Modeling of Crowd Evacuation With Assailants via a ... - IEEE Xplore

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 17, NO. 9, SEPTEMBER 2016

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Modeling of Crowd Evacuation With Assailants via a Fuzzy Logic Approach Min Zhou, Hairong Dong, Senior Member, IEEE, Ding Wen, Senior Member, IEEE, Xiuming Yao, and Xubin Sun

Abstract—Modeling and analyzing the behaviors and characteristics of crowds in emergency is a challenging task with significant practical meanings. In this paper, a fuzzy logic approach is proposed to describe crowd evacuation behaviors, taking into account the effect of assailants. First, the microscopic pedestrian model and the assailant model are developed according to their different intentions in evacuation scenarios. Pedestrians are further divided into three categories depending upon whether they are affected by assailants. The individual’s behaviors are determined by the integration of recommendations of local obstacle-avoiding behavior, regional path-searching behavior, and global goal-seeking behavior with adjustable weighting factors, which are automatically adjusted based on the perceptual information obtained from the complex interaction with surrounding environments. Then, the proposed pedestrian model is validated by comparing the simulated fundamental diagram with a large variety of empirical and experimental data. Finally, simulations in a hall with a single exit are implemented. It is shown that the model can truly reappear typical collective phenomena such as “arching and clogging” and “faster-is-slower effect.” The variations of the model and scenario parameters, such as pedestrian’s desired speed, exit width, assailant’s desired speed, and duration of attack, greatly influence the evacuation efficiency. In addition, a novel “circuity phenomenon,” i.e., pedestrians will give up the direction of goal when they encounter assailants or they see assailants and, at the same time, perceive a very crowded exit, is observed in crowd evacuation simulations. Index Terms—Crowd evacuation behavior, assailant, fuzzy logic, perceptual information.

I. I NTRODUCTION

T

HE gathering of people in public places such as metro stations, theme parks and shopping centers has become a universal phenomenon. It brings many kinds of potential lifethreatening (for example, overcrowding and trample) to people themselves, and also brings challenges to planners and administrators. Once emergency situation happens, it may result in Manuscript received August 24, 2015; revised December 16, 2015; accepted January 11, 2016. Date of publication March 25, 2016; date of current version August 25, 2016. This work was supported by the National Natural Science Foundation of China under Grant 61322307 and Grant 61233001. The Associate Editor for this paper was F.-Y. Wang. M. Zhou and H. Dong are with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China (e-mail: [email protected]; [email protected]). D. Wen is with the Center for Military Computational Experiments and Parallel Systems Technology, National University of Defense Technology, Changsha 410073, China (e-mail: [email protected]). X. Yao and X. Sun are with the School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing 100044, China (e-mail: xmyao@ bjtu.edu.cn; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TITS.2016.2521783

inestimable losses because of crowds’ irrational behaviors which caused by anxiety or even panic during evacuation process. For this reason, concerns about understanding the characteristics of crowd dynamics under normal and emergency evacuation situations have grown rapidly. Generally, the research methods of crowd evacuation mainly include real experiments and model based simulations. Experimental researches in bottleneck [1], classroom [2] and high-rise building scenarios [3] have revealed many evacuation behaviors and characteristics under normal situations. However, investigation of crowd motion by real experiments in case of an emergency evacuation is very difficult to realize because of ethical and moral questions. During the last few decades, various simulation models have been composed to study crowds evacuation dynamics in normal and emergency scenarios. Social force model, treating pedestrians as force-driven particles, have been proposed by Helbing [4] for the evacuation problem of panicking pedestrians. Varas et al. [5] used a cellular automaton model to simulate the process of evacuation of pedestrians in a room with fixed obstacles. Then, Liu et al. [6] modified cellular automaton model to simulate an evacuation experiment conducted in a classroom with obstacles. Other models, such as game theory model [7], [8], lattice gas model [9], [10] and optimization-based feedback control [11], are widely used for the study of evacuation problems in the public places. In addition, evacuation behaviors under different scenarios such as smoke filled road tunnels [12], burning hotel [13], high-rise building [14], and bioterrorism in micro-spatial environments [15] have been studied by using different approaches. These results demonstrate that affecting modes and magnitudes on crowd behaviors varied considerably with scenarios and corresponding environments. Meanwhile, research achievements available in literatures also provide many helpful advices for guiding the safe evacuation. However, many attacks such as shooting and assailant events occurred every year all over the world, which often caused huge casualties and property losses. For instance, 32 people were killed and 17 others wounded (another six people were injured escaping from classroom windows) in the Virginia Tech massacre on the campus of Virginia Polytechnic Institute and State University in Blacksburg, Virginia, United States, on April 16, 2007 [16]. A lone gunman, Derrick Bird, killed 12 people and injured 11 others before killing himself in Cumbria, England, on June 2, 2010, which is one of the worst attacks involving firearms in British history [17]. In addition, 29 civilians were killed and more than 130 others injured in a railway station violent terrorist attack in Southwest Chinese city of Kunming on March 1, 2014 [18]. Based on analyses of these

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Fig. 1. The sample chart of space representation. (a) The geometrical description of a pedestrian and his/her physical space, Pn and G represent the location of the current pedestrian and his/her goal, respectively. (b) Discretization of visual field based on five radial directions, i.e., left (l), front left (fl), front (f), front right (fr), and right (r).

