical model of traffic management that works in predictive mode will display an estimate of the optimal control parameters, as well as make correct decisions in emergency situations. Well-known mathematical models of road traffic take into account only the average values of traffic flows, and not the exact number of cars on each road section at a particular time.

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Friedrich, Jan, Simone Göttlich, and Maximilian Osztfalk. "Network models for nonlocal traffic flow." ESAIM: Mathematical Modelling and Numerical Analysis 56, no. 1 (January 2022): 213–35. http://dx.doi.org/10.1051/m2an/2022002.

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We present a network formulation for a traffic flow model with nonlocal velocity in the flux function. The modeling framework includes suitable coupling conditions at intersections to either ensure maximum flux or distribution parameters. In particular, we focus on 1-to-1, 2-to-1 and 1-to-2 junctions. Based on an upwind type numerical scheme, we prove the maximum principle and the existence of weak solutions on networks. We also investigate the limiting behavior of the proposed models when the nonlocal influence tends to infinity. Numerical examples show the difference between the proposed coupling conditions and a comparison to the Lighthill-Whitham-Richards network model.

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Zhang, Honghai, Yan Xu, Lei Yang, and Hao Liu. "Macroscopic Model and Simulation Analysis of Air Traffic Flow in Airport Terminal Area." Discrete Dynamics in Nature and Society 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/741654.

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We focus on the spatiotemporal characteristics and their evolvement law of the air traffic flow in airport terminal area to provide scientific basis for optimizing flight control processes and alleviating severe air traffic conditions. Methods in this work combine mathematical derivation and simulation analysis. Based on cell transmission model the macroscopic models of arrival and departure air traffic flow in terminal area are established. Meanwhile, the interrelationship and influential factors of the three characteristic parameters as traffic flux, density, and velocity are presented. Then according to such models, the macro emergence of traffic flow evolution is emulated with the NetLogo simulation platform, and the correlativity of basic traffic flow parameters is deduced and verified by means of sensitivity analysis. The results suggest that there are remarkable relations among the three characteristic parameters of the air traffic flow in terminal area. Moreover, such relationships evolve distinctly with the flight procedures, control separations, and ATC strategies.

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Coscia, V., M. Delitala, and P. Frasca. "On the mathematical theory of vehicular traffic flow II: Discrete velocity kinetic models." International Journal of Non-Linear Mechanics 42, no. 3 (April 2007): 411–21. http://dx.doi.org/10.1016/j.ijnonlinmec.2006.02.008.

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Delitala, Marcello. "Nonlinear models of vehicular traffic flow – new frameworks of the mathematical kinetic theory." Comptes Rendus Mécanique 331, no. 12 (December 2003): 817–22. http://dx.doi.org/10.1016/j.crme.2003.09.008.

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Paz, Alexander, Kul Shrestha, Cristian Arteaga, and Douglas Baker. "Calibration of Microscopic Traffic Flow Simulation Models considering Subsets of Links and Parameters." Journal of Advanced Transportation 2020 (October 31, 2020): 1–18. http://dx.doi.org/10.1155/2020/8897141.

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This study proposes a methodology for the calibration of microscopic traffic flow simulation models by enabling simultaneous selection of traffic links and associated parameters. The analyst selects any number and combination of links and model parameters for calibration. Most calibration methods consider the entire network and use ad hoc approaches without enabling a specific selection of location and associated parameters. In practice, only a subset of links and parameters is used for calibration based on several factors such as expert knowledge of the system or constraints imposed by local governance. In this study, the calibration problem for the simultaneous selection of links and parameters was formulated using a mathematical programming approach. The proposed methodology is capable of calibrating model parameters considering multiple time periods and performance measures simultaneously. Traffic volume and speed are the performance measures used in this study, and the methodology is developed without considering the characteristics of a specific traffic flow model. A genetic algorithm was implemented to find a solution to the proposed mathematical program. In the experiments, two traffic models were calibrated: the first set of experiments included selection of links only, while all associated parameters were considered for calibration. The second set of experiments considered simultaneous selection of links and parameters. The implications of these experiments indicate that the models were calibrated successfully subject to selection of a minimum number of links. As expected, the more links and parameters that are used for calibration, the more time it takes to find a solution, but the overall results are better. All parameter values were reasonable and within constraints after successful calibration.

