On a mean field game approach modeling congestion and aversion in pedestrian crowds

In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model, that considers smart pedestrians who rationally interact and anticipate the future. This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion. In both cases we describe the model and present numerical solvers (based on the optimization formulation and the partial differential equations respectively). Finally we present numerical tests involving anticipation phenomena and complex group behaviors such as lane formation.     

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.     

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.     

Modeling absolute and relative cost differences in stochastic user equilibrium problem

This paper aims to develop a hybrid closed-form route choice model and the corresponding stochastic user equilibrium (SUE) to alleviate the drawbacks of both Logit and Weibit models by simultaneously considering absolute cost difference and relative cost difference in travelers’ route choice decisions. The model development is based on an observation that the issues of absolute and relative cost differences are analogous to the negative exponential and power impedance functions of the trip distribution gravity model. Some theoretical properties of the hybrid model are also examined, such as the probability relationship among the three models, independence from irrelevant alternatives, and direct and indirect elasticities. To consider the congestion effect, we provide a unified modeling framework to formulate the Logit, Weibit and hybrid SUE models with the same entropy maximization objective but with different total cost constraint specifications representing the modelers’ knowledge of the system. With this, there are two ways to interpret the dual variable associated with the cost constraint: shadow price representing the marginal change in the entropy level to a marginal change in the total cost, and dispersion/shape parameter representing the travelers’ perceptions of travel costs. To further consider the route overlapping effect, a path-size factor is incorporated into the hybrid SUE model. Numerical examples are also provided to illustrate the capability of the hybrid model in handling both absolute and relative cost differences as well as the route overlapping problem in travelers’ route choice decisions.     

A framework for evaluating the dynamic impacts of a congestion pricing policy for a transportation socioeconomic system

This paper provides a modeling framework based on the system dynamics approach by which policy makers can understand the dynamic and complex nature of traffic congestion within a transportation socioeconomic system representation of a metropolitan area. This framework offers policy makers an assessment platform that focuses on the short- and long-term system behaviors arising from an area-wide congestion pricing policy along with other congestion mitigation policies. Since only a few cities in the world have implemented congestion pricing and several are about to do so, a framework that helps policy makers to understand the impacts of congestion pricing is currently quite relevant. Within this framework, improved bus and metro capacities contribute to the supply dynamics which in turn affect the travel demand of individuals and their choice of different transportation modes. Work travel and social networking activities are assumed to generate additional travel demand dynamics that are affected by travelers’ perception of the level of service of the different transportation modes, their perception of the congestion level, and the associated traveling costs. It is assumed that the, population, tourism and employment growth are exogenous factors that affect demand. Furthermore, this paper builds on a previously formulated approach where fuzzy logic concepts are used to represent linguistic variables assumed to describe consumer perceptions about transportation conditions.     

Uni- and bi-directional pedestrian flow in the view-limited condition: Experiments and modeling

In this paper, the impact of vision on the uni- and bi-directional flow has been investigated via experiment and modeling. In the experiments, pedestrians are asked to walk clockwise/anti-clockwise in a ring-shaped corridor under view-limited condition and normal view condition. As expected, the flow rate under the view-limited condition decreases comparing with that under the normal view condition, no matter in uni- or bi-directional flow. In bidirectional flow, pedestrians segregate into two opposite moving streams very quickly under the normal view condition, and clockwise/anti-clockwise walking pedestrians are always in the inner/outer ring due to right-walking preference. In the first set of experiment, spontaneous lane formation has not occurred under the view-limited condition. Pedestrian flow does not evolve into stationary state. Local congestion occurs and dissipates from time to time. However, in the later sets of experiments, spontaneous lane formation has re-occurred. This is because participants learned from the experience and adapted right-walking preference to avoid collision. To model the flow dynamics, an improved force-based model has been proposed. The driving force has been modified. The right-walking preference has been taken into account. The fact that pedestrians cannot judge the moving direction accurately under limited-view condition has been considered. Simulation results are in good agreement with the experimental ones.     

