H.M. Zhang

Driver memory, traffic viscosity and a viscous vehicular traffic flow model

This paper studies the linkage between microscopic car-following and macroscopic fluid-like behavior of traffic flow. We find that driver memory in car-following leads to viscous effects in continuum traffic flow dynamics. This linkage is further exploited to develop a second-order continuum model with viscosity. Further, we show that this viscous model contains practically every well-known continuum model as a special case (e.g., the Lighthill–Whitham–Richards model and the Payne–Whitham model), has a stable wave structure of first- and second-order waves, and controls the extent of non-anisotropic and diffusive influences through a dimensionless parameter called anisotropic factor.

Traffic experiment reveals the nature of car-following

As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation pattern of disturbances. However, the traffic theories have been controversial due to a lack of precise traffic data. We have studied traffic flow from a new perspective by carrying out large-scale car-following experiment on an open road section, which overcomes the intrinsic deficiency of empirical observations. The experiment has shown clearly the nature of car-following, which runs against the traditional traffic flow theory. Simulations show that by removing the fundamental notion in the traditional car-following models and allowing the traffic state to span a two-dimensional region in velocity-spacing plane, the growth pattern of disturbances has changed qualitatively and becomes qualitatively or even quantitatively in consistent with that observed in the experiment.

The formation and structure of vehicle clusters in the Payne-Whitham traffic flow model

Abstract In this paper, we study the Payne–Whitham (PW) model as a hyperbolic system of conservation laws with relaxation and are interested in its solution patterns when it is unstable. With numerical simulations, we observed the formation of clusters in the solutions. A cluster, which consists of a shock and a transition layer, is a “strong” traveling wave in the sense of Liu (Commun. Math. Phys. 108 (1987) 153), and its traveling speed is equal to that of the corresponding shock. The time-asymptotic structure of a transition layer is described by a first-order ordinary differential equation. We also found that, due to the instability of the PW model, we could not predict the number of clusters or the position, height, or width of each cluster. Our study also reveals the intricate relationship between the structure of vehicle clusters and the parameter c0.

Analytical investigation on the minimum traffic delay at a two-phase intersection considering the dynamical evolution process of queues

This paper has studied the minimum traffic delay at a two-phase intersection, taking into account the dynamical evolution process of queues. The feature of delay function has been studied, which indicates that the minimum traffic delay must be achieved when equality holds in at least one of the two constraints. We have derived the minimum delay as well as the corresponding traffic signal period, which shows that two situations are classified. Under certain circumstance, extra green time is needed for one phase while otherwise no extra green time should be assigned in both phases. Our work indicates that although the clearing policies were shown in many experiments to be optimal at isolated intersections, it is sometimes not the case.

Analytical investigation on the minimum traffic delay at a three-phase signalized T-type intersection

The traffic delay at intersections is crucial for the performance of urban traffic system. This paper analytically investigated the minimum traffic delay at a three-phase T-type intersection. We firstly demonstrate that the minimum traffic delay must be achieved on the surface of the 3D space constituted by the three constraints. Next, we prove that the minimum traffic delay must be achieved on the three borderlines of the surface. Finally, we show that the minimum delay is achieved either on one specific borderline or at the vertex of the surface. In the former case, extra green time is needed for the stream with largest demand, while no extra green time should be assigned to any stream in the latter case.