In this paper, we propose an advanced model and experimental study results considering an unorganized group behavior in case of an emergency. An approach to simulation of human behavior is based on the Dirk Helbing and Peter Molnar Social Force Model. This model depends on the informational impact on the individual behavior of group agents. The proposed model is adapted for crowd behavior simulation in emergencies. The model implies the behavior of an agent when it tries to determine the optimal direction to a safe place at any point in time. When the agent chooses the direction of movement, it takes into account both the number of people around, the average tra c of the crowd, and the presence of a nearby source of danger. Based on the model, a crowd behavior simulator was implemented in the AnyLogic simulation software, which reproduced the behavior of people during the tragedy at the Lame horse nightclub (December 5, 2009) in Perm, Russia. To verify our approach we conducted three groups of simulations and compared our model with the existing method of group behavior in a multi-level branched room, and with the method of moving agents along the shortest path. The results, obtained by the proposed model, most closely match the real data on the tragedy.
At present, the design of premises intended for a large number of people implies that in emergencies crowd make the proper decisions to leave it. Because of this, the time spent on evacuation is wasted irrationally, which subsequently increases the number of victims. There are many tragic examples, such as the re on 27th January 2013 at the Kiss night club, which began around 2:30 a.m. (2:00 a.m. according to other sources) in Santa Maria, Rio Grande do Sul, Brazil. The re was caused by the careless use of pyrotechnics in the club. That re killed 242 people, and 630 were injured [1]. Due to the availability of only one narrow emergency exit, a crush began, which increased the number of victims.
This event raised the importance of applying unorganized group (crowd) behavior modeling methods in the events of an emergency situations (ES) to optimize the preliminary training process and minimize victims in case of panic.
In the present work, for modeling such situations, as well as for formulating the methods, a multi-agent approach is used [2]. Based on this approach, the crowd is characterized as a group of agents with the ability to communicate and interact with each other. 2
From the existing global approaches to modeling the behavior of an unorganized group, several types can be distinguished. The simplest approach is to transfer the area along which the agents move to a discrete form, as well as to set the rules for the agent to move to a particular area. Additionally, the behavior model can be based on Newtonian mechanics or gas dynamics [3]. In these cases, the behavior of agents in certain situations is determined by the physical properties of the elements of the group. One of the more complex approaches is the use of multi-agent systems that describe both the behavior of the agent and its interaction with other participants during the simulation.
Currently, hybrid approaches [4{6] to model crowd behavior are increasingly being used. This allows to create more exible models with realistic behavior, as well as reactions of groups of agents in the system. 3
The basis of the mathematical model of human behavior in ES, used in the simulator, is the Social Force Model of Dirk Helbing and Peter Molnar [7{9]. The proposed model includes space and distance to di erent exit areas. It also covers external and internal in uences on humans as part of a weakly organized mass: physiological, social and informational.
Information in uence in this work is understood to be the impact of the environmental awareness of other group members by individual visible agents during the evacuation process. This implies the inability of the agent to choose the optimal direction of movement to achieve the goal (salvation) based on the choice of the average trajectory of other agents of the crowd.
To verify our mathematical model, it was implemented in the software simulator and tested. As a framework for simulation, AnyLogic 8.4 was used. The built-in Pedestrian library allows to building models with a large amount of information about pedestrian movements. With the help of the graphical interface and Java language functionality, it is possible to simulate the movement of agents in the premises and to program information interaction logic between them.
In this section, we describe our mathematical model of the crowd behavior in ES and approach to verify it.
