A REACTIVE DYNAMIC CONTINUUM USER EQUILIBRIUM MODEL FOR BI-DIRECTIONAL PEDESTRIAN FLOWS

In this paper, a reactive dynamic user equilibrium model is extended to simulate two groups of pedestrians traveling on crossing paths in a continuous walking facility. Each group makes path choices to minimize the travel cost to its destination in a reactive manner based on instantaneous information. The model consists of a conservation law equation coupled with an Eikonal-type equation for each group. The velocity-density relationship of pedestrian movement is obtained via an experimental method. The model is solved using a finite volume method for the conservation law equation and a fast-marching method for the Eikonal-type equation on unstructured grids. The numerical results verify the rationality of the model and the validity of the numerical method. Based on this continuum model, a number of results, e.g., the formation of strips or moving clusters composed of pedestrians walking to the same destination, are also observed.

Analysis of interrelationship between pedestrian flow parameters using artificial neural network

Pedestrian flow parameters are analysed in this study considering linear and non-linear relationships between stream flow parameters using conventional and soft computing approach. Speed-density relationship serves as a fundamental relationship, Single-regime con- cepts and deterministic models like Greenshield and Underwood were applied in the study to describe bidirec- tional flow characteristics on sidewalks and carriageways around transport terminals in India. Artificial Neural Net- work （ANN） approach is also used for traffic flow mod- elling to build a relationship between different pedestrian flow parameters. A non-linear model based on ANN is suggested and compared with the other deterministic models. Out of the aforesaid models, ANN model demonstrated good results based on accuracy measure- ment. Also these ANN models have an advantage in terms of their self-processing and intelligent behaviour. Flow parameters are estimated by ANN model using MFD （Macroscopic Fundamental Diagram）. Estimated mean absolute error （MAE） and root mean square error （RMSE）values for the best fitted ANN model are 3.83 and 4.73 m/ min, respectively, less than those for the other models for sidewalk movement. Further estimated MAE and RMSE values of ANN model for carriageway movement are 4.02 and 4.98 m/min, respectively, which are comparatively less than those of the other models. ANN model gives better performance in fitness of model and future prediction of flow parameters. Also when using linear regression model between observed and estimated values for speed and flow parameters, performance of ANN model gives better fitness to predict data as compared to deterministic model. R value for speed data prediction is 0.756 and for flow data pre- diction is 0.997 using ANN model at sidewalk movement around transport terminal.

The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The stability condition and the Korteweg-de Vries （KdV） equation are derived to describe the density wave of pedestrian congestion by linear stability and nonlinear analysis. Through theoretical analysis, the soliton solution is obtained.

Numerical simulation of pedestrian flow past a circular obstruction

In this paper, a revisiting Hughes’ dynamic continuum model is used to investigate and predict the essential macroscopic characteristics of pedestrian flow, such as flow, density and average speed, in a two dimensional continuous walking facility scattered with a circular obstruction. It is assumed that pedestrians prefer to walk a path with the lowest instantaneous travel cost from origin to destination, under the consideration of the current traffic conditions and the tendency to avoid a high-density region and an obstruction. An algorithm for the pedestrian flow model is based on a cellcentered finite volume method for a scalar conservation law equation, a fast sweeping method for an Eikonal-type equation and a second-order TVD Runge-Kutta method for the time integration on unstructured meshes. Numerical results demonstrate the effectiveness of the algorithm. It is verified that density distribution of pedestrian flow is influenced by the position of the obstruction and the path-choice behavior of pedestrians.

Analysis of dynamic features in intersecting pedestrian flows

This paper focuses on the simulation analysis of stripe formation and dynamic features of intersecting pedestrian flows.The intersecting flows consist of two streams of pedestrians and each pedestrian stream has a desired walking direction.The model adopted in the simulations is the social force model, which can reproduce the self-organization phenomena successfully. Three scenarios of different cross angles are established. The simulations confirm the empirical observations that there is a stripe formation when two streams of pedestrians intersect and the direction of the stripes is perpendicular to the sum of the directional vectors of the two streams. It can be concluded from the numerical simulation results that smaller cross angle results in higher mean speed and lower level of speed fluctuation. Moreover, the detailed pictures of pedestrians＇ moving behavior at intersections are given as well.

