Microscopic pedestrian simulation model combined with a tactical model for route choice behaviour

This study proposes a microscopic pedestrian simulation model for evaluating pedestrian flow. Recently, several pedestrian models have been proposed to evaluate pedestrian flow in crowded situations for the purpose of designing facilities. However, current pedestrian simulation models do not explain the negotiation process of collision avoidance between pedestrians, which can be important for representing pedestrian behaviour in congested situations. This study builds a microscopic model of pedestrian behaviour using a two-player game and assuming that pedestrians anticipate movements of other pedestrians so as to avoid colliding with them. A macroscopic tactical model is also proposed to determine a macroscopic path to a given destination. The results of the simulation model are compared with experimental data and observed data in a railway station. Several characteristics of pedestrian flows such as traffic volume and travel time in multidirectional flows, temporal–spatial collision avoidance behaviour and density distribution in the railway station are reproduced in the simulation.     

A new method for evaluation of level of service in pedestrian facilities

Safe and comfortable walking is essential for pedestrian movement in modern urban transportation systems. Since pedestrian traffic cannot be restricted in some specified streets, some measures for pedestrians have to be taken everywhere in urban areas. This research describes a way to evaluate ordinary sidewalks, and two different methods are proposed. One is an evaluation based on pedestrian behaviour and the other is an evaluation based on pedestrian opinion. Using the indices of pedestrian density and sidewalk width, we can estimate the level of service of sidewalk usage. But generally speaking, since it is not often that a sidewalk is insufficient to deal with pedestrian flow, another approach is necessary for its evaluation, that is, pedestrian awareness of sidewalks must be taken into account. The former method is recommended for all sidewalks, especially with comparatively heavy pedestrian traffic, and the latter method is recommended for ones with light pedestrian traffic.     

Specification and calibration of a microscopic model for pedestrian dynamic simulation at signalized intersections: A hybrid approach

Macroscopic pedestrian models for bidirectional flow analysis encounter limitations in describing microscopic dynamics at crosswalks. Pedestrian behavior at crosswalks is typically characterized by the evasive effect with conflicting pedestrians and vehicles and the following effect with leading pedestrians. This study proposes a hybrid approach (i.e., route search and social force-based approach) for modeling of pedestrian movement at signalized crosswalks. The key influential factors, i.e., leading pedestrians, conflict with opposite pedestrians, collision avoidance with vehicles, and compromise with traffic lights, are considered. Aerial video data collected at one intersection in Beijing, China were recorded and extracted. A new calibration approach based on a genetic algorithm is proposed that enables optimization of the relative error of pedestrian trajectory in two dimensions, i.e., moving distance and angle. Model validation is conducted by comparison with the observed trajectories in five typical cases of pedestrian crossing with or without conflict between pedestrians and vehicles. The characteristics of pedestrian flow, speed, acceleration, pedestrian-vehicle conflict, and the lane formation phenomenon were compared with those from two competitive models, thus demonstrating the advantage of the proposed model.     

Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications

This contribution puts forward a novel multi-class continuum model that captures some of the key dynamic features of pedestrian flows. It considers route choice behaviour on both the strategic (pre-trip) and tactical (en-route) level. To achieve this, we put forward a class-specific equilibrium direction relation of the pedestrians, which is governed by two parts: one part describing the global route choice, which is pre-determined based on the expectations of the pedestrians, and one part describing the local route choice, which is a density-gradient dependent term that reflects local adaptations based on prevailing flow conditions.Including the local route choice term in the multi-class model causes first of all dispersion of the flow: pedestrians will move away from high density areas in order to reduce their overall walking costs. Second of all, for the crossing flow and bi-directional flow cases, local route choice causes well known self-organised patterns to emerge (i.e. diagonal stripes and bi-directional lanes). We study under which demand conditions self-organisation occurs and fails, as well as what the impact is of the choices of the different model parameters. In particular, the differences in the weights reflecting the impact of the own and the other classes appear to have a very strong impact on the self-organisation process.     

