A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A nume...A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.展开更多
This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation （KdV） solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the appr...This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation （KdV） solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.展开更多
The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of t...The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.展开更多
A standard conservation form is derived in this paper.The hyperbolicity of Helbing＇s fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this model.On the ba...A standard conservation form is derived in this paper.The hyperbolicity of Helbing＇s fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this model.On the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated.This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients,and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.展开更多
This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns ...This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns of traffic development to identify road traffic safety levels in city clusters.Additionally,an evaluation index system of city cluster road traffic safety was constructed based on the spatial and temporal distribution.Then Order Exponential Evaluation Model(OEEM),a comprehensive model using order exponent function for road traffic safety evaluation,was put forward,which considers the main characteristics and the generation process of traffic accidents.The model effectively controlled the unsafe behavior of the traffic system.It could define the levels of city cluster road traffic safety and dynamically detect road safety risk.The proposed model was verified with statistical data from three Chinese city clusters by comparing the common model for road traffic safety with an ideal model.The results indicate that the order exponent approach undertaken in this study can be extended and applied to other research topics and fields.展开更多
Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent year...Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent years,crowd movements at carnival events have attracted the attention of researchers. In contrast to pedestrian behavior in other walking facilities, pedestrians whose attention is attracted by carnival displays or activities may slow down and even stop walking. The Lunar New Year Market is a traditional carnival event in Hong Kong held annually one week before the Lunar New Year. During the said event,crowd movements can be easily identified, particularly in Victoria Park, where the largest Lunar New Year Market in Hong Kong is hosted. In this study, we conducted a videobased observational survey to collect pedestrian flow and speed data at the Victoria Park Lunar New Year Market on the eve of the Lunar New Year. Using the collected data, an extant mathematical model was calibrated to capture the relationships between the relevant macroscopic quantities,thereby providing insight into pedestrian behavior at the carnival event. Bayesian inference was employed to calibrate the model by using prior data obtained from a previous controlled experiment. Results obtained enhance our understanding of crowd behavior under different conditions at carnival events, thus facilitating the improvement of the safety and efficiency of similar events in the future.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 11072141 and 11272199)the National Basic Research Program of China (No. 2012CB725404)+1 种基金the University Research Committee, HKU SPACE Research FundFaculty of Engineering Top-up Grant of the University of Hong Kong (No. 201007176059)
文摘A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries （KdV） equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.
基金supported by the National Natural Science Foundation of China(Nos.11072141 and11272199)the National Basic Research Program of China(No.2012CB725404)+2 种基金the Shanghai Program for Innovative Research Team in Universitiesthe Research Grants Council of the Hong KongSpecial Administrative Region,China(No.HKU7184/10E)the National Research Foundationof Korea(MEST)(No.NRF-2010-0029446)
文摘This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation （KdV） solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.
基金Project supported by the National Natural Science Foundation of China(No.11072141)the Shanghai Program for Innovative Research Team in Universities,the Graduate Innovation Foundation of Shanghai University(No.SHUCX101078)and the University Research Committee,HKU SPACE Research Fund and Faculty of Engineering Top-up Grant of the University of Hong Kong(No.201007176059)
文摘The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.
基金supported by the National Natural Science Foundation of China (No. 11072141)the Shanghai Program for Innovative Research Team in Universities+1 种基金the University Research Committee of the University of Hong Kong (No. 201007176059)the Outstanding Researcher Award from the University of Hong Kong
文摘A standard conservation form is derived in this paper.The hyperbolicity of Helbing＇s fluid dynamic traffic flow model is proved,which is essential to the general analytical and numerical study of this model.On the basis of this conservation form,a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently.The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated.This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients,and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.
基金Sponsored by the National Natural Science Foundation of China(Grant No.51178157)the High-level Project of the Top Six Talents in Jiangsu Province(Grant No.JXQC-021)+1 种基金the Key Science and Technology Program in Henan Province(Grant No.182102310004)the Humanities and Social Science Research Programs Foundation of Ministry of Education of China(Grant No.18YJAZH028).
文摘This study presents an order exponential model for estimating road traffic safety in city clusters.The proposed model introduces the traffic flow intrinsic properties and uses the characteristics and regular patterns of traffic development to identify road traffic safety levels in city clusters.Additionally,an evaluation index system of city cluster road traffic safety was constructed based on the spatial and temporal distribution.Then Order Exponential Evaluation Model(OEEM),a comprehensive model using order exponent function for road traffic safety evaluation,was put forward,which considers the main characteristics and the generation process of traffic accidents.The model effectively controlled the unsafe behavior of the traffic system.It could define the levels of city cluster road traffic safety and dynamically detect road safety risk.The proposed model was verified with statistical data from three Chinese city clusters by comparing the common model for road traffic safety with an ideal model.The results indicate that the order exponent approach undertaken in this study can be extended and applied to other research topics and fields.
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. Poly U 5243/13E)respectively supported by the Postdoctoral Fellow Scheme and Francis S. Y. Bong Professorship in Engineering of The University of Hong Kong
文摘Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent years,crowd movements at carnival events have attracted the attention of researchers. In contrast to pedestrian behavior in other walking facilities, pedestrians whose attention is attracted by carnival displays or activities may slow down and even stop walking. The Lunar New Year Market is a traditional carnival event in Hong Kong held annually one week before the Lunar New Year. During the said event,crowd movements can be easily identified, particularly in Victoria Park, where the largest Lunar New Year Market in Hong Kong is hosted. In this study, we conducted a videobased observational survey to collect pedestrian flow and speed data at the Victoria Park Lunar New Year Market on the eve of the Lunar New Year. Using the collected data, an extant mathematical model was calibrated to capture the relationships between the relevant macroscopic quantities,thereby providing insight into pedestrian behavior at the carnival event. Bayesian inference was employed to calibrate the model by using prior data obtained from a previous controlled experiment. Results obtained enhance our understanding of crowd behavior under different conditions at carnival events, thus facilitating the improvement of the safety and efficiency of similar events in the future.