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Cardaliaguet, Pierre, and Nicolas Forcadel. "From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models." SIAM Journal on Mathematical Analysis 53, no. 1 (January 2021): 309–22. http://dx.doi.org/10.1137/20m1314410.

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Chen, Jianzhong, Ronghui Liu, and Yanmei Hu. "High-resolution central-upwind scheme for second-order macroscopic traffic flow models." International Journal of Modern Physics C 31, no. 07 (June 23, 2020): 2050097. http://dx.doi.org/10.1142/s0129183120500977.

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Traffic flow models are important tools for traffic management applications such as traffic incident detection and traffic control. In this paper, we propose a novel numerical approximation method for second-order macroscopic traffic flow models. The method is based on the semi-discrete central-upwind numerical flux and high-order reconstructions for spatial discretizations. We then apply the designed high-resolution schemes to three representative types of second-order traffic flow models and perform a variety of numerical experiments to validate the proposed methods. The simulation results illustrate the effectiveness, simplicity and universality of the central-upwind scheme as numerical approximation method for macroscopic traffic flow models.

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MOUSSA, NAJEM. "DANGEROUS SITUATIONS IN TWO-LANE TRAFFIC FLOW MODELS." International Journal of Modern Physics C 16, no. 07 (July 2005): 1133–48. http://dx.doi.org/10.1142/s0129183105007790.

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This paper investigates the probability of car accidents (PCA) in two-lane traffic flow models. We introduce new conditions for the occurrence of dangerous situations (DS) caused by an unexpected lane changing vehicles. Two different lane changing rules are considered, say symmetric and asymmetric. For the symmetric rules, we investigate the influence of the Nagel–Schreckenberg parameters such as the maximal speed, the randomization probability, …, on the PCA when vehicle moves forward or changes lanes. It is found that the forward PCA is as likely as that in one-lane traffic model. As regards to lane changing, the properties of the PCA are qualitatively different from those in one-lane traffic. For the asymmetric rules, we investigate the effect of the slack parameter Δ, introduced to adjust the inversion point of lane-usage, on the PCA. Contrarily to one-lane traffic, the forward PCA in the right lane exhibits two maximums for some range of Δ; the first one is located at low density and the second at high density. The lane changing PCA from right to left is found to decrease with increase of Δ. However, no DS exist when vehicles change from left to right.

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Jacyna-Gołda, Ilona, Jolanta Żak, and Piotr Gołębiowski. "MODELS OF TRAFFIC FLOW DISTRIBUTION FOR VARIOUS SCENARIOS OF THE DEVELOPMENT OF PROECOLOGICAL TRANSPORT SYSTEM." Archives of Transport 32, no. 4 (December 31, 2014): 17–28. http://dx.doi.org/10.5604/08669546.1146994.

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The paper is a result of a research work concerning the development of an environmentally friendly transport system - Project EMITRANSYS. The publication contains the issues of shaping the transport system, where important factor due to the aspect of sustainable development is including the external costs in transport activity. This paper presents a mathematical model of the distribution of the traffic flow in the transport network. The paper presents selected aspects of the problem of multi-variant distribution of the traffic stream on the network transport for defined scenarios for the transport system development. Traffic distribution on the network has been made due to the criterion function – external cost connected with air pollution. The paper presents modal split of traffic ecological flow for chosen scenarios of the development domestic transport system. Key words: distribution of traffic on the network,

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Liang, Yongkai, Jingyuan Li, and Hai Liu. "GIS-based analysis of urban traffic model: Case study in Beijing." E3S Web of Conferences 268 (2021): 01056. http://dx.doi.org/10.1051/e3sconf/202126801056.

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Taking the traffic flow characteristics of Beijing's entire road network as the object, and using the low-frequency traffic big data of GIS (Geographic Information System), the roads of the whole road network are divided into four road grades, and the traffic flow-speed models are constructed respectively. In view of the deviation of the model calculation caused by the sudden rise and fall of the traveling vehicle at night, the flow of the traffic flow model is corrected by cubic polynomial fitting, and the mathematical model is compared, calibrated and verified. Focus on analyzing the influence of roads of different grades and seasons on the characteristics of road traffic flow, and provide data support for further research on intelligent transportation.

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Glushkov, Alexandr, and Vladimir Shepelev. "Development of Reliable Models of Signal-Controlled Intersections." Transport and Telecommunication Journal 22, no. 4 (November 1, 2021): 417–24. http://dx.doi.org/10.2478/ttj-2021-0032.