Microscopic modeling of large‐scale pedestrian–vehicle conflicts in the city of Madinah,Saudi Arabia

This paper presents a micro‐simulation modeling framework for evaluating pedestrian–vehicle conflicts in crowded crossing areas. The framework adopts a simulation approach that models vehicles and pedestrians at the microscopic level while satisfying two sets of constraints: (1) flow constraints and (2) non‐collision constraints. Pedestrians move across two‐directional cells as opposed to one‐dimensional lanes as in the case of vehicles; therefore, extra caution is considered when modeling the shared space between vehicles and pedestrians. The framework is used to assess large‐scale pedestrian–vehicle conflicts in a highly congested ring road in the City of Madinah that carries 20 000 vehicles/hour and crossed by 140 000 pedestrians/hour after a major congregational prayer. The quantitative and visual results of the simulation exhibits serious conflicts between pedestrians and vehicles, resulting in considerable delays for pedestrians crossing the road (9 minutes average delay) and slow traffic conditions (average speed <10 km/hour). The model is then used to evaluate the following three mitigating strategies: (1) pedestrian‐only phase; (2) grade separation; and (3) pedestrian mall. A matrix of operational measures of effectiveness for network‐wide performance (e.g., average travel time, average speed) and for pedestrian‐specific performance (e.g., mean speed, mean density, mean delay, mean moving time) is used to assess the effectiveness of the proposed strategies. Copyright © 2012 John Wiley & Sons, Ltd.     

Collection, spillback, and dissipation in pedestrian evacuation: A network-based method

We present a method of predicting pedestrian route choice behavior and physical congestion during the evacuation of indoor areas with internal obstacles. Under the proposed method, a network is first constructed by discretizing the space into regular hexagonal cells and giving these cells potentials before a modified cell transmission model is employed to predict the evolution of pedestrian flow in the network over time and space. Several properties of this cell transmission model are explored. The method can be used to predict the evolution of pedestrian flow over time and space in indoor areas with internal obstacles and to investigate the collection, spillback, and dissipation behavior of pedestrians passing through a bottleneck. The cell transmission model is further extended to imitate the movements of multiple flows of pedestrians with different destinations. An algorithm based on generalized cell potential is also developed to assign the pedestrian flow.     

Calibrating a social-force-based pedestrian walking model based on maximum likelihood estimation

Although various theories have been adopted to develop reliable pedestrian walking models, a limited effort has been made to calibrate them rigorously based on individual trajectories. Most researchers have validated their models by comparing observed and estimated traffic flow parameters such as speed, density, and flow rate, or replaced the validation by visual confirmation of some well-known phenomena such as channelization and platooning. The present study adopted maximum likelihood estimation to calibrate a social-force model based on the observed walking trajectories of pedestrians. The model was assumed to be made up of five components (i.e., inertia, desired direction, leader–follower relationship, collision avoidance, and random error), and their corresponding coefficients represented relative sensitivity. The model also included coefficients for individual-specific characteristics and for a distance-decay relationship between a pedestrian and his/her leaders or colliders. The calibration results varied with the two density levels adopted in the present study. In the case of high density, significant coefficient estimates were found with respect to both the leader–follower relationship and collision avoidance. Collision avoidance did not affect the pedestrian’s walking behavior for the low-density case due to channelization. The distance limit was confirmed, within which a pedestrian is affected by neighbors. At the low-density level, by comparison with women, men were found to more actively follow leaders, and pedestrians walking in a party were found to be less sensitive to the motion of leaders at the high-density level.     