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.     

An agent-based multimodal simulation model for capacity planning of a cross-border transit facility

Cross-border transit facilities constitute major public investment, and thus must serve the long-term needs of the communities, such as providing access to schools and businesses, contributing to a shared regional culture and lifestyle, fostering international trade, and supporting jobs for the region’s residents. Numerous studies have been conducted to evaluate the economic implications of vehicular flow delays at border crossings, however none of the studies focused on assessing cross-border flow of bus passengers and pedestrians. Since pedestrians are considered to be autonomous, intelligent, and perceptive, it is a challenging task to predict pedestrian movement and behavior in comparison to vehicular flows which follow a specific set of traffic rules. This paper presents a multiagent based multimodal simulation model to evaluate the capacity and performance of a cross-border transit facility. The significance of this research is the use of dynamic mode choice functionality in the model, which allows an individual person to make instantaneous choices between available modes of transportation. The scope of interest of the paper is limited to simulating access interface, circulation areas, ancillary and processing facilities. The developed model was calibrated to ensure realistic performance, and validated against specific performance criteria such as throughput per processing facility. In order to demonstrate the applicability of the developed simulation model, capacity and operational planning of a pedestrian transit facility was performed. The relative performance of alternative design or configuration was evaluated using the level of service criteria. Lastly, the effectiveness of each proposed capacity or operational improvement strategy was compared to the “do-nothing” scenario.     

Modeling and optimization of multimodal urban networks with limited parking and dynamic pricing

Cruising-for-parking constraints mobility in urban networks. Car-users may have to cruise for on-street parking before reaching their destinations. The accessibility and the cost of parking significantly influence people's travel behavior (such as mode choice, or parking facility choice between on-street and garage). The cruising flow causes delays eventually to everyone, even users with destinations outside limited parking areas. It is therefore important to understand the impact of parking limitation on mobility, and to identify efficient parking policies for travel cost reduction. Most existing studies on parking fall short in reproducing the dynamic spatiotemporal features of traffic congestion in general, lack the treatment of dynamics of the cruising-for-parking phenomenon, or require detailed input data that are typically costly and difficult to collect. In this paper, we propose an aggregated and dynamic approach for modeling multimodal traffic with the treatment on parking, and utilize the approach to design dynamic parking pricing strategies. The proposed approach is based on the Macroscopic Fundamental Diagram (MFD), which can capture congestion dynamics at network-level for single-mode and bi-modal (car and bus) systems. A parsimonious parking model is integrated into the MFD-based multimodal modeling framework, where the dynamics of vehicular and passenger flows are considered with a change in the aggregated behavior (e.g. mode choice and parking facility choice) caused by cruising and congestion. Pricing strategies are developed with the objective of reducing congestion, as well as lowering the total travel cost of all users. A case study is carried out for a bi-modal city network with a congested downtown region. An elegant feedback dynamic parking pricing strategy can effectively reduce travel delay of cruising and the generic congestion. Remarkably, such strategy, which is applicable in real-time management with limited available data, is fairly as efficient as a dynamic pricing scheme obtained from system optimum conditions and a global optimization with full information about the future states of the system. Stackelberg equilibrium is also investigated in a competitive behavior between different parking facility operators. Policy indications on on-street storage capacity management and pricing are provided.     

