Using Finite Elements Method for Traffic Flow Analysis

This chapter begins, in Sect. 2.1, with a brief overview of the use of models in the transportation sector, several types of models used in transportation planning, and the specific evaluation methods used. Thereafter, the theory of traffic flow is introduced which enables investigation of the dynamic properties of traffic on road sections with regard to the respective variables defined at each point in space and time. Based on the mathematical equations derived, different transportation system scenarios are investigated in Sect. 2.2. Section 2.3 examines queuing theory, the mathematical study of waiting in lines or queues. Transportation system models incorporate queuing theory to predict, for example, queuing lengths and waiting times. Section 2.4 analyzes transportation systems with regard to existing demand and the potential impact of changes resulting from transportation planning and development projects. Traffic management has become a critical issue as the number of vehicles in metropolitan areas is nearing the existing road capacity, resulting in traffic congestion. In some areas, the volume of vehicles has met and/or exceeded road capacity. The methodological background of congestion is described in Sect. 2.5. Graph theory is introduced in Sect. 2.6. It is widely used to model and study transportation networks. Section 2.7 focuses on shortages occurring in transportation systems, so-called bottlenecks. The main consequence of a bottleneck is an immediate reduction in the capacity of the transportation system infrastructure. Section 2.8 describes a ProModel-based case study for a four-arm road intersection. Section 2.9 contains comprehensive questions from the transportation model area of concentration, and the final section includes references and suggestions for further reading.KeywordsTraffic FlowTransportation PlanningRoad IntersectionTraffic Flow ModelMarkov BlanketThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper, a special integrable negative-order Calogero–Bogoyavlenskii–Schiff equation (nCBS) in fluid mechanics is studied by means of the symmetry reduction method and consistent tanh expansion method. The Painlevé integrability is investigated to confirm the compatibility conditions. This integrable nCBS equation has been transformed into different reduction equations and the corresponding invariant solutions with arbitrary functions are obtained. The corresponding structures of the invariant solutions for the nCBS equation are also shown graphically. At last, new types of soliton–cnoidal interaction solutions for the nCBS equation are presented through the consistent tanh expansion method on the basis of the truncated Painlevé expansion.

Analysis of normal traffic flow usually uses the static or dynamic model based on fluid mechanics. However, in the analysis process, the problem of massive modeling and data handling exists, and the accuracy is desirable. Finite element method has been widely applied in various domains. Based on existing theory of traffic flow, ITS and the development of finite element, the paper presents a simulation method based on finite element for solving problems in traffic flow. Using existing finite element analysis software, the traffic flow is simulated and analyzed with fluid mechanics and dynamics. The problem with massive data processing through manual modeling and Numerical Analysis is solved. Finally, a typical case of special road is analyzed with ADINA finite element analysis software.

The prevailing roadway and traffic conditions on expressways in India are vastly different when compared with the other roads in India and also, there is no perfect lane-discipline. The knowledge of roadway capacity is an important basic input required for planning, design, analysis, and operation of roadway systems. Hence, this work aims to model traffic flow on Indian urban expressways with specific reference to Delhi–Gurgaon expressway and estimate its capacity using the micro-simulation model using VISSIM 5·40. For this purpose, the field data collected on traffic-flow characteristics on expressways was used in calibration and validation of the simulation model. The validated simulation model was then used to develop fundamental traffic–flow relationships, namely, speed–flow, speed–area occupancy, and flow–area occupancy for the traffic-flow levels, starting from near-zero until the capacity of the facility. The capacity of an eight-lane divided urban expressway in level terrain with 14·0-m wide road space (one direction of traffic flow) was found to be in the range of 9700–10 000 vehicles/h. Moreover, through sensitivity analysis using simulation model, the following relationships, (i) percentage trucks in the traffic stream and capacity-level flow and (ii) percentage of trucks in the traffic stream and capacity-level traffic-stream speed, were developed. The results and the overall methodology followed in this study for modeling traffic flow on expressways in India to determine the capacity estimates under varying traffic compositions may be very useful for the practitioners and also for the continuing efforts to prepare an Indian Highway Capacity Manual.

The state of the art of macroscopic vehicle traffic flow models is discussed and the traffic flow stability of these models is analyzed. A nonlinear traffic flow stability criterion is investigated using the wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for an entire class of second-order macroscopic traffic flow models. Numerical results axe obtained using the CLAWPACK package for the well-known Payne-Whitham model, in order to illustrate the stability criterion. The newly derived stability results are consistent with previous reported results obtained using both microscopic models and approximate linearization methods. Moreover, the stability criteria derived in the paper can provide more refined information regarding the propagation of traffic flow perturbations and shock waves in second-order models than previously established methodologies.

