Impact of Stochasticity on Traffic Flow Dynamics in Macroscopic Continuum Models

Stochasticity is an indispensable factor for describing real traffic situations. Recent experimental study has shown that a model spanning a two-dimensional speed-spacing (or speed-density) relationship has the potential to reproduce the characteristics of traffic flow in both experiments and empirical observations. This paper studies the impact of stochasticity on traffic flow in macroscopic models utilizing the stochastic flow-density relationship. Numerical analysis is conducted under the periodic boundary to study the impact of stochasticity on stability. Traffic flow upstream of a bottleneck is also investigated to study the impact of stochasticity on the oscillation growth feature. It is shown that there is only a quantitative difference for model stability after introducing stochasticity. In contrast, a qualitative change of the traffic oscillation growth feature can be clearly observed. With the introduction of stochasticity, traffic oscillations begin to grow in a concave way along the road. Sensitivity analysis is also performed. It is found that, under the stochastic flow-density relationship: (i) with the decrease of relaxation time, the second-order model becomes stable; (ii) the smaller the propagation speed of small disturbance, the much stronger the traffic oscillation; (iii) the larger the fluctuation range, the sooner the traffic oscillation fully develops; and (iv) the changing probability has trivial impact on the simulation results. Finally, model calibration and validation are conducted. It is shown that the experimental spatiotemporal patterns can be captured by macroscopic models under the stochastic flow-density relationship, especially the second-order model.