Model and application of bidirectional pedestrian flows at signalized crosswalks

This research of bidirectional pedestrian flows at signalized crosswalks is divided into two parts： model and applica- tion. In the model part, a mixed survey including the questionnaire investigation and tracking investigation is conducted to gain the basic data about walking tendentiousness of a pedestrian crossing. Then, the forward, right-hand, outstripping, and influential coefficients are outlined to quantize walking tendentiousness of pedestrian crossing and estimate transition probabilities of pedestrians. At last, an improved cellular automation model is proposed to describe walking tendentious- ness and crossing behaviors of pedestrians. In the application part, channelization research of bidirectional pedestrian flows is presented for real signalized crosswalk. In this process, the effects of right-side-walking and conformity behaviors on the efficiency of pedestrian crossing are thoroughly analyzed based on simulations and experiments to obtain a final channelization method to raise the efficiency of a pedestrian crossing at the crosswalk.

Influence of bottleneck on single-file pedestrian flow:Findings from two experiments

In order to investigate the influence of bottleneck on single-file pedestrian flow,we conduct two different bottleneck experiments.The first one is on ring road,while the second one is on straight route.For the first one,the global density is always set to be 1.5 ped/m.The corresponding critical flow rate for the bottleneck activation is about 0.57 ped/s.The data of the detectors set at different locations,including the velocities and time-headways,show that the amplitude of the oscillation of the stop-and-go waves gradually increases during the upstream propagation.Besides,when the measured flow rates are the same,the different situations in the single-file experiments with and without bottleneck are compared and discussed.For the second one,lower flow rates are used and the bottleneck is always activated.In all the runs,the system can reach one stable state,and the time needed is nearly the same.Inside the stable area,the statistics of pedestrians'velocities keeps nearly constant in both time and space.Outside this area,when the waiting time is not long(X=10 s),the phenomenon observed is similar to that found on ring road,e.g.,the statistics of pedestrians'velocities also gradually increases during the upstream propagation.This phenomenon is similar to that found in vehicular traffic flow,which shows the universality of different traffic flows.But when the waiting time becomes longer(X=20 s),this situation will be broken since the actions of many pedestrians become much slower.All these results can facilitate understanding more about the influence of bottleneck on single-file pedestrian flow.

THE ONE-DIMENSIONAL HUGHES MODEL FOR PEDESTRIAN FLOW:RIEMANN-TYPE SOLUTIONS

This paper deals with a coupled system consisting of a scalar conservation law and an eikonal equation, called the Hughes model. Introduced in [24], this model attempts to describe the motion of pedestrians in a densely crowded region, in which they are seen as a ＇thinking＇ （continuum） fluid. The main mathematical difficulty is the discontinuous gradient of the solution to the eikonal equation appearing in the flux of the conservation law. On a one dimensional interval with zero Dirichlet conditions （the two edges of the interval are interpreted as ＇targets＇）, the model can be decoupled in a way to consider two classical conservation laws on two sub-domains separated by a turning point at which the pedestrians change their direction. We shall consider solutions with a possible jump discontinuity around the turning point. For simplicity, we shall assume they are locally constant on both sides of the discontinuity. We provide a detailed description of the local- in-time behavior of the solution in terms of a ＇global＇ qualitative property of the pedestrian density （that we call ＇relative evacuation rate＇）, which can be interpreted as the attitude of the pedestrians to direct towards the left or the right target. We complement our result with explicitly computable examples.

Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow

A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau （TDGL） equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential.

Simulation of High Density Pedestrian Flow: A Microscopic Model

In recent years, modelling crowd and evacuation dynamics has become very important, with increasing huge numbers of people gathering around the world for many reasons and events. The fact that our global population grows dramatically every year and the current public transport systems are able to transport large amounts of people heightens the risk of crowd panic or crush. Pedestrian models are based on macroscopic or microscopic behaviour. In this paper, we are interested in developing models that can be used for evacuation control strategies. This model will be based on microscopic pedestrian simulation models, and its evolution and design requires a lot of information and data. The people stream will be simulated, based on mathematical models derived from empirical data about pedestrian flows. This model is developed from image data bases, so called empirical data, taken from a video camera or data obtained using human detectors. We consider the individuals as autonomous particles interacting through social and physical forces, which is an approach that has been used to simulate crowd behaviour. The target of this work is to describe a comprehensive approach to model a huge number of pedestrians and to simulate high density crowd behaviour in overcrowding places, e.g. sport, concert and pilgrimage places, and to assist engineering in the resolution of complicated problems through integrating a number of models from different research domains.

