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A simplified method to provide evacuation guidance in a multi-exit building under emergency
Journal Pre-proof A simplified method to provide evacuation guidance in a multi-exit building under emergency Jin Gao, Jun He, Jinghai Gong
PII: DOI: Reference:
S0378-4371(19)31980-6 https://doi.org/10.1016/j.physa.2019.123554 PHYSA 123554
To appear in:
Physica A
Received date : 28 December 2018 Revised date : 31 October 2019 Please cite this article as: J. Gao, J. He and J. Gong, A simplified method to provide evacuation guidance in a multi-exit building under emergency, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123554. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
*Highlights (for review)
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Highlights: Propose a modified model by considering asymmetrical layout of exits or pedestrians Employ exit weight coefficient to redistribute static floor field Evacuation time decreases with individual acceptance coefficient increasing Evacuation imbalance is reduced and exits are fully utilized in modified model
*Manuscript Click here to view linked References
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A simplified method to provide evacuation guidance in a multi-exit building
2
under emergency
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Jin Gao, Jun He, Jinghai Gong (School of Naval Architecture, Ocean & Civil Engineering, civil engineering, Shanghai Jiao Tong University, Shanghai 200240, China) Abstract:
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This paper introduces a simplified method to provide evacuation guidance under emergency by employing an evacuation system, which intends to develop an effective evacuation scheme in
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Keywords: exit weight coefficient; static floor field; evacuation system; asymmetrical layout
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1. Introduction In recent years, public safety accidents occur frequently in various countries, which attracts extensive attention from governments and societies. Public buildings, such as airports, hospitals, railway stations, libraries, etc., usually have the characteristics of high crowd density and heavy traffic, so it is essential to develop evacuation plans in advance that can guide pedestrians to exits safely and rapidly under emergency. In order to generate an effective emergency evacuation scheme, a growing amount of simulation models, including macroscopic and microscopic, have been developed and applied until now. The macroscopic models, like fluid-dynamic model[1,2], human movement resembles a fluid flow and is described through differential equations, while microscopic models mainly consist of floor field cellular automata model [3,4], social force model [5,6], lattice gas model[7,8], dynamic parameters model [9,10] and queueing network model [11,12], etc., which are able to create individual behavior and interactions. Microscopic models are widely used in the researches of pedestrian evacuation dynamics
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advance to prevent overcrowding in front of exits caused by the asymmetrical layout of exits or pedestrians in a multi-exit building. A modified cellular automata model based on Floor Field theory is proposed to solve this problem. Two coefficients: exit weight coefficient and individual acceptance coefficient are put forward, which are used to redistribute the static floor field and represent personal acceptance degree of the guiding information respectively. The effectiveness of the modified model is validated by simulating a series of double-exit and four-exit evacuation areas, with uniform and concentrated distributed of pedestrian respectively. A more complex and real evacuation building is investigated to further prove the validity of the modified model. Simulation results demonstrate that proper exit weight coefficients can reduce the imbalance during evacuation procedures effectively and help to reach a higher evacuation efficiency, which can be transferred to the emergency evacuation guiding sub-system to guide pedestrians to a rational exit in the evacuation system. With the increment of individual acceptance coefficient, the evacuation time shows a downward trend. It is also found the concentrated distribution of pedestrians has an advert effect on evacuation time when compared with pedestrians' uniform distribution in four-exit evacuation areas. By this simplified method, most pedestrians are given a faster route to leave the evacuation area and not bothered by the exit selection.