Data-driven spatio-temporal discretization for pedestrian flow characterization

We propose a novel approach to pedestrian flow characterization. The definitions of density, flow and velocity existing in the literature are extended through a data-driven spatio-temporal discretization framework. The framework is based on three-dimensional Voronoi diagrams. Synthetic data is used to empirically investigate the performance of the approach and to illustrate its advantages. Our approach outperforms the considered approaches from the literature in terms of the robustness with respect to the simulation noise and with respect to the sampling frequency. Additionally, the proposed approach is by design (i) independent from an arbitrarily chosen discretization; (ii) appropriate for the multidirectional composition of pedestrian traffic; (iii) able to reflect the heterogeneity of the pedestrian population; and (iv) applicable to pedestrian trajectories described either analytically or as a sample of points.     

A model of pedestrians’ intended waiting times for street crossings at signalized intersections

For the purposes of both traffic-light control and the design of roadway layouts, it is important to understand pedestrian street-crossing behavior because it is not only crucial for improving pedestrian safety but also helps to optimize vehicle flow. This paper explores the mechanism of pedestrian street crossings during the red-man phase of traffic light signals and proposes a model for pedestrians’ waiting times at signalized intersections. We start from a simplified scenario for a particular pedestrian under specific traffic conditions. Then we take into account the interaction between vehicles and pedestrians via statistical unconditioning. We show that this in general leads to a U-shaped distribution of the pedestrians’ intended waiting time. This U-shaped distribution characterizes the nature of pedestrian street-crossing behavior, showing that in general there are a large proportion of pedestrians who cross the street immediately after arriving at the crossing point, and a large proportion of pedestrians who are willing to wait for the entire red-man phase. The U-shaped distribution is shown to reduce to a J-shaped or L-shaped distribution for certain traffic scenarios. The proposed statistical model was applied to analyze real field data.     

A macroscopic loading model for time-varying pedestrian flows in public walking areas

A macroscopic loading model applicable to time-dependent and congested pedestrian flows in public walking areas is proposed. Building on the continuum theory of pedestrian flows and the cell transmission model for car traffic, an isotropic framework is developed that can describe the simultaneous and potentially conflicting propagation of multiple pedestrian groups. The model is formulated at the aggregate level and thus computationally cheap, which is advantageous for studying large-scale problems. A detailed analysis of several basic flow patterns including counter- and cross flows, as well as two generic scenarios involving a corner- and a bottleneck flow is carried out. Various behavioral patterns ranging from disciplined queueing to impatient jostling can be realistically reproduced. Following a systematic model calibration, two case studies involving a Swiss railway station and a Dutch bottleneck flow experiment are presented. A comparison with the social force model and pedestrian tracking data shows a good performance of the proposed model with respect to predictions of travel time and density.     

Modelling shared space users via rule-based social force model

The promotion of space sharing in order to raise the quality of community living and safety of street surroundings is increasingly accepted feature of modern urban design. In this context, the development of a shared space simulation tool is essential in helping determine whether particular shared space schemes are suitable alternatives to traditional street layouts. A simulation tool that enables urban designers to visualise pedestrians and cars trajectories, extract flow and density relation in a new shared space design, achieve solutions for optimal design features before implementation, and help getting the design closer to the system optimal. This paper presents a three-layered microscopic mathematical model which is capable of representing the behaviour of pedestrians and vehicles in shared space layouts and it is implemented in a traffic simulation tool. The top layer calculates route maps based on static obstacles in the environment. It plans the shortest path towards agents’ respective destinations by generating one or more intermediate targets. In the second layer, the Social Force Model (SFM) is modified and extended for mixed traffic to produce feasible trajectories. Since car movements are not as flexible as pedestrian movements, velocity angle constraints are included for cars. The conflicts described in the third layer are resolved by rule-based constraints for shared space users. An optimisation algorithm is applied to determine the interaction parameters of the force-based model for shared space users using empirical data. This new three-layer microscopic model can be used to simulate shared space environments and assess, for example, new street designs.     

