基于概率密度演化理论的动态行程时间可靠性计算模型研究
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摘要
目前大多数行程时间可靠性计算模型仅考虑行程时间静态概率分布,无法刻画其动态随机演化过程。结合交通流动力学模型,本文利用概率密度演化理论建立随机行程时间概率密度演化模型,动态反映道路行程时间可靠性的实时波动;结合数论选点和偏微分方程TVD格式数值解设计了模型的求解算法;对上海某高架路段进行实证分析,并与传统的蒙特卡洛方法进行算法对比。结果表明,模型能够较好地刻画行程时间概率密度在不同时段的随机演化规律,且计算时耗大大低于蒙特卡洛仿真。研究能够为交通管理部门道路行程时间预测提供理论依据和工程实践参考。
Due to the uncertainty of transportation system, travel time reliability(referred to as TTR) is being paid more and more attention by both travelers and traffic management department. However, the existing TTR calculation models only consider the static situation of traffic flow and involve less the short-time dynamic evolution of TTR during peak hour, thus unable to conduct deep research into the travel time probability density short-time dynamic change process and the TTR dynamic evolution law. The main reason is that the current travel time probability density and TTR calculation methods are largely based on pure data mining instead of essential characters of traffic flow and the collected data, thus unable to explain the nature of probability relationship between sample data. These restrictions can cause huge computation time consumption, oversights and instability in final calculation results. The probability density evolution(referred to as PDE) is an effective method for study in nonlinear stochastic systems and provides better ideas for dynamic reliability evolution of stochastic system. Combining both data mining technology and system operation mechanism, PDE can reveal the inner relationship among sample data points, reflect the true essence of stochastic system, and reduce the demand of sample data size while maintaining the result accuracy and finally reducing the difficulty and computation amount. This research uses the traffic flow dynamics theory to simulate the vehicle moving process and establishes the random travel time probability density evolution model to dynamically depict the evolution trajectory of road TTR. The algorithm is designed using theoretical selection method and TVD-form partial differential equation numerical solution. An empirical analysis is carried out on parts of a highway in Shanghai. The traffic flow data collected is classified using the cluster method to fit the probability density distribution of road inflow and outflow rate during different time sections, and the dynamic evolution trajectory of travel time probability density during night and evening peak hours in order to show different characters of dynamic evolution trend under congested and smooth conditions. Comparisons are made with traditional Monte-Carlo simulation in terms of fitting accuracy and computational efficiency. The final calculation results show:(1)In smooth road condition, the dynamic stochastic road travel time varies steadily. All probability density curves show tiny difference and the TTR evolution character can be depicted using one single probability distribution function. The TTR curve remains in constant state of high reliability(;2)In congested road condition, all probability density curves show significant differences and the TTR evolution character cannot be depicted using one single probability distribution function. The TTR shows a steep shape of decreasing trend and finally down to zero; and(3)The computation consumption by PDE is much less than by Monte-Carlo simulation. To sum up, firstly this research applies the PDE method to the field of TTR dynamic evolution by taking stochastic road inflow and outflow rate into consideration. The model established by this research can not only reflect the dynamic TTR evolution laws under different traffic states, but also significantly improve the calculation efficiency, thus providing theoretical basis and practical reference for TTR real-time prediction. Future researches can firstly considers the TTR evolution patterns affected by the intersection signal timing. Secondly, the TTR evolution model can be extended to the entire transportation network and is used to analyze the TTR evolution pattern on the whole network level. Thirdly, we research on network congestion-propagation and diffusion patterns to provide an optimization strategy for emergency evacuation and TTR attenuation control.
