The LWR model is of interest since it can successfully reproduce some essential features of traffic flow, such as the formation and propagation of various waves. Recently, however, the disadvantageous aspects of traditional LWR model are attracting more and more attention. Many researchers have made great effort to develop new models based on the LWR model, such that some prominent nonlinear characteristics of traffic flow, such as platoon diffusion, capacity drop, hysteresis, and spontaneous onset of congestion are captured. In this paper, we investigate the LWR model from an uncertainty perspective. Rather than developing a new explanatory model, we attempt to analyze how reliable the LWR model prediction will be if the fundamental diagram (FD) used is not specified accurately. Our work reflects the current debate on the nature of the FD. To be specific, we postulate a form of the flux function driven by random free flow speed, which accommodates the scattering feature observed in the speed-density plot. We show the properties of the LWR model with the new flux. A third-order essentially non-oscillatory (ENO) finite difference algorithm is devised to solve the model. An approach to evaluate the predictability of traffic disturbance propagation with this model is presented. We interpret the results and conclude that if the FD cannot be undoubtedly specified, the LWR model will deteriorate and only make a reasonable prediction in relatively short time scale.
Available at: http://works.bepress.com/daiheng_ni/16/