Physica A 390 (2011) 636–646

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Physica A

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Simulation model of pedestrian interactive behaviorZhang Qi ∗, Han BaomingBeijing Jiaotong University, Beijing, China

a r t i c l e i n f o

Article history:Received 5 February 2010Received in revised form 27 July 2010Available online 20 October 2010

Keywords:Pedestrian behaviorInteractionPotential fieldSimulation model

a b s t r a c t

This paper presents a simulation model for pedestrian collective behavior. It is supposedthat the pedestriansmake individual decisions duringmovement according to their wishesand interaction with other pedestrians. The follow effect, deterrent effect and rejectioneffect are put forth as latent interactive effects influencing pedestrian decisions. Threecategories of potential fields were defined to model the pedestrian behavior by simulatingpedestrians’ decision processes. A circumstance potential field was defined to simulate thedesire to targets.Moving andwaiting potential fieldswere defined tomodel the interaction.Experiments were run for the model validation and coefficient performance verification.Performances and relationships of sensitivity coefficient, decay coefficient and diffusioncoefficient are studied to clarify the effectiveness and flexibility of the presented model ingenerating pedestrianmovement under a variety of situations. The simulation results showthe good performance of the model in reflecting pedestrian interactive behavior.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Study of pedestrian behavior has been a popular field for many years because of its necessity and significance forpedestrian trafficmanagement and facility design. Studies of pedestrianmovement include pedestrian characteristics [1–4],fundamental diagrams [5,6], and simulation modeling [7–13]. Simulation modeling provides an effective approach to thestudy of pedestrian traffic. Pedestrian simulation models include continuous models and discrete models.

The social force model [14] is one of the typical continuous models. The social force model works by assigning com-plex calculus and a thorough understanding of the Boltzmann-like gas-kinetic equations. The motion of pedestrians wasdescribed as if they were subject to social forces which were a measure for internal motivations. The force terms include aterm describing acceleration, terms reflecting that a pedestrian keeps a certain distance from other pedestrians and borders,and a term modeling attractive effects.

For the case of discrete simulation models, cellular automata (CA) and similar grid-based models have been widely used.Gipps and Marksjo developed a CA-like model called the Benefit Cost Model [15] that uses gravity-based rules to makepedestrians move. Blue and Adler [16–21] presented a CA model for a multi-directional pedestrian walking simulation.A relatively small rule set including lane change, step forward, and gap computation was proposed and applied to eachpedestrian on a lattice of square cells to capture the pedestrian behaviors. According to the rule set, the lane that bestpromotes forward movement is chosen for sidestep movement, and the allowable movement of each pedestrian is basedon the desired speed and the available gap ahead for forward movement. It shows that the CA model is capable ofeffectively capturing collective behaviors of pedestrians who are autonomous at a micro-level. Performance analysis of the

∗ Corresponding author.E-mail address: zhangqi.bjtu@163.com (Q. Zhang).

0378-4371/$ – see front matter© 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.physa.2010.10.029

Q. Zhang, B. Han / Physica A 390 (2011) 636–646 637

CAmodel [22] and its application together with multi-agent modeling [23] were studied, showing good performance of theCA model.

In recent years, researchers have shown interest in the mechanism of pedestrian dynamics and self-organization. Thesocial forcemodel has been successfully used tomodel dynamics and self-organization [24–27]. However, cellular automata-based models and their variants have also shown advantages. One of the variants is the Floor Field Model [28] presented byBurstedde. The Floor Field Model substitutes individual intelligence with a virtual floor field. A static floor field S is used tospecify regions of spacewhich aremore attractive, while the dynamic floor fieldD ismodified by the presence of pedestriansto model attractive interaction between pedestrians. It means the floor field of cells is increased when cells are occupiedor were occupied by each pedestrian. It shows the ability of cellular automata to create complex behavior out of simplerules. A similar concept was also applied to the simulation of pedestrian friction effects and clogging [29,30], movementof crowds [31,32], and evacuation [33]. The authors proposed a cellular automata-based model for alighting and boardingmovement [34] by the definition of a transition probability depending on passenger desires and ability to compete. Latentinteractions among alighting and boarding passengers were supposed to influence the decision making.