attacks, it is shown that human factors such as weakness of safe consciousness of residents, irrational evacuation behaviors, the negligence of management and unreasonable architecture design of buildings may be the major causes of greater damages of attacks. So far there are few articles focusing on the research of the effect of attackers on crowd evacuation. The aim of the present paper is to investigate the effect of assailants on crowd evacuation behaviors in a hall scenario by using a fuzzy logic approach, and ultimately provide useful advices for designers and managers. Considering the fact that the information human get from environments are perception-based information rather than measurement-based information in most situations [19], [20]. It is difficult to quantify the magnitude of environmental stimuli in real-life scenarios because a pedestrian’s perceptions in a specific environment vary from one individual to another. With this in mind, it is appropriate for researchers to model and analyze human behaviors and characteristics using linguistic information (words) rather than quantitative values. The perception-based information is often neglected in this area of researches. Similarly, the inter-relationship between pedestrian’s dynamical behavior and pedestrian’s perception towards the surrounding environment is rarely considered in previous studies. As an extension of the crisp set theory, fuzzy sets theory proposed by Zadeh [21] provides a useful tool to model and describe the uncertain nature of perception-based information. This theory has been rapidly developed since it was put forward. It has been widely used in decision making [22], performance evaluation [23], predictive control systems [24] and so on. It’s worth mentioning that besides fields enumerated above, another fontal and crucial field is the complex systems, which has made many achievements in modeling, analysis, control and evaluation of complex systems [25]–[30]. Fuzzy logic, as the theory of fuzzy sets and an approximate reasoning methodology, possesses the capability of operating on and reasoning with perception-based information. It provides a scientific approach to the management of pervasive reality of fuzziness and vagueness in human cognition [31], [32]. A fuzzy logic approach, compared with other methods, is highly robust in coping with

the uncertainty and imprecision that are inherent in perception information. It also provides a scientific approach for the management of pervasive reality of fuzziness and vagueness in human cognition. During the past five decades, fuzzy logic approach have been widely used in fields of forecasting [33], data interpretation [34] and robot navigation [35], [36] etc. It’s worth mentioning that fuzzy logic based modeling and simulation have been implemented in analyses of pedestrian dynamical behaviors under normal and panic scenarios [19], [20]. By using fuzzy logic, human spirit and perception can be computed and represented mathematically. Nasir et al. [19] proposed a genetic fuzzy system to model and simulate the pedestrian’s steering behavior in a built environments. Mauro et al. [20] proposed a fuzzy logic-based behavioral model for crowd evacuation, which incorporates fuzzy perception and anxiety embedded in human reasoning. And some of fuzzy inference systems are built to provide the direction of motion, delay in egress, and choice of exit. In this paper, the fuzzy logic-based model is proposed to take full advantage of perception-based information and human experience and knowledge, and then make rational decisions in a crowd evacuation scenario, taking into account the effect of assailants. This work is organized as follows. In Section II, we present an overview of the proposed model based on a fuzzy logic approach. The modeling processes of pedestrians and assailants are proposed in Sections III and IV, respectively. Section V simulates the behaviors of crowds and assailants in the hall evacuation scenario, and analyzes the influences of the parameters involved in the proposed models and scenarios. Conclusion are drawn in Section VI. II. OVERVIEW OF THE P ROPOSED M ODEL In order to study crowd evacuation behaviors at the microscopic level, considering the effect of assailants, the first step is to construct models for pedestrians and assailants, respectively. Previous studies have shown that vision is the main source of information used to control pedestrians’ motion [37], [38]. In this study, the visual field (V F ) of individual n, indicated by

ZHOU et al.: MODELING OF CROWD EVACUATION WITH ASSAILANTS VIA A FUZZY LOGIC APPROACH

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Fig. 2. The overall structure of the fuzzy-logic-based model, α (and α ˜ i ), V (and V˜i ) and δ˜ao (and δ˜sp , δ˜sg ) represent turning angles, movement speeds, and weighting factors, respectively.

the blue shaded area in the Fig. 1(a), is defined as a fan-shaped region with a radius of dmax = 5 m and a central angle of 2φ = 170◦ [38], [39]. The individual is seen as a person in a 3D environment with the radius of rp . Each individual n is characterized by its current position Pn , direction ξn , and movement speed Vn . From current position (xn , yn ) of the decision maker, a goal (the purple dot), which represents the place where pedestrians want to reach, lies in the “goal angle” γg at a “goal distance” dg . We adopt a radial-based method for representation of space [40]. As shown in Fig. 1(b), the visual field is divided up into 5 similar but not identical sectors, which are marked as left (l), front left (fl), front (f), front right (fr) and right (r) from left to right, and occupied the central angles of 40◦ , 30◦ , 30◦ , 30◦ , and 40◦ , respectively. The number of sectors is determined by the trade-off of model precision and complexity [19], [39]. Along with the predefined space representation method, a pedestrian’s motion states can be updated by the combination of goal details and environmental information which he/she actually perceived in all sectors of visual field. The general structure of the fuzzy logic-based model is shown in Fig. 2. This model consists of four fuzzy inference systems, which are used to describe obstacle-avoiding behavior, path-searching behavior, goal-seeking behavior and weighting’s distribution principle, respectively. The input information mainly include obstacles information, assailants information, pedestrian information, goals information and so on. For instance, the closest distance between the decision maker and obstacles dominates the obstacle-avoiding behavior, and the distance and speed of the pedestrian who walked in the opposite direction of the decision maker greatly influence the path-searching behavior. The output information of first three systems are intermediate results of turning angles and movement speeds, the last system are weighting factors which are used to decide the importance degree of each behavior under certain surrounding conditions. The magnitudes of final motion states are determined by integration of three recommendations with adjustable weighting factors. The number of linguistic fuzzy sets, which are used to cover the discourse of universe of antecedents and consequents, decides the accuracy of fuzzy logic systems. For a certain structural model, the time complexity rises exponentially as the number of input fuzzy sets increases. In this study, we choose two, three, or five fuzzy sets

