PPedestrian Simulation: A Review
Amir RasouliNoah’s Ark Laboratory, Huawei, Canada
Abstract
This article focuses on different aspects of pedestrian (crowd) model-ing and simulation. The review includes: various modeling criteria, suchas granularity, techniques, and factors involved in modeling pedestrian be-havior, and different pedestrian simulation methods with a more detailedlook at two approaches for simulating pedestrian behavior in traffic scenes.At the end, benefits and drawbacks of different simulation techniques arediscussed and recommendations are made for future research.
Pedestrian behavior in the context of driving can be modeled at the individuallevel, e.g. a pedestrian is intending to cross the road in a residential area, or aspart of a crowd of individuals, e.g. a group of pedestrians is about to cross a sig-nalized intersection. Note that the term crowd is often used in phenomenologywhere the behavior of large groups of people is studied in the context of munic-ipal road design, building evacuation system planning, shopping mall structuredesign, and many similar applications. In traffic context, the term “pedestriangroup” or group for short is often used. However, since a large body of theliterature on pedestrian simulation is involving phenomenology, I use the termcrowd throughout this report.
Before discussing different methods of modeling pedestrian and crowd behavior,it is important to understand what constitutes a crowd . The definition of crowdvaries in different fields of human behavior understanding. A generally accepteddefinition of crowd is given by Klupfel [1] who defines a crowd as “a group of1 a r X i v : . [ c s . R O ] F e b rowd Gatherings MobsCasual
Crowds
Audiences Queues Aggressive
Mobs
Panics
Lynch
Mobs
Riots
Escape Acquisitive
Figure 1: Different types of crowds. Source [1].people sharing the same space and focus and where typical crowd phenomena,such as lane formation or speed reduction due to high density, are observed”.Note that this definition is from the phenomenological perspective and mightvary in the context of traffic understanding.As illustrated in Figure 1, the type of crowd depends on the motivationof people who form it. For example, pedestrian crowds in traffic scenes can beconsidered as casual crowds that are formed organically as part of the movementson the roads.
There are a number of elements involved in modeling crowds ranging from thescope of the model to the factors that impact pedestrian behavior. A summaryof these elements are explained below.
Figure 2: Modeling granularity. From left to right: Macroscopic, mesoscopic,and microscopic. Source [2].Granularity (or scope) of modeling directly determines what factors shouldbe looked at when simulating behavior [2]. Figure 2 illustrates different levels of2ranularity of crowd simulation. At the highest level, macroscopic , the focus ismainly on the movement of the groups of pedestrians as a whole, i.e. no level ofmodeling for individual pedestrians is done. In a mesoscopic setting, individualswithin the groups are modeled but in a homogeneous fashion, meaning that allindividuals are governed by the same rules. At the lowest level, microscopic modeling defines the behavior of individuals given that their behaviors mayvary according to their personal characteristics, their surroundings, or theirinteractions with each other or the environment (see also Section 3.2).
Interaction Autonomy
People/layout/behavior
Simple aspects No individually
Goals/strategic
Response/tacticalNo behavioral rulesFunctional analogyImplicit (equation)Ruled-basedAI
Figure 3: Autonomy and behavior modeling of pedestrians. Source [1].The granularity of modeling defines to what extend the behavior of individu-als should be modeled [1]. Figure 3 shows the level of individualism in modelingpedestrian behavior. Here, we can see that depending on the level of individ-ualism in modeling more sophisticated algorithms are required to simulate theinternal motivations and decision-making processes of pedestrians.
Besides the scope of pedestrian behavior modeling, there are other criteria toaccount for as reflected in Figure 4. For example, how specific we want thedynamics to be, whether the dynamics are modeled continuously or discretely ,or whether a rule-based deterministic model is going to be used or a data-driven stochastic model [1]. 3 pecific GeneralDiscrete Continuous Stochastic DeterministicMacroscopic Microscopic Estimation First Principles
Numerical Analytical Quantitative Qualitative
Figure 4: Pedestrian behavior modeling criteria. Source [1].
In order to model pedestrians’ behaviors and their decision-making processes, weneed to understand their internal processes while making a decision, different levels of decision making, the types of decisions they have to make or choices they have, and the factors that potentially impact their decisions.
According to [1], there are three different levels of internal processes that moti-vate a human to make a decision or perform an action:1.
Desire . This determines the ultimate goal of the human or what is theirdesired future state. For example, a pedestrian wants to arrive as fastas possible to a destination or in an evacuation event, get out of the exitdoor as fast as possible.2.
