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.     

Microscopic decision model for pedestrian route choice at signalized crosswalks

In this paper, two‐tier mathematical models were developed to simulate the microscopic pedestrian decision‐making process of route choice at signalized crosswalks. In the first tier, a discrete choice model was proposed to predict the choices of walking direction. In the second tier, an exponential model was calibrated to determine the step size in the chosen direction. First, a utility function was defined in the first‐tier model to describe the change of utility in response to deviation from a pedestrian's target direction and the conflicting effects of neighboring pedestrians. A mixed logit model was adopted to estimate the effects of the explanatory variables on the pedestrians' decisions. Compared with the standard multinomial logit model, it was shown that the mixed logit model could accommodate the heterogeneity. The repeated observations for each pedestrian were grouped as panel data to ensure that the parameters remained constant for individual pedestrians but varied among the pedestrians. The mixed logit model with panel data was found to effectively address inter‐pedestrian heterogeneity and resulted in a better fit than the standard multinomial logit model. Second, an exponential model in the second tier was proposed to further determine the step size of individual pedestrians in the chosen direction; it indicates the change in walking speed in response to the presence of other pedestrians. Finally, validation was conducted on an independent set of observation data in Hong Kong. The pedestrians' routes and destinations were predicted with the two‐tier models. Compared with the tracked trajectories, the average error between the predicted destinations and the observed destinations was within an acceptable margin. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulating pedestrian movements at signalized crosswalks in Hong Kong

This paper presents a new pedestrian simulation (PS) model for signalized crosswalks in Hong Kong. This PS model is capable of estimating the variations of walking speed particularly on the effects of bi-directional pedestrian flows so as to determine the minimum required duration of pedestrian crossing time. Video records taken from the observational surveys at the selected crosswalk in urban area were used to extract the required data for model calibration. It was found that the design walking speed for signalized crosswalks should be varied by the effects of the bi-directional pedestrian flows. It was also interesting to note that the negative impact of the bi-directional flow effects (ranging from uni-directional to bi-directional pedestrian flows) on the chance of pedestrian crossing the crosswalk is increasing from free-flow to at-capacity flow conditions. The new PS model is also validated using an independent data set so as to examine the reliability of the simulation results. The validation results show that the new PS model can provide an accurate evaluation on the changes of walking speed and its standard deviation under different scenarios with particular emphasis on the effects of the bi-directional pedestrian flows. The advancement of this PS model can be applied to assess the effects of each improvement measure and to evaluate the benefits of each scenario in practice.     

Using automated walking gait analysis for the identification of pedestrian attributes

Collecting microscopic pedestrian behavior and characteristics data is important for optimizing the design of pedestrian facilities for safety, efficiency, and comfortability. This paper provides a framework for the automated classification of pedestrian attributes such as age and gender based on information extracted from their walking gait behavior. The framework extends earlier work on the automated analysis of gait parameters to include analysis of the gait acceleration data which can enable the quantification of the variability, rhythmic pattern and stability of pedestrian’s gait. In this framework, computer vision techniques are used for the automatic detection and tracking of pedestrians in an open environment resulting in pedestrian trajectories and the speed and acceleration dynamic profiles. A collection of gait features are then derived from those dynamic profiles and used for the classification of pedestrian attributes. The gait features include conventional gait parameters such as gait length and frequency and dynamic parameters related to gait variations and stability measures. Two different techniques are used for the classification: a supervised k-Nearest Neighbors (k-NN) algorithm and a newly developed semi-supervised spectral clustering. The classification framework is demonstrated with two case studies from Vancouver, British Columbia and Oakland, California. The results show the superiority of features sets including gait variations and stability measures over features relying only on conventional gait parameters. For gender, correct classification rates (CCR) of 80% and 94% were achieved for the Vancouver and Oakland case studies, respectively. The classification accuracy for gender was higher in the Oakland case which only considered pedestrians walking alone. Pedestrian age classification resulted in a CCR of 90% for the Oakland case study.     

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.     

Development of destination choice models for pedestrian travel

Most research on walking behavior has focused on mode choice or walk trip frequency. In contrast, this study is one of the first to analyze and model the destination choice behaviors of pedestrians within an entire region. Using about 4500 walk trips from a 2011 household travel survey in the Portland, Oregon, region, we estimated multinomial logit pedestrian destination choice models for six trip purposes. Independent variables included terms for impedance (walk trip distance), size (employment by type, households), supportive pedestrian environments (parks, a pedestrian index of the environment variable called PIE), barriers to walking (terrain, industrial-type employment), and traveler characteristics. Unique to this study was the use of small-scale destination zone alternatives. Distance was a significant deterrent to pedestrian destination choice, and people in carless or childless households were less sensitive to distance for some purposes. Employment (especially retail) was a strong attractor: doubling the number of jobs nearly doubled the odds of choosing a destination for home-based shopping walk trips. More attractive pedestrian environments were also positively associated with pedestrian destination choice after controlling for other factors. These results shed light on determinants of pedestrian destination choice behaviors, and sensitivities in the models highlight potential policy-levers to increase walking activity. In addition, the destination choice models can be applied in practice within existing regional travel demand models or as pedestrian planning tools to evaluate land use and transportation policy and investment scenarios.     