Traffic flow on pedestrianized streets

Giving pedestrians priority to cross a street enhances pedestrian life, especially if crosswalks are closely spaced. Explored here is the effect of this management decision on car traffic. Since queuing theory suggests that for a given pedestrian flux the closer the crosswalk spacing the lower the effect of pedestrians on cars, scenarios where pedestrians can cross anywhere should be best for both cars and pedestrians. This is the kind of pedestrianization studied.Analytic formulas are proposed for a pedestrianized street’s capacity, free-flow speed and macroscopic fundamental diagram. Of these, only the free-flow speed formula is exact. The analytic form of the capacity formula is inspired by analytic upper and lower bounds derived with variational theory for a version of the problem where cars are treated as a fluid. The formula is then calibrated against microscopic simulations with discrete cars. The MFD for the fluid version of the problem is shown to be concave and have a certain symmetry. These two geometrical properties, together with the formulae for capacity and free-flow speed, yield a simple approximation for the MFD.Both the capacity and MFD formulae match simulations with discrete cars well for all values of the pedestrian flux – errors for the capacity are well under 0.2% of the capacity before pedestrianization. Qualitatively, the formulas predict that the street’s capacity is inversely proportional to the square root of the pedestrian flux for low pedestrian fluxes, and that pedestrians increase the cars’ free-flow pace by an amount that is proportional to the pedestrian flux.     

Potential-based dynamic pedestrian flow assignment

This study proposes a potential-based dynamic pedestrian flow assignment model to optimize the evacuation time needed for all pedestrians to leave an indoor or outdoor area with internal obstacles and multiple exits, e.g., railway station, air terminal, plaza, and park. In the model, the dynamic loading of pedestrian flows on a two-dimensional space is formulated by a cell transmission model, the movement of crowds is driven by space potential, and the optimization of evacuation time is solved by a proportional swapping process. In this way, the proposed model can be applied to not only efficiently optimize the evacuation process of a crowd with large scale but also recognize local congestion dynamics during crowd evacuation. Finally, a set of numerical examples are presented to show the proposed model’s effectiveness for optimizing crowd evacuation process and its application to design a class of variable guide sign systems.     

Waiting zones for realistic modelling of pedestrian dynamics: A case study using two major German railway stations as examples

The value of a pedestrian stream simulation depends on its ability to reproduce natural behaviour of pedestrians in different situations. Most models assume that pedestrians are single-minded and constantly move towards their destinations. However, our observations at two major German railway stations made during field experiments and our analysis of video recordings at one of these stations revealed that in virtually every setting a significant proportion of pedestrians do not walk continuously. Instead, they occasionally change their route in order to visit certain locations and stand there for a period of time. By waiting, they often block walking pedestrians and thereby influence the overall dynamics.In this paper, we evaluate the impact of waiting pedestrians and propose a model for waiting pedestrians based on cellular automata. The model is able to reproduce the observed pedestrian behaviour. We illustrate the model with simulations of several real life scenarios for a major German railway station and show that during rush hour standing pedestrians may prolong walking time by up to nearly 20%. We also demonstrate how the developed model can be used for the analysis of infrastructures, and prediction of problematic areas in public spaces.     

基于乘客寻路行为的城市轨道交通车站导向标识序化设置研究

为实现轨道交通车站内客流快速疏散,避免因乘客滞留造成站内乘客出行效率低以及大客流压力导致的安全隐患等问题,本文对目前国内导向标识的设置原则及功能进行描述,依托大数据等信息化技术分析行人寻路行为机理及出行特征与导向标识序化设置间的关系,研究导向标识的序化设置,依据行人在不同交通设施的步行速度及信息处理时间,并提出在站内停顿点数量较多的通道、楼梯口及闸机处设置导向标识的位置,进而对导向标识的设置进行人性化和合理化的优化设置,对轨道车站内停顿点位置进行导向标识的合理布设,以快速引导行人进行出行决策,减少停顿点数量。     

