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Lane formation in bidirectional pedestrian streams is based on a stimulus-response mechanism and strategies of navigation in a fast-changing environment. Although microscopic models that only guarantee volume exclusion can qualitatively reproduce this phenomenon, they are not sufficient for a quantitative description. To quantitatively describe this phenomenon, a minimal anticipatory collision-free velocity model is introduced. Compared to the original velocity model, the new model reduces the occurrence of gridlocks and reproduces the movement of pedestrians more realistically. For a quantitative description of the phenomenon, the definition of an order parameter is used to describe the formation of lanes at transient states and to show that the proposed model compares relatively well with experimental data. Furthermore, the model is validated by the experimental fundamental diagrams of bidirectional flows.
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The mechanism of negative group delay (NGD) is used to understand the anticipatory capability of a retina. Experiments with retinas from bull frogs are performed to compare with the predictions of the NGD model. In particulars, whole field stochastic stimulation with various time correlations are used to probe anticipatory responses from the retina. We find that the NGD model can reproduce essential features of experimental observations characterized by the cross correlations between the stimulation and the retinal responses. The prediction horizon of a retina is found to depend on the correlation time of the stimulation as predicted by the NGD model. Experiments with dark and bright Gaussian light pulses further support the NGD mechanism; but only for the dark pulses indicating that the NGD effect of a retina might originate from its OFF response. Our finding suggests that sensory systems capable of using negative feedback for adaptation can give rise to anticipation as a consequence of the delay in the system.
Despite the vast amount of studies on pedestrian flow, the data concerning high densities are still very inadequate. We organize one large-scale pedestrian flow experiment on a ring corridor. With 278 participants, the density as high as 9 m^(-2) is reached. In the uni-directional flow, four different states are observed, including the free flow, congested state, over-congested state and hyper-congested state. The features of the hyper-congested state are similar to the crowd turbulence reported in the empirical data of Helbing et al., and the transition between the stopped state and the moving state can be found. The flow rates in the over-congested state are nearly constant, due to the downstream propagation of pedestrian clusters. In the bi-directional flow, three different types of lane formations are observed in the experiment: (1) three lanes are directly formed ; (2) two lanes are directly formed; (3) firstly three lanes are formed, and then they transit into two lanes. After the lane formation, some interesting phenomena have been observed, including the inhomogeneous distribution of pedestrians across the lanes, and the formation and dissipation of localized crowd. Our study is expected to help for better understanding and modeling the dynamics of high density pedestrian flow.
We present a new microscopic ODE-based model for pedestrian dynamics: the Gradient Navigation Model. The model uses a superposition of gradients of distance functions to directly change the direction of the velocity vector. The velocity is then integrated to obtain the location. The approach differs fundamentally from force based models needing only three equations to derive the ODE system, as opposed to four in, e.g., the Social Force Model. Also, as a result, pedestrians are no longer subject to inertia. Several other advantages ensue: Model induced oscillations are avoided completely since no actual forces are present. The derivatives in the equations of motion are smooth and therefore allow the use of fast and accurate high order numerical integrators. At the same time, existence and uniqueness of the solution to the ODE system follow almost directly from the smoothness properties. In addition, we introduce a method to calibrate parameters by theoretical arguments based on empirically validated assumptions rather than by numerical tests. These parameters, combined with the accurate integration, yield simulation results with no collisions of pedestrians. Several empirically observed system phenomena emerge without the need to recalibrate the parameter set for each scenario: obstacle avoidance, lane formation, stop-and-go waves and congestion at bottlenecks. The density evolution in the latter is shown to be quantitatively close to controlled experiments. Likewise, we observe a dependence of the crowd velocity on the local density that compares well with benchmark fundamental diagrams.
Platooning on highways with connected and automated vehicles (CAVs) has attracted considerable attention, while how to mange and coordinate platoons in urban networks remains largely an open question. This scientific gap mainly results from the maneuver complexity on urban roads, making it difficult to model the platoon formation process. Inspired by flocking behaviors in nature, this paper proposed a two-dimensional model to describe CAV group dynamics. The model is formulated based on potential fields in planar coordinates, which is composed of the inter-vehicle potential field and the cross-section potential field. The inter-vehicle potential field enables CAVs to attract each other when vehicle gaps are larger than the equilibrium distance, and repel each other otherwise. It also generates incentives for lane change maneuvers to join a platoon or to comply with the traffic management layer. The cross-section potential field is able to mimic lane keeping behavior and it also creates resistance to avoid unnecessary lane changes at very low incentives. These modeling principles can also be applied to human-driven vehicles in the mixed traffic environment. Behavioral plausibility of the model in terms of car-following rationality and car-following safety is demonstrated analytically and further verified with simulation in typical driving scenarios. The model is computationally efficient and can provide insights into platoon operations in urban networks.
In this paper, a simple dynamical model in which fractal networks are formed by self-organized critical (SOC) dynamics is proposed; the proposed model consists of growth and collapse processes. It has been shown that SOC dynamics are realized by the combined processes in the model. Thus, the distributions of the cluster size and collapse size follow a power-law function in the stationary state. Moreover, through SOC dynamics, the networks become fractal in nature. The criticality of SOC dynamics is the same as the universality class of mean-field theory. The model explains the possibility that the fractal nature in complex networks emerges by SOC dynamics in a manner similar to the case with fractal objects embedded in a Euclidean space.
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