Multilane first-order traffic flow model with endogenous representation of lane-flow equilibrium

In this study, we develop a multilane first-order traffic flow model for freeway networks. In the model, lane changing is considered as a stochastic behavior that can decrease an individual driver’s disutility or cost, and is represented as dynamics toward the equilibrium of lane-flow distribution along with longitudinal traffic dynamics. The proposed method can be differentiated from those in previous studies because in this study, the motivation of lane changing is explicitly considered and it is treated as a utility defined by the current macroscopic traffic state. In addition, the entire process of lane changing is computed macroscopically by an extension of the kinematic wave theory employing IT principle; moreover, in the model framework, the lane-flow equilibrium curve is endogenously generated because of self-motivated lane changes. Furthermore, the parsimonious representation enables parameter calibration using the data collected from conventional loop detectors. The calibration of the data collected at four different sites, including a sag bottleneck, on the Chugoku expressway in Japan reveals that the proposed method can represent the lane-flow distribution of any observation site with high accuracy, and that the estimated parameters can reasonably explain the multilane traffic dynamics and the bottleneck phenomena uphill of sag sections.     

A three-stage evacuation decision-making and behavior model for the onset of an attack

Pedestrian behavior models have successfully reproduced human movement in many situations. However, few studies focus on modeling human behavior in the context of terrorist attacks. Terrorist attacks commonly occur in crowded public areas and result in a large number of casualties. This paper proposes a three-stage model to reproduce a series of complex behaviors and decision-making processes at the onset of an attack, when pedestrians generally do not have clear targets and have to deal with fuzzy information from the attack. The first stage of the model builds a Bayesian belief network to represent the pedestrians’ initial judgment of the threat and their evacuation decisions. The second stage focuses on pedestrians’ global assessment of the situation through an analogy with diffusion processes. The third stage uses a cost function to reproduce the trade-offs of distance, safety, and emotional impact when considering a path to take. The model is validated using a video from the November 2015 Paris attack. The behavioral characteristics and trajectories of three pedestrians extracted from the video are reproduced by the simulation results based on the model. The research can be used to set rules when performing risk analysis and strategic defensive resource allocation of terrorist attacks using agent-based simulation methods.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

Maintenance optimization for transportation systems with demand responsiveness

We present a quadratic programming framework to address the problem of finding optimal maintenance policies for multifacility transportation systems. The proposed model provides a computationally-appealing framework to support decision making, while accounting for functional interdependencies that link the facilities that comprise these systems. In particular, the formulation explicitly captures the bidirectional relationship between demand and deterioration. That is, the state of a facility, i.e., its condition or capacity, impacts the demand/traffic; while simultaneously, demand determines a facility’s deterioration rate. The elements that comprise transportation systems are linked because the state of a facility can impact demand at other facilities. We provide a series of numerical examples to illustrate the advantages of the proposed framework. Specifically, we analyze simple network topologies and traffic patterns where it is optimal to coordinate (synchronize or alternate) interventions for clusters of facilities in transportation systems.     

Joint inventory-location problem under the risk of probabilistic facility disruptions

This paper studies a reliable joint inventory-location problem that optimizes facility locations, customer allocations, and inventory management decisions when facilities are subject to disruption risks (e.g., due to natural or man-made hazards). When a facility fails, its customers may be reassigned to other operational facilities in order to avoid the high penalty costs associated with losing service. We propose an integer programming model that minimizes the sum of facility construction costs, expected inventory holding costs and expected customer costs under normal and failure scenarios. We develop a Lagrangian relaxation solution framework for this problem, including a polynomial-time exact algorithm for the relaxed nonlinear subproblems. Numerical experiment results show that this proposed model is capable of providing a near-optimum solution within a short computation time. Managerial insights on the optimal facility deployment, inventory control strategies, and the corresponding cost constitutions are drawn.     

Integrated driving behavior modeling

This paper develops, implements and tests a framework for driving behavior modeling that integrates the various decisions, such as acceleration, lane changing and gap acceptance. Furthermore, the proposed framework is based on the concepts of short-term goal and short-term plan. Drivers are assumed to conceive and perform short-term plans in order to accomplish short-term goals. This behavioral framework supports a more realistic representation of the driving task, since it captures drivers’ planning capabilities and allows decisions to be based on anticipated future conditions.An integrated driving behavior model, which utilizes these concepts, is developed. The model captures both lane changing and acceleration behaviors. The driver’s short-term goal is defined by the target lane. Drivers who wish to change lanes but cannot change lanes immediately, select a short-term plan to perform the desired lane change. Short-term plans are defined by the various gaps in traffic in the target lane. Drivers adapt their acceleration behavior to facilitate the lane change using the target gap. Hence, inter-dependencies between lane changing and acceleration behaviors are captured.     