to represent state variables in order to trade-off the computing efficiency and accuracy. On the whole, the values of parameters of the membership function mainly depends on a combination of a large variety of empirical and experimental data and human experience and knowledge. It is also relate to the universe of discourse of variable, the predefined number of fuzzy sets used to cover the universe of discourse and the knowledge and empirical data about the variable. For the rule bases of fuzzy inference systems, the establishment of IF-THEN rules is based on human experience and knowledge. The intention of pedestrians is to evacuate from dangerous areas and survive, while the assailant tries to pursue and attack as many pedestrians as possible. Considering the difference of intentions and surrounding environments between assailants and pedestrians, we proposed different fuzzy logic-based models for assailants and pedestrians, respectively. The following reasonable model assumptions that relate to study modeling problem are made in order to simplify and articulate the proposed model. • All the individuals are unaware of global information of environments, but aware of regional information in their visual field and goal details. • Individuals can change between any two predefined states in a relaxation time τ of 0.5 s. • An assailant is a person armed with close-range weapons such as knife and sword. And the lengths of weapons are ignored in simulations. • The arm lengths of assailants are set as 0.75 m [41]. • Pedestrians’ defensive behaviors are not taken into account during evacuation simulations. • Security guards can stop the attack. But, we only concern the time (duration of attacks) they spend on stopping an attack. Their motion behaviors, the way of stopping an attack, the mode of interaction with other individuals and so on are all ignored during evacuation simulations. III. T HE M ODEL OF P EDESTRIANS The behaviors of pedestrians are mainly effected by the location of goals and distribution of their kind, assailants and obstacles. All pedestrians are assumed to know the locations of goals in advance. According to different surrounding environments of pedestrians, they are divided into three categories.

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Fig. 3. The sample chart of three categories of pedestrians. rA represents the radius of influence of assailants.

The sample chart of three categories of pedestrians is shown in Fig. 3. Category 1: Pedestrians are outside the scope of influence of assailants, as represented by P1 in Fig. 3; Category 2: Pedestrians appear in the scope of influence of assailants but cannot see assailants, such as P2 and P3 ; Category 3: Pedestrians see assailants, or pedestrians have seen assailants but not too far away from them, such as P4 . Fig. 4. Transition probabilities among different categories of pedestrians.

In general, the decision making process of category 1 pedestrians can be described as follows. Firstly, the decision maker scans the visual field and selects the goal based on a subjective consideration or just herding behaviors. Then, he/she walks along the direction of the goal and avoids collision with front pedestrians and obstacles with an appropriate movement speed and direction. For category 2 pedestrians, they are aware of the danger but don’t know the specific information of assailants. So, they may quicken their pace along the direction of goal as far as possible while avoid collision with other objects. If assailants appeared in the visual field of the decision maker, the last category will stay away from the assailant’s area to escape the attack of assailants taking the effects of goals and front pedestrians and obstacles into account. When the crowd density of pre-selected exit is too large to evacuate safely, they will give up the direction of the goal, and thus reduce the probability of being catched. Although avoid collisions strategies are always considered during the whole evacuation process, there may be some collisions with other pedestrians because of their irrational judgements and nervous psychology. It’s worth mentioning that pedestrians can transit from one category to another or remain constant with the change of time and surrounding environment by a certain predefined way. The transition relationships among them are shown in Fig. 4. With the approaching of assailants, category 1 pedestrian enters

the scope of influence of assailants and begins to realize the dangers, then transforms into category 2 with the probability of Pc1→c2 . Pedestrians can transit mutually between category 2 and category 3 with the probabilities of Pc2→c3 and Pc3→c2 , respectively. But category 1 pedestrian can’t transform directly into category 3 because the value of assailants rA is far larger than the radius of visual field dmax . Once pedestrians sensed or saw assailants, their can’t transform back into category 1 no matter how environments change because the consciousness to guard against dangers to life has formed and did not vanish until dangers were released. The transition probabilities among different categories are then given by following equations: (dmax − dap ) (1) , dmax dap rA Pc1→c2 = ε exp κ1 (2rp − dap ) Pc2→c3 = (1 − ε) exp , 2rp dap dmax κ2 (2) (2rp − dap ) , 2rp dap dmax Pc3→c2 = 1 − ε exp κ3 (3) Pc2→c1 = Pc1→c3 = Pc3→c1 = 0.

(4)


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TABLE I I NFERENCE RULES R0 FOR L OCAL O BSTACLE -AVOIDING B EHAVIOR

Fig. 5. Membership functions for (a) turning angle, (b) movement speed, (c) the closest distance, (d) negative energy, (e) goal distance, and (d) weighting factor.

The transition probabilities of remaining constant, i.e., Pci→ci , (i = 1, 2, 3), must meet the following equality constraint: 3 i=1

Pc1→ci =

3 i=1

Pc2→ci =

3

Pc3→ci = 1

(5)

i=1

where the variable dap represents the distance between the pedestrian and assailant, the parameter ε is zero if there is no assailant appeared in the visual field of the pedestrian (A ∈ V FPn ), and is otherwise equal to one. The parameters κ1 , κ2 , and κ3 are constant and their values are specified as 2, 8 and 1, respectively. The domains of above functions are restrained by the definitions of pedestrians’ and assailants’ parameters. Next, we present the modeling processes of three categories in detail. A. Category 1 Pedestrians Crowd evacuation behaviors are determined by integration of local obstacle-avoiding behaviors, regional path-searching behaviors and global goal-seeking behaviors with adjustable weighting factors. Without the effects of assailants, pedestrians just need avoid collision with their kind and obstacles appeared in the visual field, while moving toward the direction of the goal with an appropriate movement speed. 1) The Local Obstacle-Avoiding Behavior: The local obstacle-avoiding behavior will make pedestrians avoid front obstacles when the distances between decision maker and obstacles are close in a local scope. A fuzzy inference system is used to describe this behavior. The antecedents and consequents of the system are the closest pedestrian-obstacle distances in each sectors (replaced by dlo , dfo l , dfo , dfo r and dro from left to right) and turning angle (α1 ) and movement speed (V1 ), respectively. The turning angle and movement speed are represented by five fuzzy sets {Large-Neg, SmallNeg, Zero, Small-Pos, Large-Pos} and three fuzzy sets {Stop, Slow, Fast}, with the trapezoidal membership functions shown in Fig. 5(a) and (b), respectively. Where “Neg” and “Pos” turn the pedestrian to left and right directions, respectively. The distances d∗o are represented by two fuzzy sets {Near, Far},