Although pedestrian dynamics and self-organization are regarded as important characteristics of pedestrian traffic, aneffective method for modeling these traits is still limited. The critical problem is the description of interactions amongpedestrians. The social force model provides an effective approach to describe interactions. In the CA model presented byBlue and Adler, it supposes that only the pedestrians in the immediate neighborhood affect the movement of a pedestrian.The interactions are limited to the area of an immediate neighborhood. And the simple rule set is not applicable onmodelingmore complex behaviors. In the floor field model, interactions between pedestrians are regarded as repulsive for shortdistances and attractive for long distance. The dynamic floor fieldD is modified by the presence of pedestrians. The presenceshould not be the only trail pedestrians leave to communicate. Modification of the floor field by presence limits themodel toavoid jamming transition and an unreasonable lowdensity. In addition, in the floor fieldmodel,when there are two ‘‘species’’(with different targets) of pedestrians, each species is subjected to its own floor field. According to the authors study on thealighting and boarding model, pedestrians with opposite directions have an effect on each other. Therefore, the interactiveeffect between different groups is crucial for the pedestrians’ behavior. Furthermore, in these models, the repulsive effectis usually regarded as an effect on pedestrians keeping their distance from other pedestrians or barriers. In the real world,waiting or queuing for a long time also causes a repulsive effect that influences pedestrians’ behavior decision. The effectcaused by waiting or queuing has not been well considered.

The study in this paper is an attempt to provide an approach to model pedestrian interactions simply and flexibly. Thecircumstance potential field and interaction potential fieldwere defined tomodel the desire of targets and interactive effectsamong pedestrians. Latent effects of pedestrians during movement were analysed. The follow effect, deterrent effect andrejection effect are then regarded as important interactive factors. The follow effect describes the attractive effect betweenpedestrians with same direction. The deterrent effect is a typical effect from different ‘‘species’’. Since the latent effects areinteractive both among the same species and between the different species, in the presentedmodel the interaction potentialfield is modified by an integrated consideration of different species. In the presented model, the waiting potential field isdefined as a part of the interaction potential field to show the rejection effect caused by waiting or queuing. The evacuationexperiments (in 4.2) show the necessity and effectiveness of the waiting potential field. The presented model provides anefficient way to clarify and adjust the relative weight of the circumstance potential field and the interaction potential fieldwith sensitivity coefficients. The coefficient performance is analysed in Section 4.

The study in the paper is novel for several reasons. First, latent effects including the follow effect, deterrent effect andrejection effect among pedestrians are considered in themodeling of pedestrian interactions. Second, pedestrianmovementcan be simulated just by the generation of the integrated potential field, instead of a ‘‘modes’’ transition in the floor fieldmodel. The moving potential field considering the follow and deterrent latent effects is helpful to model pedestrian move-ment with interactions from both the same group and different groups. The waiting potential field reflecting the rejectioneffect plays an important role and shows good performance on conflict avoiding, exit choosing and self-organization. Third,the presented model is also flexible to simulate a variety of pedestrian behavior under different situations by adjusting thecoefficients.

2. Pedestrian collective behavior characteristic

Pedestrians make decisions during movement according to their desire to get to the target and their interaction withother pedestrians. Pedestrians’ desire to get to their targets basically relates to the surroundings and ease of movement.Generally, pedestrians tend to choose the shortest or fastest routes to get to their targets. However, pedestrians must beinfluenced by others during movement. Some of the interaction with others is helpful in getting to the targets, while somemay be an impediment.

There are several interactions during pedestrian movement. Three of them are considered as major effects. First, thefollow effect acts on pedestrians from those in front with same direction (Fig. 1(a)). The follow effect may trigger followingbehavior, because following the pedestrians in front can bemore easy due to less blocking or less effort in searching. Second,the deterrent effect performed on the pedestrians with an opposite direction may prevent collision (Fig. 1(b)). And the thirdis the rejection effect performed by those who are hindered, which may lead to an adjustment of decision (Fig. 1(c)).

638 Q. Zhang, B. Han / Physica A 390 (2011) 636–646

(a) Follow effect. (b) Deterrent effect. (c) Rejection effect.

Fig. 1. Passenger latent effects.

Fig. 2. Passenger and movement space.

Table 1Cell attribute.

