Traffic Flow Problems Research Articles

An optimal control problem of traffic flow on a junction

We investigate how to control optimally a traffic flow through a junction on the line by acting only on speed reduction or traffic light at the junction. We show the existence of an optimal control and, under structure assumptions, provide optimality conditions. We use this analysis to investigate thoroughly the maximization of the flux on a space-time subset and show the existence of an optimal control which is bang-bang.

A local fractional modified Crank–Nicolson scheme for fractal LWR model of traffic flow

This research proposes a modified Crank–Nicolson finite difference scheme with local fractional derivatives to approximate the solutions of local fractional LWR traffic flow model. The stability and consistency of the scheme are examined. Further, convergence of the scheme is assured by using Lax’s equivalence theorem. Some exemplary instances are discussed along with their simulations to validate the proposed method. The obtained numerical solutions show the dynamical evolution of traffic density with respect to time and space. The results derived using the proposed numerical scheme establish that they are quite effective in obtaining the numerical solution to the fractal vehicular traffic flow problem.

Bifurcation analysis and control of an improved continuous traffic model considering weather effect

PurposeHighway traffic systems are complex and variable, and studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable bifurcation points can alleviate traffic congestion from a new perspective. Bifurcation analysis is used to explain the changes in system stability, identify the unstable bifurcation points of the system, and design feedback controllers to realize the control of the unstable bifurcation points of the traffic system. It helps to control the sudden changes in the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.Design/methodology/approachIn this paper, we improve the macroscopic traffic flow model by integrating severe weather factors such as rainfall, snowfall, and dust. We use traveling wave transform to convert it into a traffic flow stability model suitable for branching analysis, thus converting the traffic flow problem into a system stability analysis problem. First, this paper derives the existence conditions of the model Hopf bifurcation and saddle-node bifurcation for the improved macroscopic model, and finds the stability mutation point of the system. Secondly, the connection between the stability mutation points and bifurcation points of the traffic system is analyzed. Finally, for the unstable bifurcation point, a nonlinear system feedback controller is designed using Chebyshev polynomial approximation and stochastic feedback control method.FindingsThe Hopf bifurcation is delayed and completely eliminated without changing the equilibrium point of the system, thus controlling the abrupt behavior of the traffic system.Originality/valueCurrently there are fewer studies to explain the changes in the stability of the transportation system through bifurcation analysis, in this paper; we design a feedback controller for the unstable bifurcation point of the system to realize the control of the transportation system. It is a new research method that helps to control the sudden change of the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.

A class of central unstaggered schemes for nonlocal conservation laws: Applications to traffic flow models

This study introduces a new class of central unstaggered finite volume methods that are used to approximate solutions to nonlocal conservation laws. The proposed method is based on Nessyahu and Tadmor's (NT). Instead of solving Riemann's problems at the level of cell interfaces, as in the NT scheme, the approach we develop implicitly uses ghost cells while still generating the numerical solution on a single grid. We use our method with the aim of solving one-dimensional nonlocal traffic flow problems. The numerical results we present demonstrate the accuracy, high resolution, and non-oscillatory nature of the proposed method and compare very favorably with those obtained using the original NT method, demonstrating the expected simplicity of a family of unstaggered central schemes and confirming that nonlocal traffic flow models can be treated very efficiently by the suggested method.

Cubic fuzzy bridges and its application to traffic flow problem

Fuzzy graphs are of great significance in the modeling and analysis of complex systems characterized by uncertain and imprecise information. Among various types of fuzzy graphs, cubic fuzzy graphs stand out due to their ability to represent the membership degree of both vertices and edges using intervals and fuzzy numbers, respectively. The study of connectivity in fuzzy graphs depends on understanding key concepts such as fuzzy bridges, cutnodes and trees, which are essential for analyzing and interpreting intricate networks. Mastery of these concepts enhances decision-making, optimization and analysis in diverse fields including transportation, social networks and communication systems. This paper introduces the concepts of partial cubic fuzzy bridges and partial cubic fuzzy cutnodes and presents their relevant findings. The necessary and sufficient conditions for an edge to be a partial cubic fuzzy bridge and cubic fuzzy bridge are derived. Furthermore, it introduces the notion of cubic fuzzy trees, provides illustrative examples and discusses results relevant to cubic fuzzy trees. The upper bonds for the number of partial cubic fuzzy bridges in a complete CFG is calculated. As an application, the concept of partial cubic fuzzy bridges is used to identify cities most severely affected by traffic congestion resulting from accidents.