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Abstract The paper considers an approach to building various mathematical models for homogeneous groups of intersections manifested through the use of clustering methods. This is because of a significant spread in their traffic capacity, as well as the influence of several random factors. The initial data on the traffic flow of many intersections was obtained from real-time recorders of the convolutional neural network. As a result of the analysis, we revealed statistically significant differences between the groups of intersections and compiled their linear regression models as a basis for the subsequent formation of generic management decisions. To demonstrate visually the influence of random factors on the traffic capacity of intersections, we built distribution fields based on the fuzzy logic methods for one of the clusters consisting of 14 homogeneous intersections. Modeling was based on the Gaussian type of membership functions as it most fully reflects the random nature of the pedestrian flow and its discontinuity.

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Нагребельна Л. П. and Поліщук В. П. "ВИКОРИСТАННЯ ТЕОРІЇ МАСОВОГО ОБСЛУГОВУВАННЯ ДЛЯ УДОСКОНАЛЕННЯ УПРАВЛІННЯ ДОРОЖНІМ РУХОМ НА МАГІСТРАЛЬНІЙ ВУЛИЧНО-ДОРОЖНІЙ МЕРЕЖІ МІСТ." International Academy Journal Web of Scholar, no. 4(46) (April 30, 2020): 8–12. http://dx.doi.org/10.31435/rsglobal_wos/30042020/7039.

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The object of the study is the improvement of traffic management on the main street and road network of the city. Actually, there are many techniques that allow simulating the traffic flows with sufficient accuracy. One of such models is a mathematical model, which allows calculating the main characteristics of a traffic flow on the basis of a few initial data and is considered as a queuing system.Modeling allows pre-determining the impact of traffic management measures on the existing street and road network without creating interference for drivers, making changes to the design of road, increasing the traffic volume, as well as involving the possible overloaded areas.An analysis of the researches of scientists who have considered similar methods in their works had been performed. The fundamental flaw of the mentioned works is that in none of them the study of the model of a real road section was performed for verifying of the model adequacy. Modeling allows understanding more accurately the behavior of an object with less approximations than mathematical models, and provides less researching and forecasting of the system behavior with significant changes in the initial concepts. It is indicated that for the first approximation it is expedient to use mathematical models, and for clarifying the characteristics – to use non- mathematical methods, in particular, simulation.It is proved that simulation is a powerful tool for studying the behavior of real systems. It is mainly used to study situations and systems that can be described as queuing systems.Using the queuing theory, it becomes possible to perform certain calculations and determine indicators of effectiveness of the queuing system.Obtained result of the indicators will help to determine the street and road network areas where a traffic jam may form for any reason, where the road will be overloaded. This makes it possible to develop a high-quality algorithm for quick elimination of traffic jam.

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Göttlich, Simone, Michael Herty, Salissou Moutari, and Jennifer Weissen. "Second-Order Traffic Flow Models on Networks." SIAM Journal on Applied Mathematics 81, no. 1 (January 2021): 258–81. http://dx.doi.org/10.1137/20m1339908.

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Marcellini, Francesca. "ODE-PDE models in traffic flow dynamics." Bulletin of the Brazilian Mathematical Society, New Series 47, no. 2 (June 2016): 533–44. http://dx.doi.org/10.1007/s00574-016-0167-5.

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MOUSSA, NAJEM. "SIMULATION STUDY OF TRAFFIC ACCIDENTS IN BIDIRECTIONAL TRAFFIC MODELS." International Journal of Modern Physics C 21, no. 12 (December 2010): 1501–15. http://dx.doi.org/10.1142/s0129183110016007.

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Conditions for the occurrence of bidirectional collisions are developed based on the Simon–Gutowitz bidirectional traffic model. Three types of dangerous situations can occur in this model. We analyze those corresponding to head-on collision; rear-end collision and lane-changing collision. Using Monte Carlo simulations, we compute the probability of the occurrence of these collisions for different values of the oncoming cars' density. It is found that the risk of collisions is important when the density of cars in one lane is small and that of the other lane is high enough. The influence of different proportions of heavy vehicles is also studied. We found that heavy vehicles cause an important reduction of traffic flow on the home lane and provoke an increase of the risk of car accidents.

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Subotić, Marko, Nemanja Stepanović, Vladan Tubić, Edis Softić, and Mouhamed Bayane Bouraima. "Models of Analysis of Credible Deviation from Speed Limits on Two-Lane Roads of Bosnia and Herzegovina." Complexity 2022 (October 7, 2022): 1–13. http://dx.doi.org/10.1155/2022/2832175.