The use of gait parameters to evaluate pedestrian behavior at scramble phase signalized intersections

Pedestrian scramble phasing is usually implemented to reduce pedestrian‐vehicle conflicts and therefore increase the safety of the intersection. However, to adequately determine the benefits of scramble phasing, it is necessary to understand how pedestrians react to such an unconventional design. This study investigates changes in pedestrian crossing behavior following the implementation of a scramble phase by examining the spatiotemporal gait parameters (step length and step frequency). This detailed microscopic‐level analysis provides insight into changes in pedestrian walking mechanisms as well as the effect of various pedestrian and intersection characteristics. The study uses video data collected at a scramble phase signalized intersection in Oakland, California. Gait parameters were found to be influenced by pedestrian gender, age, group size, crosswalk length, and pedestrian signal indications. Both average step length and walking speed were significantly higher for diagonally crossing pedestrians compared with pedestrians crossing on the conventional crosswalks. Pedestrians were found to have the tendency to increase their step length more than their step frequency to increase walking speed. It was also found that, compared with men, women generally increase their walking speed by increasing their step frequency more than step length. However, when in non‐compliance with signal indications, women increase their walking speed by increasing their step length more than step frequency. It was also found that older pedestrians do not significantly change their walking behavior when in non‐compliance with signal indications. Copyright © 2014 John Wiley & Sons, Ltd.     

Modeling pedestrian queuing using micro-simulation

The system considered is a cinema ticketing booth system. A general simulation algorithm is presented as well as the system’s operating characteristics. The results of the experiment were verified by comparing them with video observation data and theoretical values. Finally, with comparative analysis of experiment data, the developed simulation model was able to replicate the situation in which pedestrians find an available booth to occupy while waiting in a queue. The model can facilitate the availability of various pedestrian flows and a range of operating times. With some efforts of computer programming, the situations where multiple booths are available were simulated to identify pedestrian movement. The developed simulation model captures important details, such as travel time, wait time, queue length and the number of waiting pedestrians with the different number of pedestrian flows and booths. The paper presents a means to designing the pedestrian operation and plan on the basis of the estimated number of people.     

Converting mixed pedestrian flows into equivalent commuters using standard pedestrian equivalent factors

This paper develops the concept of standard pedestrian equivalent (SPE) factors for converting a mixed pedestrian flow into an equivalent commuter flow. After a comprehensive review of passenger car equivalent (PCE) methodologies, the equal total travel time method is utilised for SPE estimation. A micro-simulation approach is employed for the formulation of the total travel time–flow relationship. Field data collected on walking speed distributions for commuters and older adults in Australia are used as model inputs. An independent samples t-test confirms the significant difference between walking speeds of commuters and older adults. For this paper, a unidirectional flow on flat walkways is initially considered and evaluated across proportions of older people, different flows and different walkway widths. The introduction of older adults significantly increases total travel time especially under congested conditions. Results of this investigation can be used for evaluation or design of pedestrian facilities experiencing similar flow conditions.     

A dynamic evacuation model for pedestrian–vehicle mixed-flow networks

In urban emergency evacuation, a potentially large number of evacuees may depend either on transit or other modes, or need to walk a long distance, to access their passenger cars. In the process of approaching the designated pick-up points or parking areas for evacuation, the massive number of pedestrians may cause tremendous burden to vehicles in the roadway network. Responsible agencies often need to contend with congestion incurred by massive vehicles emanating from parking garages, evacuation buses generated from bus stops, and the conflicts between evacuees and vehicles at intersections. Hence, an effective plan for such evacuation needs to concurrently address both the multi-modal traffic route assignment and the optimization of network signal controls for mixed traffic flows. This paper presents an integrated model to produce the optimal distribution of vehicle and pedestrian flows, and the responsive network signal plan for massive mixed pedestrian–vehicle flows within the evacuation zone. The proposed model features its effectiveness in accounting for multiple types of evacuation vehicles, the interdependent relations between pedestrian and vehicle flows via some conversion locations, and the inevitable conflicts between intersection turning vehicle and pedestrian flows. An illustrating example concerning an evacuation around the M&T stadium area has been presented, and the results indicate the promising properties of our proposed model, especially on reflecting the complex interactions between vehicle and pedestrian flows and the favorable use of high-occupancy vehicles for evacuation operations.     

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.     