Optimization of mid-block pedestrian crossing network with discrete demands

In many cases, pedestrian crossing demands are distributed discretely along an arterial segment. Demand origins, destinations and crosswalks comprise a pedestrian crossing network. An integrated model for optimizing the quantity, locations and signal settings of mid-block crosswalks simultaneously is proposed to best trade-off the operational performances between pedestrians and vehicles. Pedestrian behavior of choosing crosswalks is captured under a discrete demand distribution. Detour distance and delay at signalized crosswalks are formulated as a measure of pedestrian crossing cost. Maximum bandwidths are modeled in analytical expressions as a measure of vehicular cost. To solve the proposed model, the Non-dominated Sorting Genetic Algorithm II (NSGA II) based algorithm is designed and employed to obtain the Pareto frontier efficiently. From the numerical study, it is found that there exists an optimal number of mid-block crosswalks. Excess available crosswalks may make no contributions to improvement in pedestrian cost when the constraint of the minimum interval between crosswalks and vehicular cost are taken into account. Two-stage crosswalks are more favorable than one-stage ones for the benefits of both pedestrian and vehicles. The study results show promising properties of the proposed method to assist transportation engineers in properly designing mid-block crosswalks along a road segment.     

Modeling pedestrians’ road crossing behavior in traffic system micro-simulation in China

In many Chinese cities, pedestrian’s road crossing behavior is different from that of pedestrians in developed countries. This paper presents a pedestrian model for traffic system micro-simulation in China. Considering the high rate of signal non-compliance, we classify pedestrians into two types: law-obeying ones and opportunistic ones. Opportunistic ones decide whether to violate traffic signal during red man, depending on the states of some external factors (like policeman, vehicle flow and other pedestrians’ behaviors). Questionnaires were used to determine the proportions of these two types of pedestrians under different circumstances. In addition, a time gap distribution extracted from videotape were used to determine the criterion for pedestrians to decide whether to walk or wait when they conflict with vehicle flows. However, simulation results deviate from the data extracted from videotape in some degree. By adjusting the parameters on the basis of analyzing the occurrence of the deviations, the simulation results agree with the field results better. This model has represented the high rate of pedestrians’ red light running and the mixed characteristics of traffic flows in Chinese cities, and it may be applicable in the micro-simulation of traffic system in other developing cities.     

Pedestrian delay estimation at signalized intersections in developing cities

This paper proposes a pedestrian delay model suitable for signalized intersections in developing cities, on the basis of a field study conducted in Xi’an, China. The field study consisted of two parts: Part I involved only one crosswalk, and the signal cycle was divided into 13 subphases; Part II involved 13 crosswalks, but the signal cycles were only divided into green phases and non-green phases. It was found that pedestrian arrival rates were not uniform throughout cycles; pedestrians arriving during green phases might also receive delays; pedestrian signal non-compliance was so severe that delays were greatly reduced, but non-complying pedestrians might still receive delays; and for pedestrians walking different directions, though the relationships between average delay and arrival subphase were different, the overall average delays were almost the same. On the basis of the field study results, some assumptions are made about the relationship between average pedestrian delay and arrival subphase, and a new model is developed to estimate pedestrian delays at signalized intersections. The model is validated using the field data, and the validation results indicate that in Xi’an the new model provides much more accurate estimation than the existing models.     

Assessing the usage and level-of-service of pedestrian facilities in train stations: A Swiss case study

A framework for assessing the usage and level-of-service of rail access facilities is presented. It consists of two parts. A dynamic demand estimator allows to obtain time-dependent pedestrian origin–destination demand within walking facilities. Using that demand, a traffic assignment model describes the propagation of pedestrians through the station, providing an estimate of prevalent traffic conditions in terms of flow, walking times, speed and density. The corresponding level-of-service of the facilities can be directly obtained. The framework is discussed at the example of Lausanne railway station. For this train station, a rich set of data sources including travel surveys, pedestrian counts and trajectories has been collected in collaboration with the Swiss Federal Railways. Results show a good performance of the framework. To underline its practical applicability, a six-step planning guideline is presented that can be used to design and optimize rail access facilities for new or existing train stations. In the long term, the framework may also be used for crowd management, involving real-time monitoring and control of pedestrian flows.