Cell attribute Definition Value

(x, y) Cell position Abscissa and ordinate valueOccupy Cell status 0: empty

1: occupied or about to be occupied next time stepQC Circumstance potential field value for passengers in Team C Distance between estimated cell and target cell of Team CEC,m Moving potential field value for passengers in Team C Rule of valuation and evolution shown in 3.3EC,w Waiting potential field value for passengers in Team C Rule of valuation and evolution shown in 3.3

3. Simulation model

The simulation model is based on a two-dimensional system with a square cell grid as the underlying structure. Twocategories of potential fields, the circumstance potential field and interaction potential field are constructed to trigger thepedestrian behavior. The circumstance potential field describes the pedestrians’ desire to get to their targets. The interactionpotential field for the three interactive effects is mentioned above. The potential fields work by setting potential field valueson the cells. A tendency proportion is defined to integrate the effect of these two potential fields. Thus, pedestrian behaviorin direction choice, adjustment and moving can be triggered.

3.1. Basic definition

According to ergonomics theory [35], the human body can be regarded as an elliptic basic unit (61 cm×45.6 cm). The cellsize, 0.45m on a side, partitions the lattice at the individual pedestrian level (Fig. 2). Pedestrianmovement can be performedby continuous update.

Pedestrian behavior is triggered by cell attributes setting and changing. Cell attributes are shown in Table 1. It showsthat for each pedestrian in Team C (who have the same target C), there will be three particular values in each cell, which arethe circumstance potential field value, moving potential field value and waiting potential field value. The last two can beregarded as interaction potential field values. Definitions of these potential fields are introduced in the following sections.

3.2. Circumstance potential field

The circumstance potential field is defined tomodel the circumstance effect on pedestrian desire. It is supposed that thereis a potential field in the pedestrian movement space that influences the pedestrians with a dedicated target or motive. Thecircumstance potential field acts on the pedestrians with a relative potential energy. The circumstance potential field valueof each cell can be evaluated by the energy cost (time, distance etc.) for moving to the final target cell. Thus, pedestriansmove from a cell with high potential energy to cells with a low potential energy. Fig. 3 shows the circumstance potentialfield distribution for pedestrians moving to exits. Pedestrians influenced by the corresponding circumstance potential fieldmove from cells with a high potential energy (dark color) to those with low potential energy (shallow color).

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Fig. 3. Circumstance potential field distribution for pedestrians moving to the exits.

(a) Moving potential field. (b) Waiting potential field.

Fig. 4. Interaction potential field.

The circumstance potential field is particular to pedestrians who have a dedicated target. Pedestrians with differenttargets have different circumstance potential fields. Since the circumstance potential field is usually related to the statedconfiguration of facility, it can be generated before the simulation based on the pedestrian’s movement environment.

3.3. Interaction potential field

The interaction potential field is defined to describe the latent effects in a particular area among pedestrians. Pedestriansset values to cells around according to special rules to generate the interaction potential field. The pedestrians who setinteraction potential field values are regarded as subjects. Thus cells around the subjects are defined as the effective areaΩrp(Fig. 4). The interaction potential field simulates positive and negative effects from other pedestrians, guiding the individualto act under a simulated decision. The interaction potential field generated by each individual is composed of two parts: amoving field generated during walking (Fig. 4(a)), and a waiting field generated during stopping (Fig. 4(b)). The former isfor modeling the follow effect and deterrent effect, and the latter is for the rejection effect.

The interaction potential field must be generated by pedestrians during movement. The interaction potential field is alsofor a particular pedestrian teamwith the same target, which is the same as the circumstance potential field. The interactionpotential field is generated by subject p in Team C0 according to the following procedure:

Step 1. Subject p decides the direction and instant speed on the next timestep t + 1;Step 2. Judge whether the subject pmoved on timestep t , if YES, skip to step 4, otherwise go to step 3;Step 3. Set the Add value of WPFV of cells in the effective area Ωrp of subject p as g(Ωrp);Step 4. Set the Add value of MPFV of cells in the effective area Ωrp of subject p as f (Ωrp);

where

Add value potential field value set by subject pWPFV waiting potential field valueMPFV moving potential field value.

Thus, the interaction potential field value for Team C0 can be set by cumulating the add values of all subjects in Team C0

and the present field value. On the other hand, the interaction potential field is supposed to evolve during the movement.Coefficients are defined to control the evolution process. The interaction potential field evolution procedure is as follows:

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Fig. 5. Tendency proportion.

Step 1. Check whether cell k is occupied, if YES, skip to step 3, otherwise go to step 2;Step 2. Set MPFVs of cell k as (1 − γm) × present value; set WPFVs for all the teams of cell k as (1 − γw) × present value;Step 3. Make cell k give ηm × present value of MPFVs to each neighboring cells; make cell k give ηw × present value of

WPFVs to each neighboring cells;Step 4. Cumulate all values set by all subjects of Team C0 in the current timestep;

where

γm/γw Decay coefficient of MPFV/WPFVηm/ηw Diffusion coefficient of MPFV/WPFV.