An extended social force model on unidirectional flow considering psychological and behavioral impacts of hazard source

An accurate assessment of the evacuation efficiency in case of disasters is of vital importance to the safety design of buildings and street blocks.Hazard sources not only physically but psychologically affect the pedestrians,which may further alter their behavioral patterns.This effect is especially significant in narrow spaces,such as corridors and alleys.This study aims to integrate a non-spreading hazard source into the social force model following the results from a previous experiment and simulation,and to simulate unidirectional pedestrian flows over various crowd densities and clarity–intensity properties of the hazard source.The integration include a virtual repulsion force from the hazard source and a decay on the social force term.The simulations reveal(i)that the hazard source creates virtual bottlenecks that suppress the flow,(ii)that the inter-pedestrian push forms a stabilisation phase on the flow-density curve within medium-to-high densities,and(iii)that the pedestrians are prone to a less orderly and stable pattern of movement in low clarity–intensity scenarios,possibly with lateral collisions passing the hazard source.

Extended social force model with a dynamic navigation field for bidirectional pedestrian flow

An extended social force model with a dynamic navigation field is proposed to study bidirectional pedestrian movement. The dynamic navigation field is introduced to describe the desired direction of pedestrian motion resulting from the decision-making processes of pedestrians. The macroscopic fundamental diagrams obtained using the extended model are validated against camera-based observations. Numerical results show that this extended model can reproduce collective phenomena in pedestrian traffic, such as dynamic multilane flow and stable separate-lane flow. Pedestrians＇ path choice behavior significantly affects the probability of congestion and the number of self-organized lanes.

Fundamental diagrams for pedestrian flows in a channel via an extended social force model

In this paper, an extended social force model was applied to investigate fundamental diagrams of pedestrian flows. In the presented model, both the static floor field and the view field were taken into account. Then each pedestrian can determine his/her desired walking directions according to both global and local information. The fundamental diagrams were obtained numerically under periodic boundary condition. It was found that the fundamental diagrams show good agreement with the measured data in the case of unidirectional flow, especially in the medium density range. However, the fundamental diagram for the case of bidirectional flow gave larger values than the measured data. Furthermore, the bidirectional flux is larger than the tmidirectional flux in a certain density range. It is indicated that the bidirectional flow may be more efficient than the unidirectional flow in some cases. The process of lane formation is quite quick in the model. Typical flow patterns in three scenarios were given to show some realistic applications.

Investigation on lane-formation in pedestrian flow with a new cellular automaton model

In this paper, we investigate pedestrian flows by using a newly-proposed cellular automaton （CA） model, which is based on the floor-field model. The interaction of pedestrians includes completion and cooperation, respectively reflected by a modified dynamic field and a position-changing behavior. Then we utilize this model to research lane formation phase in counter flow problem, involving the probability of lane formation phase, the average number of lanes and the microscopic behavior of pedestrians. It is found that the interaction between pedestrians and the different significant influences of average density of pedestrian flow on the features of lane formation phase.

A Bayesian modeling approach to bi-directional pedestrian flows in carnival events

Bi-directional pedestrian flows are common at crosswalks, footpaths, and shopping areas. However, the properties of pedestrian movement may vary in urban areas according to the type of walking facility. In recent years,crowd movements at carnival events have attracted the attention of researchers. In contrast to pedestrian behavior in other walking facilities, pedestrians whose attention is attracted by carnival displays or activities may slow down and even stop walking. The Lunar New Year Market is a traditional carnival event in Hong Kong held annually one week before the Lunar New Year. During the said event,crowd movements can be easily identified, particularly in Victoria Park, where the largest Lunar New Year Market in Hong Kong is hosted. In this study, we conducted a videobased observational survey to collect pedestrian flow and speed data at the Victoria Park Lunar New Year Market on the eve of the Lunar New Year. Using the collected data, an extant mathematical model was calibrated to capture the relationships between the relevant macroscopic quantities,thereby providing insight into pedestrian behavior at the carnival event. Bayesian inference was employed to calibrate the model by using prior data obtained from a previous controlled experiment. Results obtained enhance our understanding of crowd behavior under different conditions at carnival events, thus facilitating the improvement of the safety and efficiency of similar events in the future.

