Mixed Platoon Flow Dispersion Model Based on Speed-Truncated Gaussian Mixture Distribution

Abstract

A mixed traffic flow feature is presented on urban arterials in China due to a large amount of buses. Based on field data, a macroscopic mixed platoon flow dispersion model (MPFDM) was proposed to simulate the platoon dispersion process along the road section between two adjacent intersections from the flow view. More close to field observation, truncated Gaussian mixture distribution was adopted as the speed density distribution for mixed platoon. Expectation maximum (EM) algorithm was used for parameters estimation. The relationship between the arriving flow distribution at downstream intersection and the departing flow distribution at upstream intersection was investigated using the proposed model. Comparison analysis using virtual flow data was performed between the Robertson model and the MPFDM. The results confirmed the validity of the proposed model.

Heterogeneous platoon flow dispersion model based on truncated mixed simplified phase‐type distribution of travel speed

“…To enhance the descriptive ability of models, Wei et al [23] proposed truncated normal distribution to fit vehicle velocity under the condition of homogeneous traffic flow by considering the speed boundary. However, when the traffic flow features heterogeneity, for example, in the provision of bus traffic, the distribution curves of travel speed and travel time are not unimodal [5][6][7][8]24] such that simple distribution function could not achieve a good fitting result. To address this problem, Wu et al [6,7] adopted truncated mixed Gaussian (TMG) distribution to fit travel speed and travel time for heterogeneous traffic flow.…”

“…However, when the traffic flow features heterogeneity, for example, in the provision of bus traffic, the distribution curves of travel speed and travel time are not unimodal [5][6][7][8]24] such that simple distribution function could not achieve a good fitting result. To address this problem, Wu et al [6,7] adopted truncated mixed Gaussian (TMG) distribution to fit travel speed and travel time for heterogeneous traffic flow. However, the Gaussian distribution is unintegrable such that it could only obtain an approximate solution through numerical simulation or Taylor expansion.…”

“…where Q denotes saturation flow rate and t g is green time. Following Wu et al [6], by substituting Equation (18) into Equation (17), we obtain the arrival traffic flow distribution function 3 at downstream intersection x and time t. 1 The departure flow rate of the intersection changes overtime, we can therefore assume that the flow rate is constant in a very short period of time (i.e., 1 s). Consequently, the curve can be approximated by a number of discontinuous straight lines.…”

“…In this section, the proposed model is compared with Robertson's model to prove the reliability and efficiency. The parameters of Robertson's model can be obtained by the method in [19], and the parameters of TMG model can be calculated by the EM algorithm in [6]. As a result, the parameters of these two models in four periods are listed in Table III.…”

“…However, the pattern of travel time distributions is not always unimodal under heterogeneous traffic flow condition, which is quite different to the shift exponential distribution. As examined in recent works [5][6][7][8], the mixed distribution is found to be more suitable for capturing the vehicle's travel speed in the condition of heterogeneous traffic flow.…”