A Review on Burgers' Equations and It's Applications

This article presents a brief study on the review of the Burgers' equation. It also gives some concepts/ideas and techniques to solve Burgers' equation. Applying Burgers' equation to traffic flow requires concentrated effort for the solution. We develop our insights on how to obtain the Navier-Stokes equation through our inquiry into Burgers' equation. We also demonstrate how the Cole-Hopf transformation for the viscous Burgers' equation is derived. Finally, we use Burger's equation function as a model for the flow of traffic. Additionally, by employing the linear system method, we are able to obtain the answer to the one-way traffic flow problem. The Navier-Stokes equation has been derived to get in-viscid Burger's equation. The principle of Traffic flow and Navier-Stokes models have also been derived.

An Efficient Aircraft Conflict Detection and Resolution Method Based on an Improved Reinforcement Learning Framework

With the steady increase of air traffic column, an auxiliary decision tool is required to compensate the operation redundancy deficiency of more sectors of air traffic control. To solve the problem of nonconflict high-density departure and arrival traffic flow, this method is expected to rapidly establish and maintain safe separation with more flexible changing strategies for aircraft heading and speed. This paper proposes an improved reinforcement learning framework to achieve conflict detection and resolution. The proposed framework includes the first development of an air traffic flow model based on a multiagent Markov decision process. The goal reward function was then maximized by improved Monte-Carlo tree search combined with an upper confidence bound tree. Three simulation scenarios were designed for illustrating the improvements of the proposed algorithm, with the results indicating that the algorithm could establish and maintain safe separation between 20 agents in the simplified hexagon-shaped airspace of Huadong, China. Furthermore, the proposed method was demonstrated to reduce the number of conflicts between aircraft agents by up to 26.32% compared to previous research.

RL-GCN: Traffic flow prediction based on graph convolution and reinforcement learning for smart cities

The traffic flow problem has become essential in urban planning and management in today’s increasingly urbanized world. Traditional traffic flow prediction models cannot fully consider urban traffic networks’ complex and dynamic characteristics. To this end, this paper proposes a traffic flow prediction method for smart cities (RL-GCN) based on graph convolution, LSTM network and reinforcement learning, aiming to solve the problem of urban traffic flow prediction. Firstly, we use the graph convolutional neural network to process the urban traffic network data features, then use the LSTM network model to learn the temporal information, and then combine the reinforcement learning algorithm to develop the optimal traffic control strategy based on which the future traffic flow is predicted. Our experiments on several datasets show that the model developed in this paper has outstanding performance for urban traffic flow prediction. Compared with the traditional traffic flow prediction methods, the method in this paper has significantly improved prediction accuracy. Our research can provide valuable references and inspiration in urban planning and traffic management.

Deep learning for Mean Field Games with non-separable Hamiltonians

This paper introduces a new method based on Deep Galerkin Methods (DGMs) for solving high-dimensional stochastic Mean Field Games (MFGs). We achieve this by using two neural networks to approximate the unknown solutions of the MFG system and forward–backward conditions. Our method is efficient, even with a small number of iterations, and is capable of handling up to 300 dimensions with a single layer, which makes it faster than other approaches. In contrast, methods based on Generative Adversarial Networks (GANs) cannot solve MFGs with non-separable Hamiltonians. We demonstrate the effectiveness of our approach by applying it to a traffic flow problem, which was previously solved using the Newton iteration method only in the deterministic case. We compare the results of our method to analytical solutions and previous approaches, showing its efficiency. We also prove the convergence of our neural network approximation with a single hidden layer using the universal approximation theorem.