A Lattice Model for Bidirectional Pedestrian Flow on Gradient Road

Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes.This study proposes a new lattice model for bidirectional pedestrian flow on gradient road. The stability condition is obtained by using linear stability theory. The nonlinear analysis method is employed to derive the modified Korteweg-de Vries(mKdV) equation, and the space of pedestrian flow is divided into three regions: the stable region, the metastable region, and the unstable region respectively. Furthermore, the time-dependent Ginzburg–Landan(TDGL) equation is deduced and solved through the reductive perturbation method. Finally, we present detailed results obtained from the model, and it is found that the stability of the model is enhanced in uphill situation while reduced in downhill situation with increasing slope.

Pedestrian wind flow prediction using spatial-frequency generative adversarial network

Pedestrian wind flow is a critical factor in designing livable residential environments under growing complex urban conditions.Predicting pedestrian wind flow during the early design stages is essential but currently suffers from inefficiencies in numerical simulations.Deep learning,particularly generative adversarial networks(GAN),has been increasingly adopted as an alternative method to provide efficient prediction of pedestrian wind flow.However,existing GAN-based wind flow prediction schemes have limitations due to the lack of considering the spatial and frequency characteristics of wind flow images.This study proposes a novel approach termed SFGAN,which embeds spatial and frequency characteristics to enhance pedestrian wind flow prediction.In the spatial domain,Gaussian blur is employed to decompose wind flow into components containing wind speed and distinguished flow edges,which are used as the embedded spatial characteristics.Detailed information of wind flow is obtained through discrete wavelet transformation and used as the embedded frequency characteristics.These spatial and frequency characteristics of wind flow are jointly utilized to enforce consistency between the predicted wind flow and ground truth during the training phase,thereby leading to enhanced predictions.Experimental results demonstrate that SFGAN clearly improves wind flow prediction,reducing Wind_MAE,Wind_RMSE and the Fréchet Inception Distance(FID)score by 5.35%,6.52%and 12.30%,compared to the previous best method,respectively.We also analyze the effectiveness of incorporating the spatial and frequency characteristics of wind flow in predicting pedestrian wind flow.SFGAN reduces errors in predicting wind flow at large error intervals and performs well in wake regions and regions surrounding buildings.The enhanced predictions provide a better understanding of performance variability,bringing insights at the early design stage to improve pedestrian wind comfort.The proposed spatial-frequency loss term is general and can be flexibly integrated with other generative models to enhance performance with only a slight computational cost.

Study on bi-directional pedestrian movement using ant algorithms

A cellular automata model is proposed to simulate bi-directional pedestrian flow. Pedestrian movement is investigated by using ant algorithms. Ants communicate with each other by dropping a chemical, called a pheromone, on the substrate while crawling forward. Similarly, it is considered that oppositely moving pedestrians drop ＇visual pheromones＇ on their way and the visual pheromones might cause attractive or repulsive interactions. This pheromenon is introduced into mod- elling the pedestrians＇ walking preference. In this way, the decision-making process of pedestrians will be based on ＇the instinct of following＇. At some densities, the relationships of velocity-density and flux-density are analyzed for different evaporation rates of visual pheromones. Lane formation and phase transition are observed for certain evaporation rates of visual pheromones.

A modified heuristics-based model for simulating realistic pedestrian movement behavior

Pedestrian movement simulation models are used in various areas,such as building evacuation,transportation engi-neering,and safety management of large events.It also provides effective means to uncover underlying mechanisms of collective behaviors.In this work,a modified heuristics-based model is presented.In this model,the potential collisions in the moving process are explicitly considered.Meanwhile,a series of simulations is conducted in two typical scenarios to demonstrate the influence of critical parameters on model performance.It is found that when facing a wide obstacle in a corridor,the larger the visual radius,the earlier the pedestrian starts to make a detour.In addition,when a pedestrian observes a large crowd walking toward him,he chooses to make a detour and moves in the flow in a uniform direction.Furthermore,the model can reproduce the lane formation pedestrian flow phenomena in relatively high-density situations.With the increase of pedestrian visual radius and the weight of potential collision resistance,more stable pedestrian lanes and fewer moving-through-the-counterflow pedestrians can be observed.In terms of model validation,the density-speed relationship of simulation results accords well with that of the published empirical data.Our results demonstrate that the modified heuristics-based model can overcome the deficiency of the original model,and reproduce more realistic pedestrian movement behavior.