观测路径出行时间下随机网络交通需求估计

道路网络起讫点（OD）需求是城市决策长期交通规划和短期交通管理中的基础参数，准确的交通需求更是实施交通拥堵控制、限行限速、路径诱导等措施的先决条件。综合运用观测的轨迹已知和未知路径出行时间，建立随机网络交通需求估计双层规划模型。上层广义最小二乘模型最小化历史交通需求与待估交通需求、观测路径出行时间与待估路径出行时间之间的偏差，约束为交通需求、路段流量、路段出行时间与路径出行时间之间的传播关系，通过高斯混合模型（GMM）对其中轨迹未知的观测出行时间依概率聚类。下层为随机网络交通出行均衡模型，分别运用出行时间预算和随机用户均衡处理路网不确定性和出行者感知误差。上、下层之间通过交通需求和OD-路段关联比例进行信息传递。设计迭代算法框架求解双层规划模型，迭代算法包含求解上层模型的最速下降法、求解下层模型的相继平均算法和求解GMM模型的最大期望（EM）算法。通过算例表明轨迹未知的路径出行信息的加入在提升需求估计精度的同时也增大了估计值的方差；设计的迭代算法能够稳定收敛到10^-5的精度；GMM软聚类方法估计的交通需求显著优于硬聚类方法估计的需求值；交通需求值对观测路径出行时间的扰动更加敏感。研究考虑出行者风险态度，通过轨迹信息的重新构建揭示城市交通需求演化规律。

Traffic Demand Estimation Using Observed Path Travel Time in a Stochastic Network

Origin-destination(OD)demand in urban road networks is a fundamental component for long-term transportation planning or short-term traffic management in a city.Additionally,accurate trafficdemand is a prerequisite for urban traffic congestion control,road space rationing,speed limit,or route guidance.The bi-level traffic demand estimation model in a stochastic network was developed by taking advantage of the observed path travel time with known and unknown trajectories.The generalized least-squares model in the upper level minimized the differences between the historical traffic demands and estimated traffic demands,as well as the observed path travel time and estimated path travel time.The constraints were the transmission relationships between the traffic demands,link flows,link travel time,and path travel time.The Gaussian mixture model(GMM)was used to cluster the unknown trajectories of path travel time in probability.The lower level was a traffic user equilibrium model in the stochastic network,where the travel time budget and stochastic user equilibrium were used to deal with the uncertainty of the road network and travelers'perception errors,respectively.The traffic demands and OD-link flow proportions acted as bridges to transfer information between the upper-level and lower-level models.The framework of the iterative solution algorithm was designed to solve the bi-level programming model,where the method of gradient descent,method of successive average,and expectation-maximization(EM)algorithm were adopted to solve the upper-level,lower-level,and GMM models,respectively.Additionally,numerical examples demonstrate that adding the information of the path trip with unknown trajectories can improve the accuracy of traffic demand estimation.However,the unknown trajectories increase the variance of estimated values.The designed iterative solution algorithm can make convergence to the accuracy of 10-5.The soft cluster method of GMM is superior to the hard cluster method for estimating the traffic demand.Furthermore,traffic demands are more sensitive to the disturbances of observed path travel time.By considering the risk attitude of travelers and trajectory reconstruction,the evolution rules of urban traffic demands can be uncovered.