Narrow Results

We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel–Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain density regime ρ_low < ρ < ρ_high one observes plateau formation in the fundamental diagram. The plateau value depends on the input-rate of cars at the on-ramp. The on-ramp acts as a local perturbation that separates the system into two regimes: A regime of free flow and another one where only jammed states exist. This phase separation is the reason for the plateau formation and implies a behavior analogous to that of stationary defects. This analogy allows to perform very fast simulations of complex traffic networks with a large number of on- and off-ramps because one can parametrise on-ramps in an exceedingly easy way.

A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by considering a small perturbation around the homogeneous flow solution. The effect of the generalized optimal velocity function is also confirmed with numerical simulations, by examining the hysteresis loop in the headway-velocity phase space, and the relation between the flow and density of cars. In the model with a specific parameter choice, it is found that an intermediate state appears for the movement of cars, where the car keeps a certain velocity whether the headway is short or long. This phenomenon is different from the ordinary stop-and-go state.

Considering the effects of different factors on the stochastic delay probability, the delay probability has been classified into three cases. The first case corresponding to the brake state has a large delay probability if the anticipant velocity is larger than the gap between the successive cars. The second one corresponding to the following-the-leader rule has intermediate delay probability if the anticipant velocity is equal to the gap. Finally, the third case is the acceleration, which has minimum delay probability. The fundamental diagram obtained by numerical simulation shows the different properties compared to that by the NaSch model, in which there exist two different regions, corresponding to the coexistence state, and jamming state respectively.

We have numerically investigated the effect of the delay times τ_f and τ_s of a mixture of fast and slow vehicles on the fundamental diagram (the current-density relation) of the optimal velocity model. The optimal velocity function of the fast cars depends not only on the headway of each car but also on the headway of the immediately preceding one. It is found that the small delay times have almost no effects, while, for sufficiently large delay time τ_s, the current profile displays qualitatively five different forms, depending on τ_f, τ_s and the fractions d_f and d_s of the fast and slow cars, respectively. The velocity (current) exhibits first-order transitions at low and/or high densities, from freely moving phase to the congested state, and from congested state to a jamming one, respectively. The minimal current appears in intermediate values of τ_s. Furthermore, there exist a critical value of τ_f above which the metastability and hysteresis appear. The spatial-temporal traffic patterns near the congested-jamming first-order transition is also presented.

To depict the mixed traffic flow consisting of motorized (m-) and non-motorized (nm-) vehicles, a new cellular automaton model is proposed by combining the NaSch model and the BCA model, and some rules are also introduced to depict the interaction between m-vehicles and nm-vehicles. By numerical simulations, the flux-density relations are investigated in detail. It can be found that the flux-density curves of m-vehicle flow can be classified into two types, corresponding to small and large density regions of nm-vehicles, respectively. In small density region of nm-vehicles, the maximum flux as well as the critical density decreases with the increase of nm-vehicle density. Similar characteristics can also be found in large density region of nm-vehicles. However, compared with the former case, the maximum flux is much lower, the phase transition from free flow to congested flow becomes continuous and thus the corresponding critical points are non-existent. The flux-density curves of nm-vehicle flow can also be classified into two types. And interestingly, the maximum flux and the corresponding density decrease first and keep constant later as the density of m-vehicle increases. Finally, the total transport capacity of the system is investigated. The results show that the maximum capacity can be reached at appropriate proportions for m-vehicles and nm-vehicles, which induces a controlling method to promote the capacity of mixed traffic flow.

Intersections without signal control widely exist in urban road networks. This paper studied the traffic flow in a noncontrolled intersection within an iterated game framework. We assume drivers have learning ability and can repetitively adjust their strategies (to give way or to rush through) in the intersection according to memories. A cellular automata model is applied to investigate the characteristics of the traffic flow. Numerical experiments indicate two main findings. First, the traffic flow experiences a "volcano-shaped" fundamental diagram with three different phases. Second, most drivers choose to give way in the intersection, but the aggressive drivers cannot be completely eliminated, which is coincident with field observations. Analysis are also given out to explain the observed phenomena. These findings allow deeper insight of the real-world bottleneck traffic flow.

As a data set for validation of microscopic simulation models, we obtained the fundamental diagram (flux versus density relation), and the relations of velocity versus density, lane usage ratio versus density and lane-changing frequency versus density derived from a single field measurement campaign held at a Japanese urban expressway. The results were drawn from image analysis of video camera data obtained at the site.