Behavior-based consistency-seeking models as deployment alternatives to dynamic traffic assignment models

This paper proposes a behavior-based consistency-seeking (BBCS) model as an alternative to the dynamic traffic assignment paradigm for the real-time control of traffic systems under information provision. The BBCS framework uses a hybrid probabilistic–possibilistic model to capture the day-to-day evolution and the within-day dynamics of individual driver behavior. It considers heterogeneous driver classes based on the broad behavioral characteristics of drivers elicited from surveys and past studies on driver behavior. Fuzzy logic and if–then rules are used to model the various driver behavior classes. The approach enables the modeling of information characteristics and driver response to be more consistent with the real-world. The day-to-day evolution of driver behavior characteristics is reflected by updating the appropriate model parameters based on the current day’s experience. The within-day behavioral dynamics are reactive and capture drivers’ actions vis-à-vis the ambient driving conditions by updating the weights associated with the relevant if–then rules. The BBCS model is deployed by updating the ambient driver behavior class fractions so as to ensure consistency with the real-time traffic sensor measurements. Simulation experiments are conducted to investigate the real-time applicability of the proposed framework to a real-world network. The results suggest that the approach can reasonably capture the within-day variations in driver behavior model parameters and class fractions in the traffic stream. Also, they indicate that deployment-capable information strategies can be used to influence system performance. From a computational standpoint, the approach is real-time deployable.     

Effect of parking information on travelers' knowledge and behavior

In many urban centers the demand for parking increases sharply before Christmas mainly due to shopping activity — causing parking congestion. One way to ameliorate such congestion is by disseminating parking information. Informed drivers may divert to relatively under-utilized parking facilities relieving the pressure on congested facilities. The City of Nottingham in England tested a real-time parking information system designed to alleviate congestion in the City Center parking facilities. Real-time information was disseminated through the radio, while historical information regarding parking locations was disseminated through newspaper advertisements and leaflets. The objective of this study is to assess impacts of the parking information system on travelers' knowledge and decisions.Survey research was used to understand traveler response. Respondents' levels of knowledge regarding car parks were analyzed by developing Poisson regression models. Drivers were more likely to have greater knowledge of city center car parks if they used several information sources (radio broadcasts, newspaper advertisements or leaflets and word-of-mouth), were active seekers of parking information, and searched for parking rather than going directly to a parking facility. In addition, the study of behavior showed that drivers were more inclined to use the relatively under-utilized Park-and-Ride facilities instead of the city center car parks if they received parking information from Newspaper advertisements/leaflets. Overall, the parking information service in Nottingham was effective; it seems reasonable to establish such information dissemination and monitoring systems at parking facilities in other urban areas. Furthermore, to support informed travel and activity participation decisions, parking information should be integrated with traffic and transit information.     

Modelling negative interactions among pedestrians in high density situations

Situations characterised by the presence of a high density of pedestrians involved in negative interactions (e.g. flows in opposite directions) often represent a problematic scenario for simulation models, especially those taking a discrete approach to the representation and management of spatial aspects of the environment. While these situations can be relatively infrequent, and even if architects, event organisers and crowd managers actually try to prevent them as much as possible, they simply cannot be neglected and they actually represent interesting situations to be analysed by means of simulation. The paper presents specific extensions to a floor-field Cellular Automata pedestrian model that are specifically aimed at supporting the simulation of high density situations comprising negative interactions among pedestrians without incurring in the traditional limits of discrete approaches. The models are formally described and experimented in experimental and real world situations.