with the trapezoidal membership functions shown in Fig. 5(c), where ∗ ∈ {l, f l, f, f r, r}. The definition of ∗ is same as above without special request in upcoming sections. The formulation of the fuzzy inference system of the local obstacle-avoiding behavior is summarized as follows: α1 (6) = R0 dlo , dfo l , dfo , dfo r , dro V1 32 (or 25 ) IF-THEN rules (R0 ) are constructed in Table I to guide the pedestrian to avoid obstacles. An example of rule is as follows. R05 : IF dlo is Near and dfo l is Near and dfo is Far and dfo r is Near and dro is Near, THEN α1 is Zero and V1 Fast. A pedestrian tends to have a smooth and regular angular displacement, rather than a sudden change of direction [19]. So, these rules are established in a way that a pedestrian inclines to walk along the current direction in case of having the equal pedestrian-obstacle distance in all five sectors. 2) The Regional Path-Searching Behavior: The regional path-searching behavior drives a pedestrian to the safest path (i.e. minimum negative energy sector) considering the impact of surrounding environments in a regional scope. The size of negative energy in each sector (N E ∗ ) is decided by the weighted sum of impact of obstacles (OI ∗ ) and risk for collision with pedestrians (CR∗ ). The impact of an obstacle imposed on the decision maker will differ depending on the visual angle occupied by obstacle and the closest distance between the decision maker and it, which are denoted by φ∗oi and d∗oi (illustrated in Fig. 6(a)), respectively. In this paper, the definition of obstacle is that any objects appeared in the individuals’ visual field. It usually includes walls, tables, columns and so on. The formulation of a fuzzy inference system of OI ∗ for an obstacle is summarized as follows: OIi∗ = R1 (φ∗oi , d∗oi )

(7)

The general principle of OI rule set is that an obstacle which has nearer distance d∗oi and larger occupied angle φ∗oi brings larger OI for the decision maker. So the detail fuzzy rules of R1 are omitted in this section. The whole impact of obstacles in one sector is ∗ ∗ = OI (8) OI i i∈S ∗

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TABLE II I NFERENCE RULES R4 FOR G LOBAL G OAL -S EEKING B EHAVIOR

Fig. 6. Illustration of the decision maker Pn facing (a) two obstacles: one is a wall appeared in the left and left-front sector and another is a column in the right sector and (b) two pedestrians: one appeared in the left-front sector and another in the right-front sector. ∗

is the defuzzification of OI ∗ , and i = 1, 2, . . . , M where OI i i represents the number of obstacles in sector ∗ (S ∗ ). Collision risk is defined as the possibility of a collision with other pedestrians who appeared in the visual field of the ∗ decision maker. It is determined by the variables, Vj∗ and θpj ∗ (illustrated in Fig. 6(b)), where dpj is the distance between the decision maker and a nearby moving pedestrian j in the sector ∗ is defined as the ∗ of visual field, Vj∗ is the speed of j. θpj angle between the movement direction of a pedestrian j and the decision maker. The formulation of a fuzzy inference system of CR∗ for a pedestrian is summarized as follows: ∗ CRj∗ = R2 d∗pj , Vj∗ , θpj (9) The general principle of CR rule set is that the output of CRj∗ is low if a opposite pedestrian deviated from the decision maker, had a far relative distance or moved with a low speed. Conversely, a nearby pedestrian brings high risk if he/she walked toward the decision maker with a big speed. Similarly, the detail fuzzy rules of R2 are omitted in this section. The whole collision risk of pedestrians in one sector is ∗ = ∗j CR CR (10) j∈S ∗ ∗

j is the defuzzification of CR∗ , and j = 1, 2, . . . , N where CR j represents the number of pedestrians in sector ∗ (S ∗ ). The rule set of regional path-searching behavior is similar to R0 , with d∗o replaced by N E ∗ . The formulation of the fuzzy inference system is summarized as follows: α2 (11) = R3 (N E l , N E f l , N E f , N E f r , N E r ) V2 where N E ∗ is the normalization of N E ∗ , i.e., N E∗ =

max{N E} − N E ∗ max{N E} − min{N E}

The magnitude of N E ∗ in each sector is decided by the weighted sum of OI ∗ and CR∗ . ∗ + (1 − kw ) · CR ∗ N E ∗ = kw · OI

(12)

where kw ∈ [0, 1] represents the weighting factor, which is used to adjust the size of influence of OI and CR. In general, moving objects brings more negative energy than stationary objects to the path-searching behavior because of the underlying nondeterminacy of moving speeds and directions. That is, the value of kw is set to greater than 0.5. 3) The Goal-Seeking Behavior: The goal-seeking behavior is a kind of global behavior which reflects a tendency that the decision maker always moves in directions to his/her goal regardless of external environments. It is determined by the goal angle γg and goal distance dg . The goal angle γg is represented by five fuzzy sets {Large-Neg, Small-Neg, Zero, Small-Pos, Large-Pos}, with the trapezoidal membership functions similar to Fig. 5(a), and the goal distance dg by two fuzzy sets {Near, Far}, with the trapezoidal membership functions shown in Fig. 5(e). The formulation of the fuzzy inference system of the global goal-seeking behavior is summarized as follows: α3 (13) = R4 (γg , dg ) V3 A total of 10 (or 5 ∗ 2) IF-THEN rules (R4 ) are constructed in Table II to motivate the pedestrian to walk in the direction of goal. An example of rule is as follows. R43 : IF γg is Small-Pos and dg is Near, THEN α3 is SmallNeg and V3 Slow. The rule set R4 will dominate the decision maker to reduce the speed and turn to the goal direction sharply without missing the goal when the pedestrian is near to but not facing the goal. Conversely, facing the goal, he/she moves freely along the goal direction with fast speed. 4) Integration of Multiple Behaviors: The final turning angle α and movement speed V of the decision maker are integrated with the recommendations of obstacle-avoiding behavior, pathsearching behavior and goal-seeking behavior by using the weighted average method. ⎧

