Human mobility: Models and applications

In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic individual-level experimental verification, and the local mechanisms underlying the formation of collective patterns are not yet known in detail. We have conducted a set of well-controlled experiments with pedestrians performing simple avoidance tasks in order to determine the laws ruling their behaviour during interactions. The analysis of the large trajectory dataset was used to compute a behavioural map that describes the average change of the direction and speed of a pedestrian for various interaction distances and angles. The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions. The predictions of a binary interaction model based on the above findings were then compared with bidirectional flows of people recorded in a crowded street. Simulations generate two asymmetric lanes with opposite directions of motion, in quantitative agreement with our empirical observations. The knowledge of pedestrian behavioural laws is an important step ahead in the understanding of the underlying dynamics of crowd behaviour and allows for reliable predictions of collective pedestrian movements under natural conditions.

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Experimental study of the behavioural mechanisms underlying self-organization in human crowds

Based on suitable video recordings of interactive pedestrian motion and improved tracking software, we apply an evolutionary optimization algorithm to determine optimal parameter specifications for the social force model. The calibrated model is then used for large-scale pedestrian simulations of evacuation scenarios, pilgrimage, and urban environments.

Specification of the social force pedestrian model by evolutionary adjustment to video tracking data

Based on suitable video recordings of interactive pedestrian motion and improved tracking software, we apply an evolutionary optimization algorithm to determine optimal parameter
 specifications for the social force model. The calibrated model is then used for large-scale pedestrian simulations of evacuation scenarios, pilgrimage, and urban environments.

Specification of the social force pedestrian model by evolutionary adjustment to video tracking data; ; Advances in complex systems;

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces The main intention of this work is the quantitative description of pedestrian movement in several geometries Measurements of the fundamental diagram in narrow and wide corridors are performed The results of the proposed model show good agreement with empirical data obtained in controlled experiments

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Generalized centrifugal-force model for pedestrian dynamics.

An extended car following model is proposed by incorporating an intelligent transportation system in traffic. The stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by applying the reductive perturbation method. The traffic jam could be thus described by the kink-antikink soliton solution for the mKdV equation. From the simulation of space-time evolution of the vehicle headway, it is shown that the traffic jam is suppressed efficiently with taking into account the information about the motion of more vehicles in front, and the analytical result is consonant with the simulation one.

Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application.

In this paper, a centrifugal force model is developed for pedestrian dynamics. The effects of both the headway and the relative velocity among pedestrians are taken into account, which can be expressed by a "centrifugal force" term in dynamic equation. The jamming probability due to the arching at exits for crowd flows is provided. A quantitative analysis of the crowd flowing out of a hall shows that the average leaving time T is a function of the exit width W in negative power. The related simulation indicates that the proposed model is able to reproduce the self-organization phenomena of lane formation for sparse flows.

Centrifugal force model for pedestrian dynamics.

Two lattice traffic models are proposed by incorporating a cooperative driving system. The lattice versions of the hydrodynamic model of traffic flow are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained using the linear stability theory. The results show that considering more than one site ahead in vehicle motion leads to the stabilization of the system. The modified Korteweg-de Vries equation (the mKdV equation, for short) near the critical point is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by kink-anti-kink soliton solutions obtained from the mKdV equations.

Stabilization analysis and modified Korteweg-de Vries equation in a cooperative driving system.

The jams in the congested traffic are related with various density waves, which might be governed by the nonlinear wave equations, such as the Korteweg–de-Vries (KdV) equation, the Burgers equation and the modified Korteweg–de-Vries (mKdV) equation. Three different versions of optimal velocity models are examined. The stability conditions of the models are obtained by using the linear stability theory. The KdV equation near the neutral stability line and the mKdV equation around the critical point are derived by applying the reductive perturbation method, respectively. The traffic jams could be thus described by the KdV and kink–antikink soliton solutions for the two kinds of equations. The general solutions are given for, which can lead to specific solutions in previous work. Moreover, they are applied to solve a new model—the full velocity difference model and the corresponding KdV and kink–antikink soliton solutions could be quickly obtained, which demonstrates the general solutions presented herein are useful.

KdV and kink antikink solitons in car-following models

A single-lane cellular automaton model is proposed to simulate mixed traffic with motorcycles. By performing numerical simulations under the periodic boundary condition, some density-flow relations and the “lane-changing” behavior of motorcycles are investigated in detail. It is found that the maximum car flow decreases because of the “lane-changing” behavior of motorcycles. The maximum total flow increases first and then decreases with increasing motorcycle density. Moreover, the transition of the total flow from the free flow to the congested flow is smooth in this model. The “lane-changing” rate of motorcycles will decrease to zero finally with the increase of the car density. But its evolutionary trend is considerably complex. Another interesting fact is that, with the increase of the motorcycle density, the “lane-changing” rate increases first and decreases later. This phenomenon is very similar to the findings in other papers on multi-lane car flows. The“lane-changing” is almost of no use in increasing the flow of motorcycles as the motorcycle density is small. But it distinctly causes the increase in the flow of motorcycles when the motorcycle density is sufficiently large, and in this density regime, the flow of motorcycles gradually decreases to the one given with the Nagel–Schreckenberg model for motorcycles with the increase of the car density. The simulation results indicate that it is necessary to set a barrier or a lane for separating the motorcycle flow from the car flow except in some special density regime.

S. Q. Dai

Papers

Stabilization effect of traffic flow in an extended car-following model based on an intelligent transportation system application.

Centrifugal force model for pedestrian dynamics.

Stabilization analysis and modified Korteweg-de Vries equation in a cooperative driving system.

KdV and kink antikink solitons in car-following models

Cellular automaton model for mixed traffic flow with motorcycles