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time-based strategies in a simulation were analyzed and fused to construct a mixed strategy of exit selection through a cognitive coefficient in Ref. [21], which shows the effectiveness of reducing the evacuation imbalance. Meanwhile, some experiments are executed as well to further explore exit choice in a multi-exit building. S. Liu et al [22] researched the impact of occupant density around exits on human behavior by conducting an experiment in a classroom with obstacles and simulating the evacuation by a modified cellular automaton model. To further investigate the influence of neighbor egress behavior and exit familiarity on exit choice, M. Kinateder et al. [23] performed the first experimental test of exit familiarity hypothesis and researched how it interacts with social influence to determine exit choice during evacuation. These models mentioned above mainly focused on personal behavior and congestion around exits during the evacuation, most of which can reproduce exit selection behavior in real-time evacuation and reduce evacuation imbalance effectively. However, it is difficult for pedestrians to estimating the moving and queuing time in front of exits during evacuation process in real-time evacuation. Sometimes these methods may lead to a waste of individual evacuation time under emergency, some pedestrians may even fall into the dilemma of the selection of evacuation route. Therefore, it is necessary to use some simplified schemata to come up with an exit choice. This paper introduces a simplified method to provide evacuation guidance under emergency by
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because personal characteristics and moving processes can be described in detail, which helps to improve the reliability of simulation results. Considering the complexity of evacuation scenarios and individual behaviors in reality, some classical models are extended to approximate pedestrian dynamics and simulate the self-organization of pedestrian flow. During the simulation, evacuation time is a significant factor in access evacuation efficiency, which is determined by many factors, including the distribution of pedestrians, the layout of internal obstacles and exits, etc. When emergency occurs in a multi-exit building, asymmetrical layout of exits or pedestrians can lead to imbalanced evacuation process, so it is essential to conduct an evacuation scheme to help pedestrians to formulate proper exit choice and reduce the imbalanced evacuation, which is still an open problem and has been studied by many scholars frequently. A growing number of methods were proposed to solve this problem, including game theory-based exit selection model [13], logit-based discrete choice [14], reserve capacity of exit [15], dynamic background field[16,17] and artificial intelligence (AI) [18], etc. Y. Hao et al. had done a series of researches in solving evacuation imbalance in a multi-exit room [19–21]. They pointed out that the evacuation imbalance is caused by the asymmetry of exit layout in [10] and presented the “max-min” selection of actual and imaginary distance to reduce the evacuation imbalance in Ref. [19]. The impact of asymmetrical pedestrian layout on evacuation was studied in [20], which introduces the waiting distance and the imbalance coefficient from the viewpoint of the utilization of exits. Finally, distance-based and
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employing an evacuation system. The system intends to develop an effective evacuation scheme to guide evacuees to choose a faster route and reduce evacuation imbalance, which helps to prevent the overcrowding in front of exits ahead of time. To balance the evacuation process in multi-exit building, a modified cellular automata model
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2. Methodology 2.1 Introduction of evacuation system The evacuation system plays a significant role in modern buildings when an emergency occurs, which consists of three sub-systems as shown in Fig. 1. Information acquisition sub-system is used to gather the position of pedestrians, as well as the internal layout of the evacuation building, including the distribution of obstacles and exits, which are input variables in the system. Evacuation simulation sub-system is the hard-core part, which is used to build evacuation model and calculate a rational route for individual as quickly as possible. An evacuation scheme is developed according to the simulation results in evacuation simulation sub-system, which is transferred to the emergency evacuation guiding sub-system. The function of emergency evacuation guiding sub-system is to provide pedestrians with faster evacuation route identification by using luminous type indicators, ground continuous oriented indicators, individual mobile guidance equipment and so on. The evacuation system in this paper intends to formulate an effective evacuation scheme in advance according to the information obtained from the information acquisition sub-system, which can reduce imbalanced evacuation and improve evacuation efficiency in a multi-exit building.
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based on Floor Field theory considering the asymmetrical layout of exits or pedestrians is proposed in this paper. The simulation program is embedded in the evacuation system and simulation results can be transferred to the emergency evacuation guiding sub-system, which can guide pedestrians to a more reasonable exit automatically. The concept of sub-area and sub-static floor field are proposed to dominate personal movement. Exit weight coefficient and individual acceptance coefficient are put forward, which are used to redistribute the static floor field and represent individual acceptance degree of the guiding information respectively. The imbalanced evacuation procedure in multi-exit buildings, the relationship between evacuation time and the number of pedestrians and individual acceptance degree are researched by a series of simulations. The paper is organized as follows: in section 2, a brief description of the evacuation system is provided, the pedestrian evacuation model and simulation update procedures are described. The simulation scenario, results, and further comparison and discussions are presented in Section 3. In order to test and verify the modified model, section 4 simulates and analyses pedestrian evacuation in a more complex real building. The final section is a conclusion.
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Fig. 1 Composition of an evacuation system
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2.2 Modified evacuation model In order to achieve the quick calculation of the hard-core part of the evacuation system—evacuation simulation sub-system, this paper proposes a modified evacuation model, which allows for an efficient implementation for large computer simulations. The model is based on the Floor Field model (FF model), which is widely used in pedestrian evacuation researches [24–27]. FF model usually uses static floor field
and dynamic floor field
to calculate the
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transition probability
of each pedestrian. The static floor field is used to specify regions of
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space which are more attractive and not evolve with time, the value of which is inversely proportional to the distance from to an exit cell. Dynamic floor field represents attractive interaction between pedestrians, which is modified by the presence of pedestrians. And it has its own dynamics namely diffusion and decay. Pedestrians can move to a neighbor cell or stay at original cell in each time step according to the transition probability calculated by Eq.(1).