Thus, the performance area and power of the interaction potential field moves if the subjects move, and enhances anddiffuses if the subjects stop and wait, and decays or disappears if subjects leave.

3.4. Pedestrian movement decision

Tendency proportion in the Moore neighborhood (r = 1) is defined to integrate the effect of the circumstance potentialfield and interaction potential field (Fig. 5).

Tendency proportion of a pedestrian in Team C0 to make a decision in a direction can be described as a function of thecircumstance potential field, moving potential field, and waiting potential field (Eq. (1)).

PC0

ij = β11QC0 + β2

E ijC0,m

−

−Ck∈C0

E ijCk,m

+ β31EC0,w (1)

where

1QC0 Difference of circumstance potential field value (Team C0) between occupied cell and target cellE ijC0,m

MPFV (Team C0) of target cell∑Ck∈C0 E

ijCk,m MPFV (Team or Teams C0 interference C0) of target cell

1EC0,w Difference of WPFV (Team C0) between occupied cell and target cellβ1, β2, β3 Sensitivity coefficient.

Thus, pedestrians move to cells with the largest tendency proportion, which is an integrated effect of the individual desireof targets (reflected by the circumstance potential field value) and the interaction with others (reflected by the interactionpotential field value).

4. Simulation

4.1. Model performance comparison

Bi-directional experiments run on a circular lattice of 22.5 × 22.5 m. Two groups of pedestrians with equal numbersof 360 undertake bi-directional walking. Self-organization of lane formation [24,25] can be observed, which shows theeffectiveness of the presented model to simulate bi-directional pedestrian interaction. Fig. 6 shows the distribution of themoving potential field set by right → left pedestrians.

Fig. 7 shows the lane formation performance comparison of the presented model, the CA model [18], the Floor Fieldmodel [28] and the Social Force model [14]. Since it has a description of the latent follow effect and deterrent effect, thepresented model shows some characteristics on simulating the lane formation. First, the presented model reflects followbehavior towards pedestrians with the same direction effectively. The lanes formed by individual direction adjustment aremore natural as pedestrian behavior. Second, the moving potential field works for modeling the deterrent effect, which ishelpful to avoid ‘‘deadlock’’ under a relative high density of pedestrians. It is also effective on capturing the negotiationsduring walking in the real world.

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Fig. 6. Moving potential field of pedestrians walking from right to left.

(a) Presented model. (b) CA model. (c) Floor field model. (d) Social force model.

Fig. 7. Lane formation experiment comparison.

(a) For pedestrians from right to left. (b) For pedestrians from left to right.

Fig. 8. Circumstance potential field for two pedestrian teams.

Bottleneck walking experiments run on a lattice of 22.5 × 22.5 m with a wall in the middle. There is a door in the wallallowing one pedestrian to get through once. The circumstance potential fields are shown in Fig. 8.

50 pedestrians distributed on both sides (25 on each side) walk through the door to get to the other side of the wall.Bottleneck oscillation [25,26] can be observed. Fig. 9 shows the bottleneck oscillation performance comparison of thepresentedmodel and the social forcemodel. Thewaiting potential field reflecting the rejection effect is effective in describingpedestrian behavior when they walk through the bottleneck by turns, which is related to the waiting time of each group onthe same side.

4.2. Sensitivity coefficient performance

Sensitivity coefficients β1, β2 and β3 are supposed to reflect the relative relationship of the three potential fields.Experiments of bi-directional walking, bottleneck oscillation and evacuation run for the sensitivity coefficient performanceanalysis. Fig. 10 shows the Add value rule of the interaction potential field.

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(a) Presented model. (b) Social force model.

Fig. 9. Bottleneck oscillation experiment comparison.

(a) For bi-directional walkingexperiment.

(b) For bottleneck experiment. (c) For evacuationexperiment.

Fig. 10. Add value rule for three experiments.

(a) β2:β3 = 0:1. (b) β2:β3 = 1:0.

Fig. 11. Bi-directional walking experiment (density = 1.5 p/m2).