The proposed model considers the catastrophe as an event with a set of time
intervals T = ft0; t1; : : : ; tng, i.e. it can be assumed that the system exists at
di erent points in time. The crowd itself is a set of agents P = fp0; : : : ; png,
which is divided into two subsets - the number of ordinary people and the
number of informed (stewards). Each agent, at any given time, solves the problem of
nding the optimal direction of movement from its location to a safer one. The
main factors determining the direction of agents movement d(pi) are the
assessment of movement direction of other visible agents Si = s(pi) and the "weight"
w of their direction for the agent. In this case, the "weight" of other agents
directions to a particular agent depends on the agent's knowledge about the
situation (whether a certain agent was seen before an emergency or not, whether it
is informed or not) w = fwinf ; wusg, where winf { \sta " agent's weight of the
motion direction and wus { \usual" agent's weight of motion direction, which
also can be divided into sets winf = fwsinf ; wnsifng, wus = fwsus; wnsusg, where
wsinf ,wsus { weight of the direction, which agents seen before the evacuation and
wnsifn,wnsus { weight of the direction, which agents not seen before the ES, and
wsinf wnsifn wsus wnsus. In addition, each agent is de ned by its
location in space (coordinates): coordpinf , coordpus . It follows that the direction of
agent motion can be represented as a function depending on the average motion
direction of other agents (
winf P coordtpin1f + wus P coordtpus1 =
wsinf P coordtpsi1nf + wnsinf P coordtpns1inf
+ wsus P coordtpsu1s + wnsus P coordtpns1us :
jsij
jsij
(
Expressing E dtpi 1 jsij through the agents movement direction and their
locations through the weight coe cient, we obtain the nal values of the agent
pi movement direction (
Available public data on the tragedy in the night club "Lame Horse" were used to simulate crowd behavior in such a scenario. The number of agents in the simulation corresponds to the actual data on the visitors in the club at the time of the re. The blue dots in Figure 2 represent informed agents (waiters and sta members), while the green dots represent ordinary people (visitors). In addition, the simulation conditions include re, and smoke, which spreads at a certain speed through the area. The velocity of re propagation and the toxicity of the smoke are based on available data in [10], on the material ignited during the tragedy (polypropylene). Data used in the simulator: { number of agents: 322; { number of waiters (informed agents): 20; { two outputs; { evacuation start time: 10 seconds after the re starts; { time to ll the room with smoke: 60 seconds.
The simulation starts with the distribution of agents throughout the club area. After the evacuation starts, the agents start moving towards the nearest exit. In doing so, the agent continuously performs veri cations such as re detection, the detection of an informed agent, or the calculation of the median movement of the crowd. These factors in uence the further movement of the agent. The color indicates the amount of health of the agent so that once the agent is red, it loses consciousness and stops moving. These agents, as well as those who have lost their health, are counted with a simulator. Agents who managed to get to the exit are also counted by the simulator.
While the simulator is running, data on the number of agents' health is recorded, as well as their assigned status, where: 10% health agent is dead; > 10% and 40% health agent alive with low health points; > 40% of health { agent is alive. In addition, information is recorded about what exactly caused the agents to lose their health: re or smoke. The evacuation process is shown in Figure 3.
Two models, based on existing solutions for modeling crowd behavior were also implemented in the simulator to verify our approach. The rst model, without taking into account the behavior of the crowd, is implemented by the builtin tools of AnyLogic, in which the agents move to the nearest exit. The second model is based on panic group behavior in a multi-level branched area. In this model, the agent's movement is based on the existing room structure and the presence of other agents on its path.
As a result, three groups of experiments were conducted. Each group includes 322 agents, 20 informed agents, two exits (main and emergency). Time to evacuate is 10 seconds from the beginning of the re. Most people are located on the dance oor. When the re begins to spread, the smoke begins to ll the club. 6
of 16%, which is signi cantly less compared to other models. This shows the accuracy of the developed model relative to the well-known models. This fact allows saying that the proposed model is more accurate in comparison with other simulated models. 7
The results obtained with the help of the simulator are very close to the real data about the victims of the tragedy. Therefore, the obtained model of behavior of an unorganized group allows to carry out the analysis of the emergencies that have occurred and to test the existing and projected premises to ensure their safety. 8
In the present work, we propose a model of crowd behavior in emergencies and its validation. The model based on the information impact on the group, which allows bringing the data closer to real conditions. Existing approaches to model human behavior and their di erences of the proposed model are described. The model was implemented in the AnyLogic software simulator. To verify our model, the real scenario of the emergency was simulated and the results were compared with two existing approaches to model crowd behavior. Obtained results allow saying that our model could produce more relevant results, that are closer to real data compared with the simulated approaches. The presented model can be useful in the analysis of existing and planned premises to ensure safety in the event of panic in emergencies.