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Here,
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. represents the condition of pedestrian or obstacle while
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, indicates
indicates is occupied by a is empty. This paper assumes that
pedestrians are familiar with the layout of evacuation area and will not follow the evacuation trace left by others, so , . The simulation model is built on two-dimensional grids, each grid is a cell with three situations: empty, occupied by one pedestrian or obstacle. Assuming the size of each cell is according to personal size in reality and the Moore neighborhood is adopted (see Fig. 2), pedestrians can only move to one empty cell of the eight neighbor cells or stay at the central cell in each time
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(2)
is a normalization factor to guarantee
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,
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(1)
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step. To get the static floor field in a building with n exits, n is the number of exits, we use the
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algorithm as follows:
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(a) Assuming
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exit, k is the serial number of the exit among n exits. If
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to be the shortest distance from
to the cells that occupied by the
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is occupied by exits,
;
(b) Adopting
algorithm, let the exit cell be the start node. Each cell occupied by exits
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has a number: 1, 2, 3… .
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occupied by the
is the shortest distance from
exit. For each cell, a distance sequence is given. If
to the
cell that
is calculated, then
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of all cells have been obtained;
(c) After traversing all cells occupied by the sequence of
as
，
values of
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the shortest distance from
to exits in a building.
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,
(4)
of all the cells.
(5)
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to be the maximum value of
Finally, static floor field is formed that reflects the shortest distance from a cell to exit. The value of the static floor field becomes largest in exits. With the increment of the distance from to exits, the value of static floor field becomes smaller, which is zero for the cells that occupied by obstacles and walls.
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(e) Let
of other exits. Finally, each cell has n
. Comparing these n distance values of each cell, choose the smallest one as
， 147
(3)
(d) Repeating the procedure (b) and (c), get
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in the
. ，
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exit, choose the smallest
of
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put it into this sequence, until
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(a)
(b)
Fig. 2 Floor field cellular automata model (a) Moore neighborhood (b) Probability matrix of move target
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The static floor field is divided into n parts in an enclosure according to the number of exits in the computational process, which is called sub-static floor filed in the paper. The projected area on the horizontal plane of sub-static floor filed is called sub-area (see Fig. 4). To calculate sub-floor
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field and sub-area, in step (d), if the value of
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sub-area k and sub-static floor field k. According to Eq.(1), if a pedestrian in sub-area k, the transition probability will be calculated by the sub-static floor field k, so the pedestrian usually escapes from the building via the exit. When original FF model is adopted in a multi-exit
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is equal to
, then
is belong to
building with asymmetrical layout of exits or pedestrians, the evacuation process will suffer imbalance, i.e. overcrowding will appear in front of the nearest exit to pedestrians while the farthest exit is not fully utilized. According to Ref. [20], the balance evacuation can be achieved by adjusting the width of exits or altering the number of people belonging to the sub-area under the
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situation with an asymmetrical pedestrian layout. In a real building, it is almost impossible to change the position or width of exits, so changing individual evacuation routes by altering the static
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floor field is an effective way. In order to solve this problem, static floor filed
and sub-area
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are
coefficient . acts on
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redistributed
in
modified FF model by employing exit according to the layout of exits and pedestrians,
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the
weight
exit as is shown in Eq. (6).
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Proper exit weight coefficients can redistribute sub-static floor field and sub-area reasonably, the crowd in which can evacuate from the enclosure without serious congestion, so all exits can finish evacuation as simultaneous as possible, which can lead to a shorter evacuation time and higher evacuation efficiency. This paper uses c% to represent the evacuation time difference between the evacuation time of the exit that finishes evacuation firstly and the total evacuation time. Table 2 illustrates the algorithm of calculating the exit weight coefficient. The important nomenclatures in the algorithm are summarized in Table 1. and in the algorithm are calculated by the algorithm in Table 3.
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Table 1 Summary of notations
181 Symbol
Description
Symbol
The total number of exits in a building,
.
The serial number of an exit, i.e. the
Total simulation runs in the algorithm.
simulation run.
The
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The evacuation time of the
exit in the
Evacuation time of the first exit to finish evacuation in the
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Description exit,
simulation run in the algorithm,
Total evacuation time in the
.
run: .
Vector of exit weight coefficients:
simulation run:
Vector of temporary exit weight coefficients in the simulation run,
={
,
…
…
The evacuation time difference between
in the
}
and
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The temporary exit weight coefficient that is a little smaller than
s
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in the
Temporary exit weight coefficient that acts on the
step (see
exit
simulation run
Exit weight coefficient that acts on the
exit
The temporary exit weight coefficient that is a little bigger than
in the
step (see
Table 3).
Table 3).
The serial number of the exit whose temporary weight
The serial number of the last exit that finishes evacuation in
coefficient is changed in the
the first simulation run.
simulation run.