δ sg ·α

3 ⎪ ⎨α = δao ·α

1 +δsp ·α 2 + δao +δsp +δ sg (14)

·V 2 +δ sg ·V 3 ⎪ ⎩V = δao ·V 1 +δsp

δao +δsp +δsg

where represents the crisp value of the counterpart fuzzy set which is calculated by using the Center-of-Gravity


TABLE III I NFERENCE RULES R5 FOR W EIGHTING ’ S D ISTRIBUTION S YSTEM

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C. Category 3 Pedestrians Under the influence of assailants, category 3 pedestrian stays away from assailants’ area so that they can escape the attack of assailants. Similarly, the occurrence of assailants only affects the regional path-searching behavior. Compared with other pedestrians, assailants bring more collision risk for the regional path-searching behaviors. So, the CR of one sector is redefined as follows, ∗ + kc · ∗ ∗ = CR CR (17) CR j l j∈S ∗

defuzzzification method [42], and weighting factors δao , δsp and δsg are ascertained by following fuzzy inference system, ⎡ ⎤ δao ⎣δsp ⎦ = R5 dfo , N E f , dg (15) δsg The values of weighting factors δao , δsp and δsg determine the degree of effect of each behavior on the final results, which are represented by three linguistic fuzzy sets {Small, Middle, Large}, with the trapezoidal membership functions shown in Fig. 5(f). For example, if dfo is near, the decision maker will avoid the front obstacle first, rather than seek the goal. So the weighting factor of the local obstacle-avoiding behavior is much big then other behaviors. An example of weighting’s distribution rule is described as follows. R52 : IF dfo is Near and N E ∗ is Low and dg is Far, THEN δao is Large and δsp is Small and δsg is Small. Three behaviors are coordinated and restrained mutually based on rule set R5 as shown in Table III, so that pedestrians can arrive at their goals successfully, while avoiding obstacles and other pedestrians appeared in their path. B. Category 2 Pedestrians When a pedestrian perceives the existence of assailants, his/her psychological states will change and even get into anxiety or panic. And therefore, the regional path-searching behavior will be affected, contrasting with category 1 pedestrian. The category 2 pedestrians may accelerate the movement speed to evacuate from potential danger areas. V2 = (1 − kp ) · V2 + kp · Vmax

(16)

where the meaning of V2 is same as above, Vmax represented the maximum speed, and kp ∈ [0, 1] is defined as a panic coefficient, which reflects the degree of panic of the pedestrian. Researches on the socio-psychological field found that people will move or try to move considerably faster than normal when their are in a panic [4], [43], [44]. As a consequence, the pedestrian’s speed is proportional to the value of kp , but it is not bigger than Vmax . Except the regional path-searching behavior, other behaviors and weighting’s distribution system of category 2 pedestrians are the same as category 1. This means that the rule sets of these fuzzy inference systems are identical with Tables I–III.

l∈S ∗

where the first part of right of the equal sign is same as the (10), the second part describes the collision risk that derived from assailants, l = 1, 2, . . . , Q represents the number of assailants appeared in each sector of visual field, kc is a scaling factor that indicates the size of collision risk produced by assailants relative to pedestrians. Its value is much bigger than 1. Compared with category 2 pedestrian, the degree of panics will increase sharply when pedestrians see the assailants. Category 3 pedestrian may move with greater movement speed to escape the attack of assailants and evacuate from dangerous areas. V2 = 1 − kp · V2 + kp · Vmax

(18)

where the definition of kp and Vmax are exactly the same as (16). The value of kp in (18) is larger than kp in (16). IV. T HE M ODEL OF A SSAILANTS The behaviors of assailants are mainly effected by distribution of pedestrians and obstacles. However, the location of security exits normally aren’t given too much consideration. In general, the dynamical process of assailants can be described as follows. Firstly, an assailant scans the visual field, finding the candidate object in each step. Then, he/she pursues the selected object with an appropriate movement speed and direction, while avoiding collision with front obstacles. Finally, when the selected object is attacked, the assailant will move on to the next candidate until all objects are attacked or evacuated. The local obstacle-avoiding behavior of assailants is similar with pedestrians. As the goal of assailants is to pursue and attack pedestrians as many as possible, they will select paths based on the distribution of pedestrians with certain tactics. This process is similar with the target (prey) selection of predator [45]–[49]. There are three simple tactics chosen by predator: attack nearest individual, attack the most peripheral individual, and attack the most central individual [48], [49]. We introduce these tactics to study the target selection and pursuit behaviors of assailants. The nearest pedestrian is simple the one who is the closest to the assailant. In order to determine which pedestrian is most peripheral or central, the concept of peripherality is used to measure it. Peripherality of individual i is defined as the length of Pi [47], 1 ˆ Pi = (19) dn ; G = {n ∈ V FA ; n = i} |G| n∈G

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where i is the observed current pedestrian, n is a pedestrian located in the visual field except i, dˆn = dn /dn is the unit vector pointing from the current position of the observed pedestrian to the current position of the assailant, G is the set of pedestrian n. The pedestrian that is the nearest is the one whose distance from the assailant is the smallest in the visual field: dmin = min dn ; n∈T

T = {n ∈ V FA }.