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Any deviation of speed in a traffic flow from a speed limit represents a potential risk of traffic accidents, so speed management appears as an imperative. However, an inadequately set speed limit often causes drivers’ noncompliance to it in the conditions of real traffic flow. By determining the value of exceeding the speed limit according to vehicle classes, it is possible to recommend a credible speeding value that can be considered credible up to a value above the speed limit. In this paper, deterministic multistep mathematical models of speed deviation from the speed limit as a function of longitudinal gradient for the proposed vehicle classes were developed. A total of 11 measuring sections with different traffic flow types were analyzed. Based on a detailed analysis of speeding, models for the deviation of the 15th, 50th, and 85th percentiles were obtained, with the aim of adjusting the credible deviation to control measures. The results obtained in this study were compared with a survey of traffic flow speeding on two-lane roads conducted in Serbia.

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Кадасев, D. Kadasev, Коротнев, and V. Korotnev. "MATHEMATICAL MODELING OF TRAFFIC FLOWS ON THE ROAD NETWORK CITY." Alternative energy sources in the transport-technological complex: problems and prospects of rational use of 3, no. 1 (March 16, 2016): 236–40. http://dx.doi.org/10.12737/17887.

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This article describes a practical method of constructing mathematical models of traffic flow, the most suitable for a particular city highway. The initial data are: instant speed, time, distance, flux density, intensity of movement of vehicles. Using the obtained data, built regression model, and conducted correlation analysis. The choice of the mathematical model that most faithfully describes the transport process was made on the basis of the correlation coefficient

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Vasyutina, A. A., V. V. Popov, A. I. Kondratyev, and A. L. Boran-Keshishyan. "Improvement of the vessel traffic control system for accident-free electronic navigation in the port area." Journal of Physics: Conference Series 2061, no. 1 (October 1, 2021): 012105. http://dx.doi.org/10.1088/1742-6596/2061/1/012105.

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Abstract The increase in the intensity of navigation leads to unsafe navigation, which necessitates the improvement of existing measures to ensure safe navigation using specific mathematical models and methods. The configuration of the mathematical model of the traffic flow of ships obtained in this study is realizable on modern computer technology and can be applied by embedding advanced ship traffic control systems, which is an object of the infrastructure of a modern seaport.

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Hoogendoorn, Serge P., and Piet H. L. Bovy. "Modeling Multiple User-Class Traffic." Transportation Research Record: Journal of the Transportation Research Board 1644, no. 1 (January 1998): 57–69. http://dx.doi.org/10.3141/1644-07.

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In contemporary traffic flow theory, the distinction between user classes is rarely made. However, we envisage that the accuracy and the descriptive power of the macroscopic traffic flow models can be improved significantly by separating user classes and their specific flow characteristics. As a consequence, the possibility of improved estimation and prediction of traffic flow conditions becomes available. Additionally, the availability of a realistic multiple user-class traffic flow model enables the automated generation of user-dedicated traffic control policies by means of mathematical optimal control theory. A macroscopic multiple user-class model is derived from mesoscopic principles. In opposition to earlier multiple user-class models, the model presented here implicitly defines equilibrium relationships between traffic density and equilibrium velocities as a function of current traffic conditions, traffic composition, and distribution of user-class-dependent desired velocities. Additionally, the velocity variance variable is introduced describing deviations from the average speed within the user classes. The multiple user-class model identifies competing processes. On the one hand, drivers attempt to traverse the freeway at their desired velocity; on the other hand, they adjust their velocity because of interaction with slower vehicles. These processes can result in self-formation of apparently random local structures. Finally, the proposed model satisfies the anisotropy condition and the invariant personality condition.

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BORSCHE, R., A. KLAR, S. KÜHN, and A. MEURER. "COUPLING TRAFFIC FLOW NETWORKS TO PEDESTRIAN MOTION." Mathematical Models and Methods in Applied Sciences 24, no. 02 (December 12, 2013): 359–80. http://dx.doi.org/10.1142/s0218202513400113.

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In this paper scalar macroscopic models for traffic and pedestrian flows are coupled and the resulting system is investigated numerically. For the traffic flow the classical Lighthill–Whitham Richards model on a network of roads and for the pedestrian flow the Hughes model are used. These models are coupled via terms in the fundamental diagrams modeling an influence of the traffic and pedestrian flow on the maximal velocities of the corresponding models. Several physical situations, where pedestrians and cars interact, are investigated.

