Traffic Instability Research Articles

Comparison study of the reactive and predictive dynamic models for pedestrian flow

This paper formulates the reactive and predictive dynamic models for pedestrian flow and presents a comparison of the two models. The path-choice behavior of pedestrians in the reactive dynamic model is described that pedestrians tend to walk along a path with the lowest instantaneous cost. The desired walking direction of pedestrians in the predictive dynamic model is chosen to minimize the actual cost based on predictive traffic conditions. An algorithm used to solve the two models encompasses a cell-centered finite volume method for a hyperbolic system of conservation laws and a time-dependent Hamilton–Jacobi equation, a fast sweeping method for an Eikonal-type equation, and a self-adaptive method of successive averages for an arisen discrete fixed point problem. The two models and their algorithm are applied to investigate the spatio-temporal patterns of flux or density and path-choice behaviors of pedestrian flow marching in a facility scattered with an obstacle. Numerical results show that the two models are able to capture macroscopic features of pedestrian flow, traffic instability and other complex nonlinear phenomena in pedestrian traffic, such as the formation of stop-and-go waves and clogging at bottlenecks. Different path-choice strategies of pedestrians cause different spatial distributions of pedestrian density specially in the high-density regions (near the obstacle and exits).

An Improved Macro Model of Traffic Flow with the Consideration of Ramps and Numerical Tests

We present an improved macro model for traffic flow based on the existing models. The equilibrium point equation of the model is obtained. The stop-and-go traffic phenomenon is described in phase plane and the relationship between traffic jams and system instability is clearly shown in the phase plane diagrams. Using the improved model, some traffic phenomena on a highway with ramps are found in this paper. The numerical simulation is carried out to investigate various nonlinear traffic phenomena with a single ramp generated by different initial densities and vehicle generation rates. According to the actual road sections of Xi’an-Baoji highways, the situations of morning peak with several ramps are also analyzed. All these results are consistent with real traffic, which shows that the improved model is reasonable.

Network capacity, traffic instability, and adaptive driving: findings from simulated urban network experiments

This paper provides a discussion of network traffic flow stability and network capacity including existing definitions and measurement methods in the literature. To characterize network traffic flow, three phases are defined as free flow (F), inhomogenously congested (IC), and homogenously congested. It is shown that in large non-homogenous networks, the F → IC transition is usually a hysteretic phase transition. This paper examines the effects of adaptive driving on network capacity and traffic instability in a simulated network model of the Chicago metropolitan area as a large-scale highly congested complex network with exit flows. Results show that when the number of adaptive drivers increases, the general trend for network capacity is also increasing with some fluctuations due to randomness of traffic and overlapping effects of route choices. It is also found that adaptive driving may increase average network flow but may not necessarily improve network output, especially when the population of adaptive drivers is large and no gridlock exists. Results also suggest that with a larger population of adaptive drivers, hysteresis and gridlock are less likely to form. However, it is shown that bifurcation and multivaluedness can still occur even when the entire population of drivers is adaptive.

Understanding the Dynamics of Heavy Vehicle Interactions in Car-Following

Heavy vehicles and passenger cars differ in their maneuverability and acceleration capabilities. Heavy vehicles thus influence other traffic in a different manner than passenger vehicles, causing different levels of traffic instability. Increasing number and proportion of heavy vehicles in the traffic stream may result in quite different traffic flow characteristics. Over the last five decades many studies have investigated passenger car drivers’ car-following behavior. However, the existence of heavy vehicles in the traffic stream has not received the same attention. This paper investigates the different car-following behavior of drivers in congested heterogeneous traffic conditions. It specifically focuses on the existence of heavy vehicles in general traffic and their interaction with other vehicles. Four different combinations of passenger car and heavy vehicle were considered. These combinations include passenger car-following a passenger car, passenger car-following a heavy vehicle, heavy vehicle following a passenger car, and heavy vehicle following another heavy vehicle. A data set from a freeway in the United States was used to show the different car-following behavior of drivers for each combination. This study analyzes space and time headways, drivers’ reaction times, and vehicle accelerations. It also introduces different car-following thresholds for each car-following combination. It was found that the presence of heavy vehicles causes larger space and time headways, longer reaction time, and more robust car-following behavior. It also shows that the car-following thresholds are of the four combinations studies. The findings of this paper indicate that further research is required to develop a generalized car-following model that can be used when different vehicle types are in the traffic stream.

Exploring Properties of Networkwide Flow–Density Relations in a Freeway Network

The objective of this study is to investigate the properties of network-level traffic flow relationships in a freeway network with the use of commonly available loop detector data. The impact of the spatial and temporal distribution of congestion in a selected network on the shape and properties of the flow–density relation is investigated, with emphasis on the formation and characterization of hysteresis patterns. Accordingly, a path-dependent characterization of hysteresis patterns in freeway networks is introduced and illustrated conceptually as well as through empirical observations. Comparison of the spatial and temporal distribution of congestion throughout a selected subnetwork on different days suggests a relationship between the size of the hysteresis loop and the inhomogeneity of the traffic distribution. The maximum network average flow is not a constant value but varies across different days. In addition, for the same value of average network occupancy, the variation of occupancy is higher during the recovery period compared with the loading period. The observed large variation in network occupancy during recovery implies the formation of fragmented queues and traffic instability. A chaotic pattern is also to be expected in the networkwide flow–occupancy plane when the spatial distribution of link densities is inhomogeneous and the average network occupancy remains consistently high and roughly unchanged for successive time intervals. Overall, the study results provide a deeper understanding of the properties of networkwide relations on freeway networks.

Highway Capacity Loss Induced by Rainfall

The effect of rainfall on capacity reduction on highways has been investigated. Traffic data was generated for both wet and dry conditions. The data analysis showed that the highway section studied was operating in free flow region. A 2.7% capacity loss was obtained for the road. It is argued that no traffic instability could arise from this situation if the state of traffic remains in the free flow regime. However, in the event of the coincidence of fixed bottlenecks and rainfall, instabilities arising from that could lead to further capacity loss.

A higher-order macroscopic model for pedestrian flows

This paper develops a higher-order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two-dimensional Euler equations with relaxation. The desired directional motion of pedestrians is determined by an Eikonal-type equation, which describes a problem that minimizes the instantaneous total walking cost from origin to destination. A linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows. The algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms, a second-order positivity-preserving central-upwind scheme for hyperbolic conservation laws, and a fast-sweeping method for the Eikonal-type equation on unstructured meshes. To test the applicability of the model, we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two-dimensional continuous walking facility. The numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow. The simulation results are compared with those obtained by the two-dimensional Lighthill–Whitham–Richards pedestrian flow model with various model parameters, which further shows that the macroscopic model is able to correctly describe complex phenomena such as “stop-and-go waves” observed in empirical pedestrian flows.