Introduction. Problematic sections of the road network are intersections with high traffic intensity of conflicting pedestrian and traffic flow, in particular, right and left turns. At such crossings, there are significant traffic delays. In the case of vehicles turning left or right at an intersection when passing at a traffic light signal that allows traffic, should give way to pedestrians crossing the roadway on the crosswalk. In the case of high intensity of pedestrian traffic, it is impossible to complete the turn of such vehicles, they remain at the intersection, so there are significant traffic delays for returning vehicles.Purpose. Therefore, the work aims to study the interaction of traffic and pedestrian flows with high intensity at regulated intersections to improve their capacity.Methods. To study the parameters of traffic flows, in particular, the length of congestion, we used traffic flow models, which include a psychophysiological model of following a vehicle moving in front, and a model based on traffic rules. To model, pedestrian flows the Wiedemann model was used. The leastsquares method was used to obtain empirical nonlinear dependences of congestion length on the intensities of conflicting pedestrian and traffic flows.Results. The paper uses known methods for solving applied problems in the field of traffic for some unique cases, namely the intersection of intensive -traffic and pedestrian flows. Studies of road and pedestrian traffic parameters at crossings have shown that the length of congestion significantly depends on the intensity of traffic flow, but with increas-ing intensity of pedestrian traffic more than 1000 people/h, the length of congestion changes insignificantly. If there are trams at the intersection, the length of congestion increases by an average of 1.14% and depends significantly on the intensity of traffic and pedestrian flows.It is proposed to introduce three-phase traffic light regulation on such sections when one of the phases allows traffic only for pedestrians. The simulation results showed that the length of congestion in the absence of rail vehicles on the approaches to the intersection decreases by an average of 45.3% and is weakly dependent on the intensity of pedestrian flows. If there are rail vehicles at the crossing, the length of congestion can reduce by an average of 13.7%. But in some cases may increase.Conclusion. The research methodology presented in this paper can be used for intersections with another traffic organization scheme to justify the feasibility of introducing threephase traffic light control when one of the phases allows traffic only to pedestrians.

Multilane widely exists in the urban traffic system and its traffic flow is more complex than the single-lane traffic flow since it may be affected by each lane’s width, the number of lanes and lane-changing. In this paper, we first use empirical data to study the impacts of lane width and the number of lanes on multilane traffic flow, then propose a new multilane traffic flow model and finally use numerical tests to explore the influences of the variation of lane width, closing lane and changing the number of lanes on each lane’s traffic flow. The numerical results show that the new model can qualitatively reproduce the complex traffic phenomena resulted by the variation of lane width, closing lane and changing the number of lanes and that changing each lane’s width, closing lane and changing the number of lanes may reduce the reliability of the multilane traffic system. In addition, some numerical results are qualitatively consistent with the phenomena that are resulted by the heavy rain in Beijing on July 21, 2012, which shows that our model can perfectly reproduce some complex traffic phenomena in multilane system from the qualitative perspective.

Traffic congestion in urban areas is posing many challenges, and a traffic flow model that accurately predicts traffic conditions can be useful in responding to them. With the limitation of infrastructure and the difficulty for real world experiment, traffic simulation is a good tool for the validation and future potential applications of the traffic flow model. This research presents a stochastic traffic flow model which uses a stochastic partial differential equation to describe the evolution of traffic flow on the highway. The stochastic model is calibrated and validated by real traffic data on a highway and is proved to have better predictive power than the deterministic model. Also, a microscopic traffic simulation is built and calibrated by the same highway data, and the validation result shows that the simulation is capable of representing the real traffic. By using traffic simulation to further explore the capability of the stochastic model, the validation demonstrated that the prediction works well at most locations, and the interpolation error may be improved by considering the influence of ramps and the change in the number of lanes.

Traffic flow prediction plays an important role in intelligent transportation systems and is of great significance in the applications of traffic control and urban planning. Due to the complexity of road traffic flow data, traffic flow prediction has been one of the challenging tasks to fully exploit the spatiotemporal characteristics of roads to improve prediction accuracy. In this study, a combined flow direction level traffic flow prediction graph convolutional network (GCN) and long short-term memory (LSTM) model based on spatiotemporal characteristics is proposed. First, a GCN model is employed to capture the topological structure of the data graph and extract the spatial features of road networks. Additionally, due to the capability to handle long-term dependencies, the long-term memory is used to predict the time series of traffic flow and extract the time features. The proposed model is evaluated using real-world data, which are obtained from the intersection of Liuquan Road and Zhongrun Avenue in the Zibo High-Tech Zone of China. The results show that the developed combined GCN-LSTM flow direction level traffic flow prediction model can perform better than the single models of the LSTM model and GCN model, and the combined ARIMA-LSTM model in traffic flow has a strong spatiotemporal correlation.