(20)

Fig. 7. The unidirectional pedestrian flow walking from left to right in a corridor scenario. The green box represents a measurement segment.

The pedestrian that is the most peripheral is one with the highest measure of peripherality: Pmax = max Pn ; n∈T

T = {n ∈ V FA }.

(21)

The pedestrian that is the most central is one with the lowest measure of peripherality: Pmin = min Pn ; n∈T

T = {n ∈ V FA }.

(22)

Compared with simple tactics, a rational complex tactic is to select the most attractiveness sector firstly, then choose a target in the selected sector based on above simple tactics. The attractiveness is defined as follows: A∗ =

d˜∗aj 360 · N ∗ · e− ka π · θ∗ · d2max ∗

(23)

j∈S

where N ∗ denotes the number of pedestrians in each sector S ∗ , θ∗ represents the central angle of each sector S ∗ , d˜∗aj denotes the distance between the decision maker and pedestrian j, and ka is a constant which reflects the magnitude of the effect of distance on attractiveness. We can see from equation (23) that the more the pedestrians and the nearer the distance, the bigger the attractiveness will be in one sector. For simple tactics, the negative energy of the sector will set as 0 if the selected pedestrian is located in this sector, other sectors are set as 1. For the complex tactic, the N E is replaced by attractiveness A as the critical factor of the path-searching behavior. And its rule set is similar with those described in above section, with N E ∗ replaced by A∗ . If there are no pedestrians appeared in the visual field of the assailant, the distance (peripherality) or attractiveness will set as +∞ or 0, respectively. It means that all sectors are set as same values, and the assailant is recommended to walk along the current direction. After the object is selected, the global goal-seeking behavior makes assailants to pursue pedestrians. For simplicity, we assume that the global goal-seeking behavior for assailants is same as pedestrians. The rule set of weighting’s distribution ∗ system is similar to R5 , with N E ∗ replaced by A for complex tactic. If there are no pedestrians appeared in the visual field of an assailant, i.e. the assailant without any candidate objects, the rule set of global goal-seeking behavior defined above will not be implemented successfully. In this situation, we assume that the global goal-seeking behavior dominates them to slow speed and turn a certain angle,while looking for possible objects. In addition, they will walk along the direction of goal when no pedestrians are found after a full scale search.

Fig. 8. Density–speed relation in unidirectional flow.

In this paper, a pedestrian will be considered attacked by an assailant if the distance d∗aj is less than the assailant’s arm length. Meanwhile we assume that once pedestrians are attacked, their will fall down and become obstacles immediately. V. S IMULATIONS AND R ESULTS In this section, we first validate the aforementioned fuzzy logic-based models by comparing the basic density-speed relation of unidirectional pedestrian flow with published empirical data in a corridor scenario. Then two case of simulation, involving crowd evacuation with and without assailants, are conduced in a large hall scenario. The effects of different parameters, such as pedestrian’s desired speed, exit width, and assailant’s desired speed, on evacuation efficiency are analyzed based on these simulations. A. Simulation of Unidirectional Pedestrian Flow At first, we perform the simulation of unidirectional pedestrian flow in a corridor scenario. It is used to measure the speeddensity relation which is known as the fundamental diagram obeyed by pedestrian dynamics. The corridor is 20 m long and 4 m wide with periodic boundary conditions as shown in Fig. 7. A measurement segment of 4 m × 4 m is set in the middle of the corridor (the green box in Fig. 7). The global density of the corridor is controlled by adjusting the total number N at initial time, and the number of pedestrians is varied from 0 to 240 in this simulation. A fixed number of pedestrians with random directions are scattered in the hallway without overlap between each other. Their desired speeds are assumed to be Gaussian


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Fig. 9. Typical stages of the evacuation dynamics: (a) beginning evacuation (t = 0); (b) middle stages; (c) end stage of evacuation with only a few evacuating pedestrians.

distributed with mean value 1.34 m/s and standard deviation 0.26 m/s (V 0) [53]–[55]. Pedestrians cross the corridor from the left to the right hand side, and reenter the hallway from left-hand boundary once they are quitted from the right-hand boundary. In this study, the desired speed is defined as a speed that an individual wants to achieve in free movement state. The setting of a certain value is realized through adjusting rule sets and parameters of membership function of variables. Take the speed for example. According to the rule sets summarized above, we assume that the desired speed of category 1 pedestrian is “slow” in free movement state, and the corresponding crisp value is 1.34 m/s. We adjust the values of parameters Vb , Vc , Vd , Ve , Vf (shown in Fig. 5(b)) to make the degree of membership satisfying the constraints of μslow (1.34) = 1 and μfast (1.34) = μstop (1.34) = 0. For other variables, we adopt the same strategy unless otherwise specified. We use the method introduced by Ref. [54] to measure the average speed and density. The results of speed-density relation (bright blue circles) are shown in Fig. 8. It can be found that the tendency of the fundamental diagram is consistent with that derived by the former researchers [50]–[52] at the density domain 0 < ρ < 3 p/m2 . When the density is below 0.5, pedestrians will move at a desired speed because of the adequate space and slight effects of other pedestrians. The average speed decreases obviously with the increase of density. Further, the crowd almost remained stationary when the density exceeds the critical condition. B. Simulation of Crowd Evacuation The next simulation is carried out in a square hall by using the proposed pedestrian model, which scale is 15 m × 15 m with an exit of W = 1 m in the middle of the wall. The initial number of pedestrian is N = 200, they are randomly distributed in the hall. Their desired speeds follow a Gaussian distributed with mean value 1.34 m/s and standard deviation 0.26 m/s (V 0). Fig. 9 displays the snapshots of evacuation dynamics initially with 200 pedestrians at different stages. Firstly, all pedestrians walk towards the exit at a desired speed. In the middle picture, a half-circle jamming configuration in front of the exit is easy to spot. At last, the remanent part of pedestrians evacuate from the room in an orderly manner. The simulation results of the proposed model are in accord with social force model introduced by Helbing et al. [4].