A study of the bi-directional pedestrian flow characteristics at Hong Kong signalized crosswalk facilities

This paper investigates the bi-directional flow characteristics at signalized crosswalk facilities in Hong Kong. Pedestrian flow measurements were conducted at selected signalized crosswalks in Hong Kong urban area with and without the Light Rail Transit (LRT) railway tracks in the median of the carriageway. The pedestrian speed-flow functions for these crosswalk facilities were calibrated. The relationships between the walking speed at capacity and directional distribution of pedestrian flow (or flow ratio) are determined. The effects of different flow ratio on the effective capacity are also investigated. The bi-directional pedestrian flow effects on signalized crosswalk facilities with LRT tracks are found more significant than those without LRT tracks. The result could be used as a basis to improve the assessment of the crosswalk's capacity and to determine the design walking speeds under different flow ratios at signalized crosswalks in Hong Kong and in other Asian cities with similar environments.     

Does the pedestrian environment affect the utility of walking? A case of path choice in downtown Boston

There is a lack of consensus as to whether the relationship between the built environment and travel is causal and, if it is, the extent of this causality. This problem is largely caused by inappropriate research designs adopted in many studies. This paper proposes a new method (based on path choice) to investigate the causal effect of the pedestrian environment on the utility of walking. Specifically, the paper examines how the pedestrian environment affects subway commuters’ egress path choice from a station to their workplaces in downtown Boston. The path-based measure is sensitive enough to capture minor differences in the environment experienced by pedestrians. More importantly, path choice is less likely to correlate with job and housing location choices, and therefore largely avoids the self-selection problem. The results suggest that the pedestrian environment can significantly affect a person’s walking experience and the utility of walking along a path.     

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.     

Heuristic estimation of pedestrian traffic volumes

In order to monitor pedestrian volumes in the Johannesburg Central Business District (CBD), a streamlined approach was needed that would provide useable information quickly and cheaply. To this end a computerised model was developed which uses a limited number of observations of pedestrian density in order to compute mean and peak traffic volumes. Although the data input is parsimonious in the extreme, the model has been able to match the accuracy required for pedestrian volume monitoring.     

Planning for pedestrian networks in North American downtowns

While North American urban regions are served by mechanical modes of transportation, downtowns are largely pedestrian environments. The growth and consolidation of office districts over the last twenty years have revived interest in developing coherent and efficient pedestrian networks, which can be coordinated with other transportation needs within the downtown. Ambitious plans for expansion of the downtown for offices, the retail and service industries as well as for housing and entertainment have been adopted in many North American cities during the 1980s. The successful integration of these large central areas depends to a considerable extent on the implementation of expanded pedestrian networks. This paper discusses certain spatial characteristics of North American cities which call for specific network designs and research into the walking environments of central areas. More knowledge is needed of the relative contributions to pedestrian regeneration of land use combinations, the design of networks and of walking paths.     

Perceived cost potential field cellular automata model with an aggregated force field for pedestrian dynamics

This paper proposes a perceived potential field and an aggregated force field for navigation of pedestrians in a walking domain with poor visibility or complex geometries. While the former field used in uncrowded cells simply reflects the pedestrians’ desire to minimize their travel costs, the latter field used in crowded cells suggests much stronger interaction between pedestrians. Compared with a formulation that does not include the latter field, the proposed model displays an advantage in simulating over-crowded pedestrian flows, e.g., at the front of a bottleneck or at a left/right turn in a corridor; the simulated phenomena, including phase transitions and fundamental diagrams, agree well with the observation and studies in the literature.     

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.     

Investigating the applicability of exclusive pedestrian phase at two‐phase actuated controlled intersections

The exclusive pedestrian phase (EPP) has been used in many countries to promote walking around downtown areas by increasing the ease and convenience of pedestrian crossing. However, its applicability has not been systematically demonstrated, especially when an intersection is operated in actuated mode. This paper presents an extensive simulation‐based analysis of the applicability of EPP as compared with a normal concurrent pedestrian‐phase pattern at an isolated intersection controlled by actuated logic. Actuated signal control logics for EPP‐actuated and conventional concurrent pedestrian phase‐actuated controls are developed. Both of these control logics consider pedestrian crossing demands and can adapt to changes in vehicle traffic to reduce vehicle delay as well. A simulation model of a two‐phase controlled intersection is built and calibrated based on field data using VISSIM (PTV Planung Transport Verkehr AG in Karlsruhe, Germany). Extensive analysis is conducted to reveal fully the applicable EPP domain in terms of vehicle traffic demand, pedestrian demand, vehicle turning ratio, and pedestrian diagonal crossing ratio. The results show that the performance and applicable domain of EPP are jointly determined by those five factors. EPP significantly outperforms concurrent pedestrian phase if the vehicle turning ratio is greater than 0.6 and the pedestrian diagonal crossing ratio is greater than 0.6. These results can help traffic engineers in choosing the appropriate pedestrian‐phase patterns at actuated signalized intersections. Copyright © 2015 John Wiley & Sons, Ltd.