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Taha, Mohammed Y., and Abd Al-Kareem N. Abood. "A Statistical Analysis of Traffic Flow Characteristics of Multilane Highways in Baghdad City, Part A: Traffic Elements Characteristics." Tikrit Journal of Engineering Sciences 14, no. 3 (September 30, 2007): 1–23. http://dx.doi.org/10.25130/tjes.14.3.01.

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Basic traffic elements (flow, speed, density) are used in many stages of transportation process. Flow-speed-density relationship isan important concept, which translates traffic stream characteristicsinto mathematical or statistical rnodels. These models are widely usedin transportation engineering. The main objective of this research is finding out the nature of the relationships between the basic traffic elements characteristics for multi-lane highways in Baghdad city. Data has been collected throughout an extensive field survey on twenty selected sections in the study area. Photograph technique is usedto deterrnine the basic traffic elements. Statistical technique is applied analyze the collected data in order to present the best models to describe flow-speed-density relationships. The results of this study indicate that the linear relationship between speed and density is signification with confidence level (99%). The nature of this relation is considered during theformulation of the other relation-ships between traffic elements.

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Darbha, S., K. R. Rajagopal, and V. Tyagi. "A review of mathematical models for the flow of traffic and some recent results." Nonlinear Analysis: Theory, Methods & Applications 69, no. 3 (August 2008): 950–70. http://dx.doi.org/10.1016/j.na.2008.02.123.

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Knowles, J. K. "On entropy conditions and traffic flow models." ZAMM 88, no. 1 (January 16, 2008): 64–73. http://dx.doi.org/10.1002/zamm.200700093.

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Bassan, Shy, Abishai Polus, and Ardeshir Faghri. "Modeling of freeway breakdown process with log-periodic oscillations." Canadian Journal of Civil Engineering 34, no. 12 (December 2007): 1577–86. http://dx.doi.org/10.1139/l07-071.

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Urban and suburban freeways are designed to allow smooth traffic flow at high speed. However, when traffic demand is high or during irregular events, significant congestion may develop. Traffic breakdown occurs during the phase transition from dense congested stable (DCS) flow to breakdown flow. In this study, the process of freeway flow breakdown was investigated by calibrating models in the density–time plane using morning peak data from Interstate 66, a US highway connecting Washington, D.C., and Virginia. It was shown that the models, which describe the collective behavior of drivers using the mathematical property of the log-periodic oscillations (LPO) process, reflect suitably the phase transition in freeway traffic flow. The LPO process has been used in the past to model stock market crashes and the occurrences of large earthquakes. The cyclic properties of the LPO models developd in this study were found to identify the “critical transition period,” which triggers the traffic breakdown process. This period starts when the density rate of change reaches its maximum during the first cycle that follows the DCS flow regime. This triggers a breakdown of flow conditions, which occur 5–8 min after the density rate of change has achieved its maximum.

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Mohammadian, Saeed, and Femke van Wageningen-Kessels. "Improved Numerical Method for Aw-Rascle Type Continuum Traffic Flow Models." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 20 (July 24, 2018): 262–76. http://dx.doi.org/10.1177/0361198118784402.

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Continuum traffic flow models are essentially nonlinear hyperbolic systems of partial differential equations. Except for limited specific cases, these systems must be solved numerically. Mathematical structure of continuum models can be different for each class of models. As a result, suitable numerical schemes for some classes may not be efficient for others. In this study, an improved numerical method is proposed for a class of second-order traffic flow models. The method is based on McCormack scheme, which is a widely-used method for non-homogeneous second-order traffic flow models, but fails to produce reasonable results for homogeneous models including Aw-Rascle type models which are the focus of this paper. It is shown that this is mainly due to spurious numerical oscillations. Smoothing methods to overcome these issues are studied and applied. Central dispersion and artificial viscosity (AV) methods are incorporated into the standard McCormack scheme and tested. To reduce numerical diffusion, a total variation diminishing Runge-Kutta time stepping scheme is applied. Results show the capability of the proposed methods, and especially the AV method, to eliminate the oscillations of the standard McCormack scheme as well as controlling numerical diffusion.

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Journal articles on the topic 'Traffic flow Mathematical models'

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