4.2.1. Bi-directional walking experimentThe experimental conditions are the same as in 4.1. The performance of sensitivity coefficients β2 and β3 is estimated

when the decay coefficient and diffusion coefficient are 0.5. Fig. 11 shows the instance status of the simulation test.The results show that: β2, as sensitivity coefficient of moving potential field, mainly affects the behavior of following

and collision prevention. Lane formation fails to be observed with β2 = 0 (Fig. 11(a)). Tendency of lane formation is moreobvious with larger β2 (Fig. 11(b)). β3, as a sensitivity coefficient of waiting potential field, mainly affects the bypassingbehavior in high density areas. Pedestrians lose patience with congestion with larger β3. The average speed is at the highestlevel when β2:β3 = 1:1. Deceleration happens for a high density in each direction caused by excessive lane formation withlarger β2 and also for intense collision between two groups caused by less evident lane formation with larger β3.

4.2.2. Bottleneck oscillation experimentThe experimental condition are the same as in 4.1. The performance of the sensitivity coefficients β1, β2 and β3 is

estimated when γm, ηm = 0.5, γw = 0.2 and ηw = 0.8. Table 2 shows the results.The results show that: β1 mainly affects pedestrians’ chosen direction. Pedestrians fail to move to the door if β1 = 0. But

a relative large β1 possibly leads to deadlock on the bottleneck due to the lack of negotiation between two groups. β2 mainly

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Table 2Sensitivity coefficient effect on bottleneck behavior.

β1:β2:β3 Total evacuation time (s) Average holding time (s) Proportion of block time (%)

1:1:5 315 11.2 431:1:10 315 10.88 381:0:5 382 9.55 522:1:5 450 12.77 662:0:5 715 11.38 71

Note: 1. Total evacuation time: time for all the pedestrians on both sides getting through the door.2. Average holding time: average time for pedestrians from the same side occupying the door continu-ously.3. Block time: accumulated time of nobody getting through the door.

Fig. 12. Waiting potential field.

(a) Scenario 1: beginning. (b) Scenario 2: beginning of second group. (c) Waiting potential field.

Fig. 13. Scenarios and waiting potential field.

affects the behavior of following and collision prevention. Blocks are easier to observe when β2 is 0. The total evacuationtime increases with larger β1 or smaller β2.

β3 mainly affects the ability of competition of pedestrians to occupy the door. There will be no bottleneck oscillationwith relative small β3. Tests show the sensitivity coefficients should satisfy the following condition to show bottleneckoscillation:

β1 = 0 and β2/β3 ≤ 1/5.

β3 is critical for bottleneck oscillation and it helps decrease the proportion of block time. Fig. 12 shows the distribution ofthe waiting potential field, whose coefficient is β3.

4.2.3. Evacuation experimentExperiments of exit choice run on a lattice of 22.5 × 22.5 m with three exits for evacuation. The circumstance potential

field is shown in Fig. 3. The performance of the sensitivity coefficientsβ1 andβ3 is estimatedwhen the decay coefficient is 0.5and the diffusion coefficient is 1. Two scenarios are considered in the experiments. Scenario 1 (Fig. 13(a)): 50 pedestriansbegin to move towards the exits from the original position. Scenario 2 (Fig. 13(b)): 50 pedestrians arrive at the exits andmake queues, then 30 s later, another 50 pedestrians begin to move and arrive (see Table 3).

The results show that: β3 is critical to pedestrians’ exit choice decision, reflecting whether the three exits can be equallyused. The waiting potential field is more powerful on the pedestrians with larger β3, thus pedestrians tend to move to

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Table 3Sensitivity coefficient effect on exit choice behavior.

Scenario 1 Scenario 2β1:β3 Evacuation time (s) (Max−Min)/total β1:β3 Evacuation time (s) (Max−Min)/total

1:1 55 0.56 1:1 87 0.341:3 53 0.42 1:3 80 0.221:5 49 0.36 1:5 81 0.22

Note: 1. Evacuation time: total time for all pedestrians to get through the exits.2. (Max − Min)/total: (the biggest number of pedestrians evacuated among the three exits − the smallestnumber of pedestrians evacuated)/total pedestrian number.

Table 4Time of lane formation with different parameters.

ηm ηw γm γw Time of lane formation (s)

0.2 0.20.5 0.5

650.5 0.5 38.50.8 0.8 25

0.5 0.50.2 0.2 250.5 0.5 38.50.8 0.8 50

Table 5Contrast of behavior performance.

η γ Total evacuation time (s) Average holding time (s) Proportion of block time (%)

0.5 0.5 370 8.89 480.8 394 17 581.0 445 9.4 62

Note: 1. Total evacuation time: time for all the pedestrians on both sides getting through the door.2. Average holding time: average time for pedestrians from the same side occupying the doorcontinuously.3. Block time: accumulated time of nobody getting through the door.

the exits with shorter queues, leading to an equal distribution of pedestrians on each exit and a shorter evacuation time.However, the effect of β3 tends to be weaker with increasing total pedestrian number.