Then we conduct comparative simulations to illustrate the effect of assailants in the same hall scenario. There is an assailant appeared in a random location of the hall with the desired speed of “Very Fast.” And the desired speeds of three categories of pedestrians are set as “Slow,” “Fast”, and “Very Fast,” respectively. The fuzzy operator of “Very” is defined as [Very Fast] [Fast]2 . The states of an assailant are determined by the model proposed in the previous section. Pedestrians, according to their surrounding environments, are automatically divided into three categories. And different kinds of models are used to update their movement speeds and directions. Other settings are entirely the same as the above simulation. Typical results of crowd evacuation dynamics with an assailant are shown in Fig. 10. The middle picture shows that a number of pedestrians are attacked and fell down in the middle of the room, and the rest of pedestrians are competing to evacuate from the hall with the larger desired speed. The reason for this phenomenon is that the assailant attacks pedestrians from behind with a faster speed, and these pedestrians can not see the assailant and escape the attack in time. In addition, a novel “circuity phenomenon” that pedestrians (as shown in the purple ellipse region of Fig. 10(b)) who encountered the assailant choose the direction of relatively safe region rather than the exit directly is observed in simulations. As shown in Fig. 10(c), many pedestrians are attacked near the exit. This is because all pedestrians want to evacuate from hall as soon as possible, and more and more pedestrians gathered near the exit, which lead to jams and decrease the success rate of evacuation in turn. In Fig. 11, we plot the evacuation time T versus pedestrian’s desired speed Vp for different scenarios and models. The pedestrian’s desired speed are varied from 0.6 m/s to 4 m/s. The simulation results derive from averaging the values of repeated simulations with the same model parameters. The following results are got by the same way, unless otherwise stated. The green dotted line in Fig. 11 is the result of simulations of crowd evacuation using the proposed pedestrian model in a hall scenario without the effect of assailants, which shows a similar changing trends with the results of Helbing et al. [4] and Song et al. [56]. The red chain line reflects the relationship between T and Vp under the effect of an assailant. It can be found that the evacuation time T is less than other scenarios. This is because a number of pedestrians are attacked and fell down, who don’t need anymore evacuation time. And then the mean degree of congestion of the hall is reduced. But meanwhile

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Fig. 10. Typical stages of the evacuation dynamics with an assailant: (a) beginning evacuation (t = 0); (b) middle stages; (c) end stage of evacuation with a number of attacked pedestrians.

Fig. 11. Evacuation time T versus pedestrian’s desired speed Vp for different scenarios and models.

T might not decline too much because of the “circuity phenomenon” and the effect of attacked pedestrians who fall down and become obstacles, which may result in increase of evacuation time and reduction of evacuation efficiency in turn. The effects of different door widths on evacuation time and number of attacked pedestrians are analyzed. Fig. 12 shows the tendency of evacuation time T and attacked pedestrians against different exit widths W in the above scenario with the same settings. Evacuation time T will decrease nonlinearly when the exit width W is increased, eventually reach a saturation state where further increase in W dose not have significant impacts on T . The congestion around the exit will not occur when the exit width is wide enough. Once pedestrians arrive at the exit, they can escape the hall immediately. We can see from the pink dotted line of Fig. 12 that the changing trend of the number of attacked pedestrians against variable exit widths almost exactly similar with evacuation time. Therefore, it is an efficient way of improving evacuation efficiency by expanding the exit width in this scenario. For the designing of parameters, a critical size of the exit will be determined if the hall size and expected density are given. Fig. 13 shows the plot of the pedestrians’ desired speeds Vp against the number of attacked pedestrians Nsum for N = 100 and 200 with the presetting value of assailant’s desired speed Va = Very Fast. The desired speeds of pedestrians are varied from 0.5 m/s to 6 m/s. As we can see, the Nsum will decrease with the increasing of Vp when Vp is small. And when Vp gets larger than the critical speed, the increasing of Vp will no longer

Fig. 12. Evacuation time T and attacked pedestrians Nnum for various exit width W values.

Fig. 13. Plot of the pedestrian’s desired speed Vp against the attacked pedestrians Nsum for different initial densities.

reduce the Nsum sharply. This indicates that the increasing of speed will help reducing the number of attacked pedestrians to some extent, but it’s not true to say that the faster the better. The presented simulation results support the observation of “faster-is-slower effect” [4], which implies that a properly regulated crowd flow is more efficient from the safe standpoint than a hurried and disordered flow. The variety of pedestrians’ density do not affect the inverse-correlative property of curves, but affect the number of attacked pedestrians. The number of attacked pedestrians is not increased proportionally to the density of pedestrians. Then, we check the effects of different assailants’ desired speeds on evacuation efficiency. The variation of the assailant’s desired speed Va against the number of attacked pedestrians


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after a certain time tc . Thus it can be seen that how to stop attack as quickly as possible plays a crucial role in reducing losses and avoiding an evacuation crisis.

VI. C ONCLUSION

Fig. 14. Assailant’s desired speeds Va versus the attacked pedestrians Nsum for different initial densities.

Fig. 15. Duration of attacks versus the attacked pedestrians Nsum for different initial densities.