Belief . The types of decisions the human makes or actions they performare motivated by their beliefs, i.e. what they think is the best wayof accomplishing a task. Recalling our previous examples, this can becrossing in the middle of a busy street (e.g. jaywalking) in the case ofthe pedestrian on the road, or as in the evacuation scenario following thededicated escape routes.3.
Intention . This term refers to how humans want to accomplish theirgoals. In the above scenarios, for example, the pedestrian does not wantto be involved in an accident or the evacuee does not have an intention,or do not want, to harm anyone in the process of leaving the building.In the context of pedestrian behavior understanding in traffic scenes,some scholars [3, 4] refer to intention as the type of action that a givenpedestrian wants to perform next. This is more in line with the definitionof desire as in [1], which shows what to expect from the pedestrian in thefuture other than what they hope to accomplish.4 .2 Different decision levels
A human (or a pedestrian) can make a decision at different levels [1] including,1.
Strategic . This reflects the long-term goal of the pedestrian which mayinvolve the routes taken to the destination, time of date for commuting,or the means of transportation. These types of decisions are generallythe focus of studies of urban design.2.
Tactical . This type of decision involves a simple set of rules that thebehavior of the pedestrian is motivated by or as Klupfel [1] calls it humanconscious.3.
Operational . This type of decision includes automatic responses orsubconscious of the pedestrian, such as keeping a distance from others,walking slowly downstairs, or avoid collisions when crossing the road.
When making decisions, pedestrians are facing different choices at different lev-els of the decision-making process. To discuss these choices, I refer to the workof Bierlaire and Robin [5] who enumerate what choices pedestrians have whenmaking a decision. Note that the choices listed below are very general andencompass all levels of decision-making some of which are more relevant to mu-nicipal transportation system design other than immediate pedestrian behaviorunderstanding or simulation.1.
Activity choice . This simply refers to the choice of the next activity.Activity choice can occur at different levels of decision making, suchas activity pattern (strategic level), activity scheduling (tactical level),path-choice, or decision of crossing the road.2.
Destination choice . This refers to the choice of the location of theactivity, which can be either the final destination of choice or a local goaldestination, e.g. moving to the other side of a street.3.
Mode choice . The mode is the type of transportation or means ofcommuting. For example, while walking, a pedestrian has the choice ofusing elevators or taking stairs.4.
Route choice . Selecting which route to take is more related to theplanning stage of making a trip and often might evolve throughout thecommuting process.5.
The choices while walking . These choices perhaps are the most rele-5ant when modeling pedestrian (or crowd dynamics) locally. They are,(a)
The choice of next step , which defines how the movement ortrajectory of a given pedestrian evolves. From a modeling per-spective, this choice can be modeled as the next movement, e.g.to a next local destination depending on the number of occupiedcells around the pedestrians (called “driven” random walk), or asa continuous path, e.g. by selecting a predefined trajectory out ofa number of alternatives.(b)
The choice of speed which reflects how a pedestrian’s movementspeed changes in a given situation.Both choices of location and speed depend on various environmental, e.g.road structure, or social, e.g. social forces (see Section 3.3.2) factors.6.
Interactions . Although interaction is listed as one of the pedestrianchoices, it can also be a form of reaction to the environment. In amulti-agent setting, interaction is perhaps one of the most importantphenomena that can determine the types of actions the pedestrian wouldperform. Some of the factors to consider in interaction understandinginclude the types of behavior individuals perform in a given group, self-organization behaviors in crowds, and interaction with the environmentor other individuals in the environment.