4.3. Decay and diffusion coefficient performance

Decay coefficient γ and diffusion coefficient η, which are related to the environment and the behavior characteristics,reflect the development of the waiting andmoving potential field. Different behavior characteristics correspond to differentdecay and diffusion coefficients while modeling.

4.3.1. Bi-directional walking experimentThe experimental conditions are the same as in 4.2.1. The effects of the decay coefficient and diffusion coefficient on lane

formation are estimated when the sensitivity coefficients β2 and β3 are 1 (see Table 4).The results show that the time of lane formation is shorter with a relative larger diffusion coefficient and also with a

relative larger decay coefficient. This is reasonable because a higher diffusion coefficient helps individuals to keep followingthe pedestrians ahead and a higher decay coefficient weakens the latent effect.

4.3.2. Bottleneck oscillation experimentThe experimental conditions are the same as in 4.2.2. 100 pedestrians are generated at the beginning of the experiment

with 50 on each side. The performance of the decay coefficient and diffusion coefficient are estimated when β1 and β2 are1, and β3 is 5 (see Table 5).

Experiments show that a smaller diffusion coefficient or smaller decay coefficient leads to deadlock easily because pedes-trians tend to freeze instead of moving actively. A larger diffusion coefficient or larger decay coefficient leads to congestionin the bottleneck (proportion of block time increases).

4.3.3. Evacuation experimentThe experimental conditions are the same as Scenario 1 in 4.2.3. The performance of the decay coefficient and diffusion

coefficient is estimated when β1 = 1 and β3 = 5 (see Table 6).When the decay coefficient is stated, a decrease of the diffusion coefficient leads to a decrease of the pedestrians’

sensitivity to queue length, which causes a large difference of queue length among exits and a longer evacuation time.

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Table 6Contrast of evacuation performance.

γ = 0.5 η = 1η Evacuation time (s) (Max−Min)/total γ Evacuation time (s) (Max−Min)/total

1 49 0.36 0.8 54 0.520.5 48.3 0.36 0.5 49 0.360.2 57 0.46 0.2 52 0.14

Note: 1. Evacuation time: total time for all pedestrians to get through the exits.2. (Max − Min)/total: (the biggest number of pedestrians evacuated among the three exits − the smallestnumber of pedestrians evacuated)/total pedestrian number.

When the diffusion coefficient is stated, a larger decay coefficient also leads to a larger difference of queue length amongexits which prolongs the evacuation time.

5. Conclusion

The presented simulation model captures individual characteristics and collective behaviors which were once difficultto model. The follow effect, deterrent effect and rejection effect are considered in pedestrian interaction modeling. Theintegrated potential field make it simple and effective to model pedestrian decisions. The modeled pedestrians appear toexhibit reasonable intelligence and diversity, including the response to the circumstances and latent effects from others.

Bi-directional walking experiments and bottleneck experiments show the good performance of the presented model incapturing collective behavior traits in comparison with the classic model and experience data.

Coefficient experiments and results analysis show that the presented model is able to model various performances withdifferent coefficients. Sensitivity coefficients β1, β2 and β3 reflect the relative extent of effects in the circumstance potentialfield, moving potential field and waiting potential field. Therefore, adjustment of the sensitivity coefficients enables thesimulation model to capture pedestrian behavior under different circumstances flexibly. For example, the effect of self-organization on collective movement can be studied by setting β2 and/or β3. The performance of pedestrian waiting inqueues can be observed by setting β3. Decay coefficients γm and γw control the duration of the interactive effect amongpedestrians. Larger decay coefficients can be set to simulate pedestrian movement under blind situations, such as badvisibility caused by fire, which makes following more difficult. Diffusion coefficients ηm and ηw control the power to spreadthe interaction effect among pedestrians. A larger diffusion coefficient is helpful to simulate the movement of pedestrianswith high sensitivity to situational awareness. According to the coefficient effect, the model can be adapted to simulate avariety of pedestrian behaviors under different circumstances by adjusting the coefficients. Thus, the presented model isflexible for application in various situations.

The model provides effective methods and tools for pedestrian organization and safe design practices. Further researchhas to be done to perform more observations and to extend the parameter calibration and validation.

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