Nsum for N = 100 and 200 is shown in Fig. 14. The desired speeds of three categories pedestrians are set as “Slow,” “Fast,” and “Very Fast,” respectively. The desired speed of the assailant are varied from 0.5 m/s to 6 m/s. Findings from simulations have shown that the number of attacked pedestrians is positively correlated with the assailants’ speeds. The number of attacked pedestrians Nsum increases steadily as the assailants’ speeds Va increases. The trend of dramatic growth of attacked pedestrians is slowed and stabilized when the Va exceeded the critical speed. The variety of pedestrians’ density do not affect the positive-correlative property of curves, but affect the number of attacked pedestrians. At last, the effect of security guards is taken into account during evacuation simulations. We assume that security guards can stop the attack. But, we only concern the time they spend on stopping an attack, i.e., the duration of attacks. Their motion behaviors, the way of stopping an attack, mode of interaction with other individuals and so on are all ignored during evacuation simulations. The desired speeds of three categories pedestrians are set as “Slow,” “Fast,” and “Very Fast,” respectively. Fig. 15 shows the variation of duration of attacks Td against the attacked pedestrians Nsum for N = 50, 100, 150 and 200 with the presetting value of assailant’s desired speed Va = Very Fast. From the figure, it can be clearly found that the longer the duration of attacks T , the bigger the number of attacked pedestrians Nsum will be. When the density is lower (blue line), the number of attacked pedestrians Nsum tends to be constant with the time T exceeding the threshold tc . This occurs because the evacuation process is already completed

In this paper, we have proposed four kinds of fuzzy logicbased models according to different intentions and surrounding environments of pedestrians and assailants. In these models, the obstacle-avoiding behavior, path-searching behavior and goalseeking behavior were considered separately, and final results were integrated with recommendations of these behaviors by weighted average method. The major advantage of a fuzzy logic approach is that it has the ability of making the most of perceptual-based information during the modeling procedure. Also, taking into account human experience and knowledge in modeling process, the proposed models can simulate and predict crowd evacuation behaviors realistically. The preliminary validation of the proposed pedestrian model was made by comparing the simulated fundamental diagram of unidirectional pedestrian flow with published experimental data in an corridor scenario. Then, the effect of assailants on crowd evacuation behaviors was investigated in a hall scenario by 3D simulation technology. A novel “circuity phenomenon” was observed in simulations. In addition, the relationship between pedestrian’s desired speed and evacuation times was discussed and compared with empirical results. Without the effect of assailants, it has the similar changing trends with the empirical results. The effects of pedestrian’s desired speed, exit width, assailant’s desired speed and duration of an attack on evacuation efficiency were discussed. The simulation results show that suitable pedestrian’s desired speed and exit width might improve the evacuation efficiency. However, a larger assailant’s desired speed, a smaller pedestrian’s desired speed or longer duration of attack might lead to serious casualties. These results may offer recommendations for architects and managers, such as how to design exits and corridors, develop evacuation strategies, and set emergency refuge areas. In this paper, we just concentrate on the crowd evacuation under the effect of an assailant in a simple hall scenario. The future study will focus on the emergency evacuation in a more complex scenario such as a hall with N-assailantN-exit, subway station and stadium. This can be helpful in guiding the design of big buildings and formulating efficient evacuation plans. R EFERENCES [1] S. P. Hoogendoorn and W. Daamen, “Pedestrian behavior at bottlenecks,” Transp. Sci., vol. 39, no. 2, pp. 147–159, May 2005. [2] J. Zhang, W. Song, and X. Xu, “Experiment and multi-grid modeling of evacuation from a classroom,” Phys. A, Stat. Mech. Appl., vol. 387, no. 23, pp. 5901–5909, Oct. 2008. [3] J. Ma, W. Song, W. Tian, S. M. Lo, and G. Liao, “Experimental study on an ultra high-rise building evacuation in China,” Safety Sci., vol. 50, no. 8, pp. 1665–1674, Oct. 2012. [4] D. Helbing, I. Farkas, and T. Vicsek, “Simulating dynamical features of escape panic,” Nature, vol. 407, no. 6803, pp. 487–490, Sep. 2000. [5] A. Varas et al., “Cellular automaton model for evacuation process with obstacles,” Phys. A, Stat. Mech. Appl., vol. 382, no. 2, pp. 631–642, Aug. 2007.

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Min Zhou received the M.S. degree from the School of Electrical and Information Engineering from Changsha University of Science and Technology, Changsha, China, in 2013. He is currently working toward the Ph.D. degree in the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China. His research interests include pedestrian dynamics, emergency management and evacuation on urban rail transit, fuzzy logic, and linguistic dynamic systems.


Hairong Dong (M’12–SM’12) received the B.S. and M.S. degrees in automatic control and basic mathematics from Zhengzhou University, Zhengzhou, China, in 1996 and 1999, respectively, and the Ph.D. degree in general and fundamental mechanics from Peking University, Beijing, China, in 2002. She is currently a Professor with the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University. Her research interests include stability and robustness of complex systems, control theory, intelligent transportation systems, automatic train operation, and parallel control and management for high-speed railway systems.

Ding Wen (M’95–SM’99) is a Professor with the National University of Defense Technology (NUDT), Changsha, China, and a Senior Advisor with the Research Center for Military Computational Experiments and Parallel Systems Technology, NUDT. He has published extensively and received numerous awards for his work in his areas of interest. His main research interests include behavioral operation management, human resource management, management information systems, and intelligent systems.

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Xiuming Yao received the B.S. degree in measurement, control technology, and instrument from North China Electric Power University, Baoding, China, in 2005 and the Ph.D. degree in control science and engineering from Harbin Institute of Technology, Harbin, China, in 2010. She is currently an Associate Professor with the School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, China. Her current research interests include hybrid systems, networked control systems, and robust control.

Xubin Sun received the B.S. degree in electrical engineering and automation from Beijing Jiaotong University, Beijing, China, in 2002 and the Ph.D. degree in control theory and control engineering from the Institute of Automation, Chinese Academy of Sciences, Beijing, in 2007. He is currently an Associate Professor with the School of Electronic and Information Engineering, Beijing Jiaotong University. His research interests include parallel control and management of urban rail transit and high-speed railway systems.