In addition to pedestrians’ decision-making processes and their choices, it isimportant to understand the context in which behavior is modeled. Contextcan directly impact pedestrians’ behaviors and, as a result, their movements.The context may vary significantly depending on the situation individualsare observed in or their behaviors, which we intend to model. There are manystudies that focus on identifying the factors that impact pedestrian behavior,such as those in the context of behavior understanding in traffic scenes [7, 8,9, 10, 11, 12]. Discussing all these factors is beyond the scope of this report,therefore I briefly elaborate on some of these factors by referring to a recentsurvey on pedestrian behavior [6].According to [6], there are two sets of factors that impact pedestrian behav-ior: Pedestrian and environmental (see Figure 5). Pedestrian factors are relatedto target pedestrians or the pedestrians surrounding them. At the personallevel, the characteristics (e.g. age, gender or culture) or abilities of pedestri-6igure 5: Contextual factors that impact pedestrian crossing behavior. Thecircles refer to the factors and the dashed lines show the interconnection betweendifferent factors and arrows show the direction of influence. Source [6].ans (e.g. ability to perceive their environment) directly impact their behaviorsand actions. At the social level, norms or the characteristics of the pedes-trian group (e.g. size or flow) are among the factors that impact pedestrians’decision-making process or their dynamics.Environmental factors are those related to various static and dynamics enti-ties around pedestrians, such as road structure, lighting conditions, state of sig-nals, traffic flow, traffic characteristics, or even communication between pedes-trians and other road users.What makes modeling contextual factors difficult, besides their quantity, isthe fact that these factors are highly interconnected, meaning that they canimpact each other, i.e. the influence of one factor on pedestrian behavior mayvary depending on the presence of one or more other factors.7
Pedestrian Simulation
Simulation is about generating output (e.g. pedestrian behavior) from an es-tablished model. This often takes the form of a visual representation depictingbehaviors expected from pedestrians in different scenarios. It should be notedthat modeling behavior and simulation are very closely related terms and oftenwhen one talks about simulation, they discuss various aspects of modeling be-havior. In this report, however, I am discussing the practical aspects of modelingunder simulation section to distinguish between theory and practice.
Generally, there are three stages to ensure that the simulation method captureswhat is expected of it [1]:1.
Verification . The method of simulation should be verified by ensuringthat it is correctly implemented. This process may involve analyticaltests , numerical tests (in the case of numerical models), sensitivity anal-ysis (to ensure how target variables are changed with respect to othervariables), and code checking .2. Validation . The simulation method should be validated to ensure thatit accurately models the part of the reality that it is supposed to. Factorsto consider during validation include whether the method is valid (cor-respond to the real data), objective (different persons obtain the sameresults under the same initial and boundary conditions), and reliable (whether the results are repeatable).3.
Calibration . This is the process of adjusting the model parameters toachieve better simulated results closer to empirical results. This processis also known as fitting .Additionally, one must ensure that the model parameters are fewer than thedata points and the data used for verification is different from the calibrationdata
Similar to modeling behavior, depending on the granularity level (macroscopic,mesoscopic, or microscopic), the pedestrian crowd can be simulated in threedifferent scales [13]: Flow-based, entity-based, and agent-based.8 .2.1 Flow-based approach
In this method, the crowd is simulated as a whole and pedestrians do not haveany distinct behavior, and factors that impact behavior are largely reduced.This method is commonly used in the estimation of the movement of densecrowds of people, e.g. during evacuation procedures, entertainment events, etc.
In this method, individual pedestrians are considered as homogeneous entitiesand their behavior is modeled as such. There are a set of predefined global phys-ical laws that govern the movement of pedestrians who do not have individualpersonality or capacity to act or think differently. This method is desirable forsimulating small to medium-sized crowds.
This is, perhaps, the most complex and sophisticated method of simulation inwhich individuals are considered autonomous and will interact with one another.The behaviors of the individuals are impacted by their surroundings and theycan react and adapt to complex dynamic environments. In this setting, the be-haviors of pedestrians are regulated by sets of decision rules and the pedestriansmay make decisions independently.According to [13], in an agent-based setting, there are three main aspectsthat should be considered:1.
Navigation.
Navigation determines how the agents move around in thevirtual environment. The common approaches used for navigation aresimilar to path planning or steering algorithms.2.
Decision making.
This determines what a pedestrian would do in agiven situation. There are often a set of decision rules, which may varyin their complexity or sophistication, that govern agents’ behaviors. Oneexample is discrete choice model which is based on the utility theory andhow a decision result in a particular reward for a given pedestrian [5].3.
Animation is concerned with the visual representation of the pedestri-ans and can be useful for the validation of behavior models. For example,subject matter experts can compare the simulated crowd behavior withtheir knowledge and experience.9 .3 Common simulation techniques
The network-based method is one of the earliest techniques used for simulatingpedestrian behavior [14]. Originally proposed for modeling pedestrian shoppingbehavior, this method defines the environment as a network with N links (shop-ping streets) connecting city intersections represented as nodes. In this method,there are three key elements:1. Destination choice , which defines the transition of the pedestrians fromone state to another and is a function of the distance between differentlinks and other applications specific factors, such as the purpose of acertain shop or floor plan of the shop.2.
Route choice . The authors assume that, in order to select a route, pedes-trians assign a utility value to each alternative route calculated based onvarious characteristics of the given route.3.