Review of Vehicle Type Recognition Methods

With the booming social and economic development, the number of domestic and foreign motor vehicles has increased dramatically, resulting in increasing traffic flow, traffic congestion, and traffic safety problems. To better relieve traffic pressure, intelligent transportation has become the mainstream development direction and an important means of modern transportation, of which vehicle type recognition is the core component of intelligent transportation. Therefore, the research on vehicle identification is of great significance in both scientific research and real-life applications, and it is also a challenging task. Among the various detection and recognition methods, deep learning has been proved to be a more effective one, so this paper discusses the current research on deep learning and vehicle model recognition.

Residual Neural Networks for Origin–Destination Trip Matrix Estimation from Traffic Sensor Information

Traffic management and control applications require comprehensive knowledge of traffic flow data. Typically, such information is gathered using traffic sensors, which have two basic challenges: First, it is impractical or impossible to install sensors on every arc in a network. Second, sensors do not provide direct information on origin-to-destination (O–D) demand flows. Consequently, it is essential to identify the optimal locations for deploying traffic sensors and then enhance the knowledge gained from this link flow sample to forecast the network’s traffic flow. This article presents residual neural networks—a very deep set of neural networks—to the problem for the first time. The suggested architecture reliably predicts the whole network’s O–D flows utilizing link flows, hence inverting the standard traffic assignment problem. It deduces a relevant correlation between traffic flow statistics and network topology from traffic flow characteristics. To train the proposed deep learning architecture, random synthetic flow data was generated from the historical demand data of the network. A large-scale network was used to test and confirm the model’s performance. Then, the Sioux Falls network was used to compare the results with the literature. The robustness of applying the proposed framework to this particular combined traffic flow problem was determined by maintaining superior prediction accuracy over the literature with a moderate number of traffic sensors.

STGNN-FAM: A Traffic Flow Prediction Model for Spatiotemporal Graph Networks Based on Fusion of Attention Mechanisms

Network traffic state prediction has been constantly challenged by complex spatiotemporal features of traffic information as well as imperfection in streaming data. This paper proposes a traffic flow prediction model for spatiotemporal graph networks based on fusion of attention mechanisms (STGNN-FAM) to simultaneously tackle these challenges. This model contains a spatial feature extraction layer, a bidirectional temporal feature extraction layer, and an attention fusion layer, which not only fully considers the temporal and spatial features of the traffic flow problem but also uses the attention mechanism to enhance the critical temporal and spatial features to achieve more accurate and robust predictions. Experimental results on a network traffic speed dataset PeMSD7 show that the proposed STGNN-FAM outperforms several important benchmarks in prediction accuracy and the ability to withstand interference in the data stream, especially for mid- and long-term prediction of 30 minutes and 45 minutes.

Congestion-Aware Dynamic Optimal Traffic Power Flow in Coupled Transportation Power Systems

Electrification of vehicles is strengthening the interaction between power systems and transportation systems, formulating the coupled transportation power systems (CTPSs). A novel optimal traffic power flow (OTPF) problem is proposed to analyze the spatial and temporal congestion propagation on CTPSs, under congested roads, transmission lines, and charging stations. The traffic flow is depicted by the spatial and temporal distribution of electric vehicles (EVs) on roads and charging stations, connected by multilayer time-space networks (TSNs). This distribution is the solution to a mesoscale traffic assignment problem of EV fleets on TSNs, where the charging, discharging, routing, and origin–destination pairing can be optimized simultaneously. The power flow is captured by the optima of dynamic optimal power flow problems with security constraints. An extended alternating direction multiplier method algorithm with the convex-concave procedure is proposed to solve OTPFs. Results verify the effectiveness of the proposed scheme for congestion management on CTPSs.

