Investigation of traffic characteristics in vehicular transport

Abstract

The number of automobiles increased as a result of population growth and economic expansion. The high availability of transportation complicates vehicle interaction, which may cause the occurrence of traffic congestion. Therefore, the traffic flow phenomenon has become one of the critical complex systems. Mathematical models can be used to understand and visualize traffic flow in mathematical terms. In this light, the current research puts up models and analyses of several actual traffic features by adopting a lattice hydrodynamic methodology (approach). The lattice hydrodynamic model has become the most famous because of its simpler approach. In this approach, space is discretized into lattice sites. The model comprises continuity and momentum equations that explain the aggregate behavior of traffic flow at each lattice site. In this thesis, the effects of predictive effect have been examined on one-lane system when overtaking is permitted, two-lane system with rule of lane change, two-dimensional system having junction on road. Further, a new lattice model is developed by considering the influences of uncertainty of historical information on downstream. Furthermore, the factor area occupancy is included in lattice model which is related to heterogeneous traffic. All the models are analyzed theoretically by linear and nonlinear analysis. Theoretical findings are confirmed by numerical simulations. Additionally, the thesis is presented in seven chapters: Based on traffic flow theory, Chapter 1 reviews the literature regarding the general traffic system noted by the researchers, the potential hurdles to the transportation system, and possible solutions. Assumptions and requirements of traffic flow modeling are discussed. Various modeling approaches, such as microscopic models, macroscopic models, and lattice hydrodynamic models, are briefly discussed, describing important features of the traffic phenomenon. In addition, the scope and limitations of the existing models are presented. The predictive effect and overtaking (passing) are interrelated in the traffic environment. When faster-moving vehicles receive prior information regarding the downstream circumstances, this information helps them decide whether to accelerate or slow down vehicle speed and also aids them in overtaking slower-moving vehicles. Therefore, motivated by the explained phenomenon, the investigation of the passing with predictive effect for a unidirectional single-lane highway is explored in Chapter 2. Further, the model is analyzed theoretically by employing stability analysis. The influence of the predictive effect is examined on traffic stream stability through linear stability analysis when passing is perviimitted. It is shown that the accurate expected behavior of the vehicles ahead can enhance the stability of traffic flow for any rate of passing. Using nonlinear stability analysis, we obtained the critical value of the passing constant for which the kink soliton solution of the mKdV equation exists. When the passing constant is smaller than a critical value, the jamming transition occurs between uniform and kink flows. In contrast, for the higher value of passing constant, the jamming transitions occur from uniform flow to kink density wave flow through a chaotic phase. Numerical simulations verify the theoretical predictions, which show that traffic congestion can be suppressed efficiently by considering the predictive effect in a single-lane traffic system when passing is allowed. Finally, the results are summarized. Chapter 3 aims to propose a new hydrodynamic lattice model by considering the predictive effect and the optimal current difference effect (OCDE) on a two-lane unidirectional traffic system. Stability analysis is used to conduct a theoretical investigation of the model. In a two-lane system with permitted lane changing, the contribution of the predictive effect, including consideration of OCDE, is examined on traffic stability by linear stability analysis. The mKdV equation is derived using nonlinear stability analysis, and the density wave in terms of the kink-antikink wave is obtained around the critical point. It is observed that the predictive effect plays an important role in enhancing traffic flow stability in a two-lane system. Numerical simulations are performed to validate the theoretical predictions, demonstrating that traffic jams can be alleviated more efficiently by considering the predictive effect in the vehicular system where lane change is permitted. At the end of the Chapter, the summary of the outcomes is presented with future scope. In Chapter 4, a two-dimensional (2D) lattice model by incorporating the predictive effect with the junction on the road is proposed. According to the situation, drivers can change their driving behavior while using their skills in advance with the help of prior information, and they change their path through the turning point on the road. At the junction of the road, traffic can enter into various downstream lanes from the upstream. The intensity of downstream traffic may vary depending on the proportion of traffic. To analyze the proposed model, the stability condition is obtained without and with the control signal through the control method, which shows that the stable region increases when the control signal is considered into account. The theoretical findings indicate that the predictive effect could affect the stability of diverging traffic. Numerical simulations validate the theoretical findings, showing that the predictive effect for junction roads is beneficial in enhancing traffic flow stability. In the last section, the conclusion of the results and the possible future scope are given. Several real-time feedback tactics have been presented and applied for traffic dynamics,such as historical density information, historic flux information, etc. Moreover, complex uncertainties such as equipment malfunctions, network fluctuations, driver personality, and traffic disruption may affect traffic information. Therefore, Chapter 5 is devoted to reflecting better the reality of traffic situations in the transportation system by considering uncertainty about historical information of density (UHDI) based on the lattice approach. The UHDI effect is probed using linear stability analysis and nonlinear stability analysis. The instability is found with an increased value of the UHDI coefficient. The modified Korteweg-de-Vries equation (mKdV) is obtained to describe the characteristics of traffic congestion. Finally, numerical simulations are implemented to analyze the results of theoretical findings. The numerical and hypothetical results show that the UHDI factor significantly affects traffic flow. Chapter 6 deals with analyzing the impact of the heterogeneous behavior of vehicles on traffic dynamics. In developing countries, traffic not only consists of a wide range of vehicles, including automobiles, trucks, buses, motorbikes, etc. but is also disordered. Controlling and managing increasingly complex transport networks depend heavily on modeling the mechanics of mixed (heterogeneous) traffic. Vehicles having different speeds and sizes behave accordingly to their characteristics in traffic flow. Hence, a new lattice model is designed by considering the area occupancy of different vehicles in a heterogeneous disorder traffic system with a variable proportion of slow-moving to fast-moving automobiles. In addition, stability analysis is done to investigate the ability of a heterogeneous traffic model. The mixed traffic phase diagrams show a link between traffic stability and the fraction of vehicles. Moreover, a reduction perturbation approach is used to explore the behavior of the disordered traffic, and the mKdV equation is achieved near the critical point. It is demonstrated that larger vehicles cause traffic jams, whereas smaller ones are apt to ease traffic jams. Furthermore, numerical simulations are performed to verify the consistency of theoretical analysis. Results portray that a higher fraction of small vehicles is beneficial for stabilizing the traffic flow. Further, Chapter 7 summarizes the obtained results from the proposed models. The future scope is given based on some real traffic characteristics.