Due to the uncertainty of transportation system, travel time reliability(referred to as TTR) is being paid more and more attention by both travelers and traffic management department. However, the existing TTR calculation models only consider the static situation of traffic flow and involve less the short-time dynamic evolution of TTR during peak hour, thus unable to conduct deep research into the travel time probability density short-time dynamic change process and the TTR dynamic evolution law. The main reason is that the current travel time probability density and TTR calculation methods are largely based on pure data mining instead of essential characters of traffic flow and the collected data, thus unable to explain the nature of probability relationship between sample data. These restrictions can cause huge computation time consumption, oversights and instability in final calculation results. The probability density evolution(referred to as PDE) is an effective method for study in nonlinear stochastic systems and provides better ideas for dynamic reliability evolution of stochastic system. Combining both data mining technology and system operation mechanism, PDE can reveal the inner relationship among sample data points, reflect the true essence of stochastic system, and reduce the demand of sample data size while maintaining the result accuracy and finally reducing the difficulty and computation amount. This research uses the traffic flow dynamics theory to simulate the vehicle moving process and establishes the random travel time probability density evolution model to dynamically depict the evolution trajectory of road TTR. The algorithm is designed using theoretical selection method and TVD-form partial differential equation numerical solution. An empirical analysis is carried out on parts of a highway in Shanghai. The traffic flow data collected is classified using the cluster method to fit the probability density distribution of road inflow and outflow rate during different time sections, and the dynamic evolution trajectory of travel time probability density during night and evening peak hours in order to show different characters of dynamic evolution trend under congested and smooth conditions. Comparisons are made with traditional Monte-Carlo simulation in terms of fitting accuracy and computational efficiency. The final calculation results show:(1)In smooth road condition, the dynamic stochastic road travel time varies steadily. All probability density curves show tiny difference and the TTR evolution character can be depicted using one single probability distribution function. The TTR curve remains in constant state of high reliability(;2)In congested road condition, all probability density curves show significant differences and the TTR evolution character cannot be depicted using one single probability distribution function. The TTR shows a steep shape of decreasing trend and finally down to zero; and(3)The computation consumption by PDE is much less than by Monte-Carlo simulation. To sum up, firstly this research applies the PDE method to the field of TTR dynamic evolution by taking stochastic road inflow and outflow rate into consideration. The model established by this research can not only reflect the dynamic TTR evolution laws under different traffic states, but also significantly improve the calculation efficiency, thus providing theoretical basis and practical reference for TTR real-time prediction. Future researches can firstly considers the TTR evolution patterns affected by the intersection signal timing. Secondly, the TTR evolution model can be extended to the entire transportation network and is used to analyze the TTR evolution pattern on the whole network level. Thirdly, we research on network congestion-propagation and diffusion patterns to provide an optimization strategy for emergency evacuation and TTR attenuation control.
引文
[1]Asakura Y,Kashiwadani M.Road network reliability caused by daily fluctuation of traffic flow[A].In Proceedings of 19th PTRC Summer Annual Meeting[C],Brighton:University of Sussex,1991,73-84
[2]Shao H,Lam W H K,Meng Q,et al.Demand-driven traffic assignment problem based on travel time reliability[J].Transportation Research Record,2006(19):220–230.
[3]Jenelius E.The value of travel time variability with trip chains,flexible scheduling and correlated travel times[J].Transportation Research Part B:Methodological,2012,46(3):762-780.
[4]Tu H,Li H,Van Lint H,et al.Modeling travel time reliability of freeways using risk assessment techniques[J].Transportation Research Part A:Policy and Practice,2012,46(10):1528-1540.
[5]侯立文,蒋馥.城市道路网的可靠性仿真[J].系统仿真学报,2002,14(5):664-668.
[6]Bell M G H,Iida Y.Transportation network analysis[M].New York:John Wiley and Sons.1997,2(1):179-192.
[7]Clark S,Watling D.Modelling network travel time reliability under stochastic demand[J].Transportation Research Part B:Methodological,2005,39(2):119-140.
[8]Ng M W,Waller S T.A computationally efficient methodology to characterize travel time reliability using the fast Fourier transform[J].Transportation Research Part B:Methodological,2010,44(10):1202-1219.
[9]陈富坚,柳本民,郭忠印,等.基于贝叶斯分析的道路交通系统可靠性模型[J].同济大学学报(自然科学版),2011,39(2):220-225.
[10]Du L,Peeta S,Kim Y H.An adaptive information fusion model to predict the short-term link travel time distribution in dynamic traffic networks[J].Transportation Research Part B:Methodological,2012,46(1):235-252.
[11]Taylor M A P.Modelling Travel time reliability with the Burr distribution[J].Procedia-Social and Behavioral Sciences,2012,54(1):75-83.
[12]Yeon J,Elefteriadou L,Lawphongpanich S.Travel time estimation on a freeway using discrete time Markov chains[J].Transportation Research Part B:Methodological,2008,42(4):325-338.
[13]Ramezani M,Geroliminis N.On the estimation of arterial route travel time distribution with Markov chains[J].Transportation Research Part B:Methodological,2012,46(10):1576-1590.
[14]Fosgerau M,Fukuda D.Valuing travel time variability:Characteristics of the travel time distribution on an urban road[J].Transportation Research Part C:Emerging Technologies,2012,24(1):83-101.