Development of RBL-STEM Learning Tools to Improve Students’ Computational Thinking Skills Solving Rainbow Antimagic Coloring Problems and Their Application to Traffic Flow Problems with Spatial Temporal Graph Neural Network

Computational thinking is thinking process that is needed in formulating problems and solutions, so that these solutions can be effective information processing agents in solving problems. Indicators of computational thinking consist of problem decomposition, algorithmic thinking, pattern recognition, abstraction and generalization. To improve higher-order thinking skills, we apply RBL learning integrated with STEM approach. To improve students’ thinking skills, it is necessary to develop tools that support the success of learning activities. The learning tools that have been developed meet the criteria of valid, practical, and effective. The validity scores obtained by each device are 3.5 for the face-to-face plan, 3.41 for the student worksheet, and 3.56 for the learning outcomes test. The observation result of the learning implementation score was 3.8 with a percentage of 95%. There were 23 students who completed or around 88,46%, percentage of average score of student activities was 94.17%, and as many as 94.47% of students gave a positive response.

Fuzzy model of transport demand

The development of transport networks is costly and cannot solve all transport problems. In this regard, scientifically based planning of the development of the transport complex acquires an important role to improve the quality of the functioning of the transport system, such as improving the organization of traffic in various parts of the network, optimizing the system of public transport routes, creating convenient transfer hubs, etc. To solve such problems, the paper considers the development of intelligent transport systems and mathematical modeling of transport demand. The central task of developing a transport model is to determine the equilibrium state of the transport system, i.e., the problem of the distribution of flows in the network, which involves two main stages. In the first stage, one or several correspondence matrices are evaluated based on the traffic flow's initial data and behavior. The second stage consists of the distribution of traffic matrices on the graph of the transport network, i.e., in solving the problem of finding traffic flows or the problem of transport equilibrium. The problem of transport equilibrium is reduced to an optimization problem in which restrictions are imposed depending on the values of the elements of the traffic matrix. The search for new methods for solving optimization problems of weakly formalized processes is caused by the presence of processes and phenomena, which is difficult to describe by methods of classical mathematics due to their indeterminacy and unreliability, incompleteness, and fuzziness of the initial information. The mathematical model of the optimization problem is described by the objective function and constraints. Classical mathematical programming and its variations are largely a normative methodology for effective choice. Fuzzy programming highlights the natural multiplicity of inaccurately defined goals, restrictions, and their meanings.

Highly efficient numerical scheme for solving fuzzy system of linear and non-linear equations with application in differential equations

ABSTRACT In this research, we suggested a numerical iterative scheme for investigating the numerical solution of fuzzy linear and nonlinear systems of equations, particularly where the linear or nonlinear system co-efficient is a crisp number and the right-hand side vector is a triangular fuzzy number. Triangular fuzzy systems of linear and nonlinear equations play a critical role in a variety of engineering, scientific challenges, mathematics, chemistry, physics, artificial intelligence, biology, medical, economics, finance, statistics, machine and deep learning, computer science, robotics and smart cars, programming, in the military and engineering industries, linear and nonlinear programming problems and traffic flow problems. In biomedical engineering, fluid flow problems, and differential equations, triangular fuzzy linear and nonlinear systems of equations also play a key role in determining the level of uncertainty. Convergence analysis illustrates that the proposed numerical technique's order of convergence for solving a triangular fuzzy system of linear and nonlinear equations is three. The newly developed numerical scheme was then applied to solve several triangular fuzzy boundary value problems. In terms of convergence rate, computing time, and residual error, numerical test problems indicate that the newly developed methods are more efficient than the current methods in the literature.

A Time-Continuous Embedding Method for Scalar Hyperbolic Conservation Laws on Manifolds

