高速公路交通流量的齐次泊松过程模型检验

Test for the Homogeneous Poisson Process Model of Highway Traffic Flows

摘要: 为检验高速路上车辆到达时刻是否服从齐次泊松过程模型，使用实测的交通数据资料，记录车辆到达监测点的时间，构成一个随机点过程。基于空间点过程的理论，将Ripley的K函数应用到一维随机点过程中，依据齐次泊松过程情形下K函数的特殊形式，结合包络检验，提出了一种齐次泊松过程的图形化检验方法，并通过随机模拟验证了检验方法的有效性。使用该图形化方法对车辆到达常台高速监测点的时间所构成的点过程进行检验，结果表明该点过程是一个齐次泊松过程，通过估计其参数得出常台高速该时段车流量的齐次泊松过程模型。

Abstract: In order to build a traffic model of vehicles arrival times of highway, using the observed traffic data, a stochastic point pattern is composed by recording vehicles arrival times. Based on the theory of spatial point process, the Ripley’s K function is applied to one-dimensional stochastic point process. According to the characteristics of Homogeneous Poisson Process, a graphical approach is proposed to test Homogeneous Poisson Process combined with envelope test. And the effectiveness of the test is verified by simulation. Then the graphical approach is applied to the patterns, and the result indicates that arrival times of vehicles composed a Homogeneous Poisson Process. Finally, the traffic model of Chang-Tai freeway is obtained by estimating the parameter of the Homogeneous Poisson Process.