Impulse stops . This parameter is specific to the shopping scenario. Theauthors assume that, in addition to planned shopping, the pedestriansmight have impulse buying habits which is a function of a link’s attributesand the number of pedestrians passing through the link. This factor isprimarily used to measure the demand for a particular retail outlet whichmay impact the likelihood of destination choice.
As the name implies, this group of models relies on laws of physics, (e.g. fluiddynamics) to model the interaction between individuals [15, 16, 17] or groupsof pedestrians [18, 19].Perhaps one of the most known techniques in this category is the socialforces method [20] which models changes in pedestrian behavior based on forcescalculated by combining three components (see Figure 7): acceleration force which captures an individual desire to reach a certain velocity, repulsive forces ,which shows the tendency of pedestrians to keep a certain distance from theirneighboring individuals, and repulsive forces from obstacles , (e.g. walls).10igure 6: Social forces in pedestrian motion modeling. Source: Future ICT . Cellular Automaton (CA) methods are very popular in simulating crowd dy-namics [22, 23, 24, 25]. The idea behind this approach is to locally modelpedestrian movements by discretizing the active areas into cells. In this grid ofcells, pedestrians are free to move to each neighboring cell according to transi-tion criteria. For example, in a 2-dimensional model, the transition is given by a3 × This group of models is inspired by nature. One such method is known as theemotional ant model [27] which defines different psychological states of the crowd(e.g. panic or safety) and how these states impact the transition of individualsand the selection of one path over the others.
With the emergence of machine learning techniques and increase in computa-tion power, many recent approaches rely on data-driven approaches to learnand predict different patterns of pedestrian behavior [28, 29, 30]. There is awide range of deep learning approaches used for producing future pedestrian http://futurict.blogspot.com/2014/12/social-forces-revealing-causes-of.html In this section, a detailed review of two pedestrian behavior models for trafficscenarios will be presented. Here, the deep learning predictive models are omit-ted because their primary purpose is for scene understanding. A comprehensivereview of these models can be found in [49].
Figure 8: Psychological process of pedestrian behavior at signalized intersectionpresented in [50].The first paper is by Zeng et al. [50] who propose a method for pedestriancrossing behavior at signalized crosswalks based on the social forces model.As illustrated in Figure 8, the authors define the psychological process ofpedestrians with two levels:
Strategic level in which pedestrians decide theirintended direction and operational level where pedestrians adjust their walkingbehavior. 13 a) OD zones, entering and exiting posi-tions at crosswalk (b) Desired direction and driving force
Figure 9: Definition of OD and desired direction from [50].In this model, there are four designated origin-destination (OD) zones (seeFigure 9) and three stages for pedestrians while finishing crossing:1.
Stage 1 : From origin to crosswalk entering position2.
Stage 2 : From crosswalk entering position to crosswalk exit position3.
Stage 3 : From crosswalk exit position to the destinationEach state is represented as a vector connecting the current position to the next.The focus of this model is only on stage 2 . Desired entering and exit positions.
These positions are estimatedbased on empirical data in the form of a Weilbull distribution, which is a functionof crosswalk geometry, pedestrian OD movement, previous passing position, andthe densities of other road users.
Stop/go decision model.
The probability of stop/go behavior is definedas a function of pedestrian walking speed and distance to the crosswalk at theonset of pedestrian flashing green (PFG), or when the signal is in transition modebetween green to red allowing pedestrians to finish walking. This probability isdefined as a binary logit-based model with an error term in the form of Gumbeldistribution.
Social forces model.
The overall social forces term is the sum of fivedifferent forces:1.
Driving force towards the destination. The authors argue that the speed14f pedestrians changes dynamically due to the stimulus of the surround-ing environment causing deviation from a desired speed of movement.There is a force to induce pedestrians to reach the desired speed whichis a function of the desired direction, current speed, desired speed, andthe acceleration of the pedestrians. This force is denoted in Figure 9 as −→ F d .2. Force from crosswalk boundary which has two components: A repul-sive force inducing pedestrians to stay within the crosswalk boundariesand an attractive force that pushes pedestrians to walk back within theboundaries if, for example, they stepped out due to the high density ofpedestrians crossing. Both of these forces are a function of position withrespect to crosswalk boundaries.3.
Force from surrounding pedestrians.
This force contains two repulsiveforces, the one from opposing group of pedestrians that are closing inand the one that is resulted from pedestrians in the private sphere of thetarget pedestrian.4.
Force from conflicting vehicles which is a repulsive force from the vehicleturning into the intersection, in this case from the left side which is afunction of the position of the vehicle and its speed.5.