A time-continuous (tc-)embedding method is first proposed for solving nonlinear scalar hyperbolic conservation laws with discontinuous solutions (shocks and rarefaction waves) on codimension 1, connected, smooth, and closed manifolds (surface PDEs or SPDEs in {mathbb {R}}^2 and {mathbb {R}}^3). The new embedding method improves upon the classical closest point (cp-)embedding method, which requires re-establishments of the constant-along-normal (CAN-)property of the extension function at every time step, in terms of accuracy and efficiency, by incorporating the CAN-property analytically and explicitly in the embedding equation. The tc-embedding SPDEs are solved by the second-order nonlinear central finite volume scheme with a nonlinear minmod slope limiter in space, and the third-order total variation diminished Runge-Kutta scheme in time. An adaptive nonlinear essentially non-oscillatory polynomial interpolation is used to obtain the solution values at the ghost cells. Numerical results in solving the linear wave equation and the Burgers’ equation show that the proposed tc-embedding method has better accuracy, improved resolution, and reduced CPU times than the classical cp-embedding method. The Burgers’ equation, the traffic flow problem, and the Buckley-Leverett equation are solved to demonstrate the robust performance of the tc-embedding method in resolving fine-scale structures efficiently even in the presence of a shock and the essentially non-oscillatory capturing of shocks and rarefaction waves on simple and complex shaped one-dimensional manifolds. Burgers’ equation is also solved on the two-dimensional torus-shaped and spherical-shaped manifolds.

Bifurcation analysis of a new stochastic traffic flow model

Abstract The stochastic function describing the stochastic behavior of traffic flow in the process of acceleration or deceleration can better capture the stochastic characteristics of traffic flow. Based on this, we introduce the stochastic function into a high-order viscous continuous traffic flow model and propose a stochastic traffic flow model. Furthermore, we performed the bifurcation analysis of traffic flow system based on the model. Accordingly, the traffic flow problem is transformed into the stability analysis problem of the system, highlighting the unstable traffic characteristics such as congestion. The model can be used to study the nonlinear dynamic behavior of traffic flow. Based on this model, the existence of Hopf bifurcation and the saddle-node bifurcation is theoretically proved. And the type of the Hopf bifurcation is theoretically derived. The model can also be used to study the mutation behavior of system stability at bifurcation point. From the density space-time diagram of the system, we find that the system undergoes a stability mutation when it passes through the bifurcation point, which is consistent with the theoretical analysis results.

The impacts of longitudinal separation, efficiency loss, and cruise speed adjustment in robust terminal traffic flow problem under uncertainty

ABSTRACT Minimization of approaching time and maximization of the utilization of air route and airport resources are the two ultimate goals of air traffic control. This research considers arrival sequence and the uncertain arrival times at entry waypoints of flights and investigates the impact of air traffic controller specific parameters in the model. The two-stage optimization framework will first determine a deterministic schedule and optimize the approaching time while considering additional longitudinal separation, efficiency loss from deterministic schedule, and cruise speed adjustment in the second-stage optimization model via sample average approximation. The numerical experiments suggested an efficiency loss of 20%, which can absorb the empirical probabilistic lateness at entry waypoints with the real-world data. The proposed method could determine the estimated average delay time at runways with different settings of additional buffer for longitudinal separation and trade-off parameters between the estimated average delay time and estimated penalty cost of cruise speed adjustment.

Traffic Flow Prediction using Machine Learning Techniques - A Systematic Literature Review

Purpose: Traffic control in large cities is extremely tough. To alleviate costs associated with traffic congestion, some nations of the world have implemented Intelligent Transportation Systems (ITS). This paper reviews the application of artificial neural network (ANN) and machine learning (ML) techniques and also their implementation issues in TFP. Techniques other than ML and ANN have also been discussed. Methodology: The survey of literature on TFP (TFP) and ITS was conducted using several secondary sources of information such as conference proceedings Journals, Books, and Research Reports published in various publications, and then the kinds of literature that are reported as promising have been included. The collected information is then reviewed to discover possible key areas of concern in the TFP and ITS. Findings/Results: Traffic management in cities is important for smooth traffic flow. TFP and ITS are drawing much attention from researchers these days. Application of ML, ANN, and other techniques are being tried to alleviate the traffic flow problem in cities. TFP using ITS employing ML techniques to overcome the problem of traffic congestion looks promising. Originality: This review of literature is conducted using secondary data gathered from various sources. The information acquired will be useful to expand on existing theories and frameworks or to develop a new technique or modify to improve the accuracy of TFP. Tables containing categories of prediction, ML Pipelining, open-source ML tools available, standard datasets available have been included. Paper Type: Literature Review.