Short-Term Freeway Traffic Prediction by Payne-Whitham Model Considering Driver’s Anticipation Effect

Abstract

In this research, we study a macroscopic traffic model, Payne-Whitham (PW) model, with an anticipation source term. The anticipation source describes how the traffic adjusts its speed based on the condition ahead. With the calibration of driver’s anticipation effect in PW model, this study 1) proposes a short-term freeway traffic prediction method, 2) validates the method with real world data from PeMS, 3) assesses the method by MAPE, VAPE and PPE, 4) compares the method in different traffic conditions and prediction periods, 5) provides a guideline in the range of driver’s anticipation parameter. The results indicate the average relative error of predicting speed in 5-min is 3.48% with a variance of 5.33%. The comparisons revealed the anticipation parameter increases with a decreasing in the size of predictable VDSs as the traffic becomes more congested. For a longer prediction period, the reduction in the size of predictable VDSs is higher. We recommend taking a value between 8 to 14 for the anticipation parameter when modelling the traffic with LOS from C to F; from 3 to 9 for traffic between LOS B and C; from 0 to 4 for traffic with LOS A. These recommended ranges could guide practitioners without knowing the shape of traveling wave when using PW model or PW prediction method. The traffic prediction method developed in this study differs from data-driven prediction methods. It is derived from the solutions of PW model; hence, it underlies flow studies and the process includes the concept of traffic dynamics. It reduces the size of predictable data points, because a perturbation method was assumed in solving the PW model. The results show under a congested traffic, there are about 77.6% of data points satisfied for a 5-min PW prediction, 63.6% of data points satisfied for a one-hour PW prediction. This indicates the limitation does not have large impact on the PW predictions in general.