This study examines the cellular automata traffic flow model, which considers the asynchronous update of vehicles’ velocities. Computer simulations are used to identify three typical phases: linear free flow phase, nonlinear moving phase and traffic jam phase. Compared to the original NaSch model, the system of the present model can reach the maximum flow when the vehicle density is higher. The influence of the delay probability and the maximum time step in which drivers intend to keep their current velocity on fundamental diagram is discussed.

This paper studies a road tolling problem in which a road user travels from A to B either via road 1 by paying or via road 2 without charge. The route choice also obeys the user-equilibrium principle. However, the travel time is formulated as a strictly increasing function of the density through the velocity–density relationship or fundamental diagram, which significantly improves the formulation in the classical traffic assignment problem. Accordingly, the influence of toll rate on the road users, the administration department and the road runner is analyzed in detail, by assuming that the user demand is rigid and maximizing the total traffic flow and the runner’s benefits from the collection of toll fees.

Due to the lack of natural driving databases containing heterogeneous traffic in the existing heterogeneous car-following modeling research, there is an urgent need for the support of a large amount of measured trajectory data for modeling. To this end, four different car-following modes of heterogeneous traffic under the influence of different vehicle types are extracted from the HighD data set, with which the statistical characteristics of the following car speed, speed difference, gap, time headway and acceleration in each mode are studied separately. Moreover, the correlation analysis of two parameters in speed-gap and speed difference-gap is carried out. On this basis, the intelligent driver model (IDM) and the full velocity difference (FVD) model are, respectively, employed to model the car-following characteristics in each mode. The results show that the existence of the truck in the following vehicle pair makes the following vehicle tend to maintain a larger gap and a smaller following speed, that is, larger time headway and gap. With the increase of trucks’ ratio, the capacity of traffic decreases. The research can lay the foundation for more accurate mixed traffic flow modeling of heterogeneous human driving vehicles, and even subsequent research on heterogeneous traffic characteristics under a mixture of human driving vehicles and autonomous vehicles.

The study of crowd dynamics is interesting because of the various self-organization phenomena resulting from the interactions of many pedestrians, which may improve or obstruct their flow. Besides formation of lanes of uniform walking direction and oscillations at bottlenecks at moderate densities, it was recently discovered that stop-and-go waves [D. Helbing et al., Phys. Rev. Lett.97 (2006) 168001] and a phenomenon called "crowd turbulence" can occur at high pedestrian densities [D. Helbing et al., Phys. Rev. E75 (2007) 046109]. Although the behavior of pedestrian crowds under extreme conditions is decisive for the safety of crowds during the access to or egress from mass events as well as for situations of emergency evacuation, there is still a lack of empirical studies of extreme crowding. Therefore, this paper discusses how one may study high-density conditions based on suitable video data. This is illustrated at the example of pilgrim flows entering the previous Jamarat Bridge in Mina, 5 kilometers from the Holy Mosque in Makkah, Saudi-Arabia. Our results reveal previously unexpected pattern formation phenomena and show that the average individual speed does not go to zero even at local densities of 10 persons per square meter. Since the maximum density and flow are different from measurements in other countries, this has implications for the capacity assessment and dimensioning of facilities for mass events. When conditions become congested, the flow drops significantly, which can cause stop-and-go waves and a further increase of the density until critical crowd conditions are reached. Then, "crowd turbulence" sets in, which may trigger crowd disasters. For this reason, it is important to operate pedestrian facilities sufficiently below their maximum capacity and to take measures to improve crowd safety, some of which are discussed in the end.

The relation between speed and density is connected with every self-organization phenomenon of pedestrian dynamics and offers the opportunity to analyze them quantitatively. But even for the simplest systems, like pedestrian streams in corridors, this fundamental relation is not completely understood. A comparison of data from literature shows that specifications in text books as well as measurements under various experimental conditions differ significantly. In this contribution it is studied whether cultural influences and length of the corridor can be the causes for these deviations. To reduce as much as possible unintentional effects, a system is chosen with reduced degrees of freedom and thus the most simple system, namely the movement of pedestrians along a line under closed boundary conditions. It is found that the speed of Indian test persons is less dependent on density than the speed of German test persons. Surprisingly the more unordered behavior of the Indians is more effective than the ordered behavior of the Germans. This may be due to differences in their self-organization behavior. Without any statistical measure one cannot conclude about whether there are differences or not. By hypothesis test it is found quantitatively that these differences exist, suggesting cultural differences in the fundamental diagram of pedestrians.