[15]李杰,陈建兵,张琳琳.随机过程的概率密度函数估计[J].应用力学学报,2010,27(3):482-485.
[16]Lighthill M J,Whitham G B.On kinematic waves.II.A theory of traffic flow on long crowded roads[J].Proceedings of the Royal Society of London.Series A.Mathematical and Physical Sciences,1955,22(11):317-345.
[17]Xue Y,Dai S Q.Continuum traffic model with the consideration of two delay time scales[J].Physical Review E,2003,68(6):66-123.
[18]陈建兵,李杰.随机结构动力可靠度分析的极值概率密度方法[J].地震工程与工程振动,2004,24(6):39-44.
[19]Li J,Chen J B.The principle of preservation of probability and the generalized density evolution equation[J].Structual Safety,2008,30(1):65-77
[20]陈建兵,李杰.随机结构反应概率密度演化分析的切球选点法[J].振动工程学报,2006,19(1):1-8.
[21]Li J,Chen J B.Advances of the probability density evolution method for nonlinear stochastic systems[J].Probabilistic Engineering Mechanics,2012,28(1):132-142.
[2]Shao H,Lam W H K,Meng Q,et al.Demand-driven traffic assignment problem based on travel time reliability[J].Transportation Research Record,2006(19):220–230.
[3]Jenelius E.The value of travel time variability with trip chains,flexible scheduling and correlated travel times[J].Transportation Research Part B:Methodological,2012,46(3):762-780.
[4]Tu H,Li H,Van Lint H,et al.Modeling travel time reliability of freeways using risk assessment techniques[J].Transportation Research Part A:Policy and Practice,2012,46(10):1528-1540.
[5]侯立文,蒋馥.城市道路网的可靠性仿真[J].系统仿真学报,2002,14(5):664-668.
[6]Bell M G H,Iida Y.Transportation network analysis[M].New York:John Wiley and Sons.1997,2(1):179-192.
[7]Clark S,Watling D.Modelling network travel time reliability under stochastic demand[J].Transportation Research Part B:Methodological,2005,39(2):119-140.
[8]Ng M W,Waller S T.A computationally efficient methodology to characterize travel time reliability using the fast Fourier transform[J].Transportation Research Part B:Methodological,2010,44(10):1202-1219.
[9]陈富坚,柳本民,郭忠印,等.基于贝叶斯分析的道路交通系统可靠性模型[J].同济大学学报(自然科学版),2011,39(2):220-225.
[10]Du L,Peeta S,Kim Y H.An adaptive information fusion model to predict the short-term link travel time distribution in dynamic traffic networks[J].Transportation Research Part B:Methodological,2012,46(1):235-252.
[11]Taylor M A P.Modelling Travel time reliability with the Burr distribution[J].Procedia-Social and Behavioral Sciences,2012,54(1):75-83.
[12]Yeon J,Elefteriadou L,Lawphongpanich S.Travel time estimation on a freeway using discrete time Markov chains[J].Transportation Research Part B:Methodological,2008,42(4):325-338.
[13]Ramezani M,Geroliminis N.On the estimation of arterial route travel time distribution with Markov chains[J].Transportation Research Part B:Methodological,2012,46(10):1576-1590.
[14]Fosgerau M,Fukuda D.Valuing travel time variability:Characteristics of the travel time distribution on an urban road[J].Transportation Research Part C:Emerging Technologies,2012,24(1):83-101.
[15]李杰,陈建兵,张琳琳.随机过程的概率密度函数估计[J].应用力学学报,2010,27(3):482-485.
[16]Lighthill M J,Whitham G B.On kinematic waves.II.A theory of traffic flow on long crowded roads[J].Proceedings of the Royal Society of London.Series A.Mathematical and Physical Sciences,1955,22(11):317-345.
[17]Xue Y,Dai S Q.Continuum traffic model with the consideration of two delay time scales[J].Physical Review E,2003,68(6):66-123.
[18]陈建兵,李杰.随机结构动力可靠度分析的极值概率密度方法[J].地震工程与工程振动,2004,24(6):39-44.
[19]Li J,Chen J B.The principle of preservation of probability and the generalized density evolution equation[J].Structual Safety,2008,30(1):65-77
[20]陈建兵,李杰.随机结构反应概率密度演化分析的切球选点法[J].振动工程学报,2006,19(1):1-8.
[21]Li J,Chen J B.Advances of the probability density evolution method for nonlinear stochastic systems[J].Probabilistic Engineering Mechanics,2012,28(1):132-142.