Force from the signal phase.
This is an attractive force triggered bygreen (or flashing green) light. It is assumed that during flashing state,pedestrians will increase their speed, which is linearly related to theirdesired exit point position. The force exists until the maximum speed isreached at which point the force becomes zero.
This model is introduced by Yang et al. [51] who model the crossing behaviorof pedestrians in China. The authors categorize pedestrians into two groups:1.
Law obeying who are people that comply with traffic laws. The elderlymainly fall into this group.2.
Opportunistic ones that look for appropriate gaps between vehicles tocross during the red pedestrian signal. This group, as claimed by theauthors, includes most pedestrians in China.There are three external factors that impact pedestrian crossing behavior (orwhich group of pedestrians they will belong to). These factors are the presenceof a police officer, the behaviors of other pedestrians, and traffic flow.15igure 10: An overview of the method proposed in [51].Based on the above criteria, the authors propose a model based on a statemachine framework depicted in Figure 10. In this illustration, r is the propor-tion of law obeying pedestrians. A portion of these pedestrians, presented by r , might break the law and follow others against the signal if some people startcrossing at the red signal. 16edestrian crossing decision is motivated by the time gap ∆ T which reflectsthe safe time gap between two consecutive vehicles calculated according to thedistance between the pedestrian and the front of the approaching vehicle D ,its instantaneous velocity V and width w , the distance between the currentposition of the pedestrian and the vehicle’s lateral edge d and the averagewalking speed of the pedestrian V ped . In this model, the authors denote theportion of the pedestrians who accept a certain time gap ∆ T as r . In this article, I have presented an overview of pedestrian behavior modelingand simulation techniques. Issues such as the scale of modeling and factorsto be considered for modeling were discussed. A group of these factors arethe dynamic elements of the scene such the movements of pedestrians and theagents surrounding them. Another group includes interpersonal, social, andenvironmental factors, ranging from internal motivations and decision-makingprocesses to social interactions with others, the structure of the environment,and many more.In the second part of this paper, I discussed various methods of pedestrianbehavior simulation, such as physics-based methods that model dynamics ofpedestrians, e.g. by determining different social and environmental forces in thesocial forces method, cellular automation methods which discretize environmentand model pedestrian behavior in terms of transitioning between different cells,and more recent deep learning approaches, which implicitly learn various aspectsof pedestrian behavior from data.The main question one needs to answer is which methodology is deemedto be most effective for pedestrian behavior simulation? The answer to thisquestion is not easy, and of course, largely depends on the scale of simulationand the type of the application.There are some considerations when simulating pedestrian behavior. Clas-sical methods, such as those that model pedestrian dynamics have been usedsuccessfully in many applications, such as macroscopic crowd simulation. Oncethese models are applied to microscopic simulations, the number of parametersto be estimated increases exponentially, especially if one intends to capture com-plex dynamics and behavioral components of pedestrians. Calibration of theseparameters is not easy, and in many cases, it is not possible to derive them from17ata. On the positive side, if the parameters are well estimated, these methodsare potentially more generalizable to many alternative scenarios compared topurely data-driven approaches.To remedy the challenges with the parameterization of classical models,thanks to the recent increase in computation power, many recent approachesuse deep learning approaches and try to learn different aspects of pedestrian be-havior implicitly from data. These models are shown to perform very well undercertain conditions while removing the need for complex numerical modeling ofbehavioral factors as well as complex calibration techniques needed to tune var-ious parameters of classical models. Deep learning methods, however, have amajor drawback that is they learn patterns from data samples. This means, toenhance their generalizability, one needs more data with distinct characteristics.Besides the fact that collecting more data is cumbersome and can potentiallyadd to computational resources needed for training the models, learning all as-pects of pedestrian behavior with all the factors involved, does not seem feasibleor even possible.So what would be a good solution to pedestrian behavior modeling? Theanswer yet again is not easy and as shown by many years of research in thefield, we are still far from achieving a general model for pedestrian behavior,even in a limited context. One general direction of research can perhaps be thehybridization of different modeling techniques, which of course have been suc-cessfully done by, e.g. combining physics-based and CA methods. The proposedhybridization, however, is more on the line of marrying classical techniques withmodern deep learning approaches. For instance, deep learning approaches canbe used to infer dynamic aspects of pedestrian behavior, such as the move-ment or interaction with other agents, which are more constant across differentscenarios, whereas classical models can be used for modeling decision makingprocesses motivated by environmental conditions, such as signal, traffic struc-ture, or characteristics of pedestrians.
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