Prelims

With the emergence of connected and automated vehicle (CAV) technologies, research on traffic flow modeling and analysis will play a very important role in improving our understanding of the fundamental characteristics of traffic flow. The frontier of studies on CAV systems have examined the impacts of CAVs on freeway bottleneck capacity, and macroscopic traffic flow, CAV applications on optimization of individual vehicle trajectories, potentials of CAV in traffic signal control, and applications of CAV in network routing. For current and future research initiatives, the greatest challenge lies in the potential inconsistencies between user, operator, and manufacturer goals. Specific research needs were identified on data collection and analysis on CAV behavior and applications. This paper summarizes the presentations and discussions during the Automated Vehicles Symposium 2015 (AVS15) held in Ypsilanti, Michigan, on July 20–23, 2015.

As the most promising alternative to internal combustion engines (ICEs), electric vehicles (EVs) have an excellent development outlook. The charging route scheduling of EVs can simultaneously affect traffic congestion in the transportation network (TN) and power flow distribution in the power distribution network (PDN). The research on TN and PDN coupling networks based on the static traffic flow model is relatively mature; however, it ignores that the traffic flow will spread across periods in a short scheduling period. In this paper, a semi‐dynamic traffic flow model is proposed to represent the dynamic propagation characteristics of EVs and ICEs flow. Furthermore, the cost of carbon emission and system operation are combined as the overall goal of system optimisation. Since the model has become a more complex non‐linear model, this paper proposes to combine the heuristic sequential boundary tightening and binary expansion method to linearise the model. The study compared four cases and found that a 20% penetration rate of EVs can reduce carbon emissions by 4.2% while reducing the system's total cost by 10%. Moreover, the impact of network congestion on the spatiotemporal distribution of traffic flow and power flow in the coupled network is alleviated.

Nowadays, congestion and accidents are creating major risks to cities, including delays, higher fuel usage, and compromised safety. Effective traffic modelling and accident data analysis are critical for identifying high risk identifying accident-prone locations, understanding the causes of accidents and creating focused actions to enhance traffic flow and safety. GIS is an effective tool for integrating, analysing and visualizing different geographical data relevant to transportation networks such as, traffic flow, infrastructure, and safety. It enables geographical analysis and visualization of accident hotspots by integrating accident data, road conditions, traffic numbers, and environmental factors. The use of GIS in traffic modelling and accident data analysis provides considerable benefits in urban transportation planning and management. The aim of the paper is to provide an overview of the application of GIS in traffic modelling and accidental data analysis, highlighting the methodologies, advancements, and challenges in this field. The review shall provide a comprehensive assessment of the current state of traffic modelling and accidental data analysis using GIS. It will highlight the significant contributions of GIS technology, identify key research gaps, and offer insights into future directions for enhancing transportation planning and decision-making processes.

Mixed lump-stripe, bright rogue wave-stripe, dark rogue wave-stripe and dark rogue wave solutions of a generalized Kadomtsev–Petviashvili equation in fluid mechanics

Freight transport is essential to modern urban civilization. No urban area could exist without a reliable freight transport system. Although the private sector is responsible for much of this system, the public sector has a vital role to play in the provision of infrastructure and the establishment of a social and legal framework within which transport can occur. For these reasons, goods movement deserves and is increasingly receiving, explicit consideration in urban transport policy and planning. Many cities around the world have conducted studies aimed at resolving urban goods movement problems and a considerable, if disparate, body of research results are available. This book brings together much of this knowledge and experience in a comprehensive source of information on urban freight, particularly from a public policy or planning viewpoint. It provides both a conceptual basis for urban goods movement analysis and detailed, practical guidelines which may be used directly by those responsible for urban freight policy and planning. The author has worked for over twenty years in this field and he draws upon his experience in Australia, the United States, Great Britain, Canada and The Philippines to produce a book which is international in scope and perspective. The book is written for practising professionals, such as engineers, economists and planners, working in local government, urban transport planning agencies, highway authorities, consultancies, or research institutes; it is also relevant to graduate courses in transport planning, traffic engineering or urban policy. It is of interest to all who have a concern for contemporary issues in urban development.