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Table 2 Algorithm for calculating exit weight coefficient =1, initialize exit weight coefficients: =1, do the first simulation run, get the results: {
and
2: While
}. , do:
3:
If:
=1,
4:
Then: find the exit
Else: find the exit
12:
If:
13:
Else：
14:
End if
15: with
,
,
18:
,
Else:
7:
End if
.
End if
=
19:
,s)
={
,
…
…
}in Eq. (6),
,
}.
.
20: Wend
If: there is an exit
with
,
;
21:
) runs:
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2: For all temporary exit weight coefficients in first (
and smaller than lb
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If: a temporary exit weight coefficient is bigger than
Then:
(
apply
,
Table 3 Algorithm for calculating
4:
,
.
{
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3:
,
and obtain a new solution:
.
Else:
1: initialize
with , Then：
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with
.
16： End if
find the exit
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11:
17:
If:
9:
Then：calculate
which is fixed in the following calculation.
5:
8:
10:
of
1:
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= the temporary exit weight coefficient
( =1,2…n),
and
5:
End if
6:
If: a temporary exit weight coefficient is smaller than
,
and bigger than ls 7:
Then:
8:
End if
= the temporary exit weight coefficient
9: End for
Given the stochastic nature of the modified model, in Table 2, step 1 and 18 can be carried out
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several times to get the mean value of simulation results { and , } if the exit weight coefficient does not converge for in this program, which can improve the convergence, though it may reduce the computation efficiency. This model adopts parallel update of evacuation rules. Individual velocity is a function of age according to the data published by Ando et al [28] and A. Poulos et al [29]. Considering pedestrians in the evacuation are adults [30], the mean velocity is 1.34 m/s in the evacuation and each time step is about 0.3s in the paper.
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(1) In every time step, pedestrian selects an target cell based on the transition probability
,
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who will choose a cell randomly from the eight neighbor cells and central cell according to
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(2) When conflict occurs, more than one pedestrian selects the same target cell as moving target, only one of them will be chosen randomly to move to the target cell in a time step according to their
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transition probability
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(3) When a pedestrian moves into exit cells, in the next time step, the pedestrian will leave the evacuation area and will not return to the evacuation area. (4) With the last pedestrian leaving the evacuation area, the simulation procedure is finished. And the evacuation time of the last pedestrian to evacuate is the total evacuation time.
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Simulation results obtained from the evacuation simulation sub-system will be transferred to the emergency evacuation guiding sub-system, which can help pedestrians to choose an evacuation route under emergency. To indicate individual acceptance degree of the guiding information from the emergency evacuation guiding sub-system, an acceptance coefficient is introduced.
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. Others will not move and stay at the original position.
(7)
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.
Here, . indicates that pedestrians ignore the guide information from guidance equipment completely and they elapse from the evacuation area just according to the shortest
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3. Simulation
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A simple case that pedestrians evacuate from an evacuation area of which size is is researched in this section and the area is defined as the size of , i.e. the size of each cell is . Cells with gray color represent the boundary, like walls and obstacles, black color represents that the cell is occupied by a pedestrian and the other color cells are free
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spaces that pedestrians can move into. This part investigates the imbalanced evacuation caused by the asymmetrical layout of exits or pedestrians in double-exit and four-exit rooms respectively. Because of the probabilistic nature of the evacuation process and the simulation model, 50 different simulations are carried out for each case. Simulation results in the following context adopt the average value from 50 times simulation.
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distance to exits, which means the evacuation model degrades into original FF model. will rise up with individual acceptance degree increasing. represents that pedestrians can select an exit to evacuate from a multi-exit building according to the evacuation guidance absolutely.
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3.1 Simulation of double-exit evacuation areas A double-exit evacuation area is taken for example with two exits locating on the central of opposite walls as shown in Fig. 3. Let the width of exit 1 to be 1, 2, 3, 4……10 cells respectively, the width and position of exit 2 remain unchanged, then ten kinds of evacuation areas are obtained. A series of evacuation models are conducted with 500 pedestrians distributed uniformly, the positions of these pedestrians are identical for each test case. The simulation results are listed in . The proper value of
is found by employing the simulation program, which can guarantee
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both two exits finish the evacuation almost simultaneously. With the increment of the width of exit 1, the evacuation time shows a descendent trend in the modified model while that keeps almost unchanged in the original FF model.
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Table 4 The reasonable value of
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for double-exit evacuation areas
1
2
3
4
5
6
Width of exit 1 (cells)
1
2
3
4
5
6
150.30
150.84
149.96
149.73
149.48
147.24
{1,1}
{0.592,1}
{0.510,1}
{0.429,1}
{0.419,1}
{0.353,1}
150.30
101.74
84.00
62.90
56.29
48.57
(original FF model) Exit weight coefficient Evacuation time (s) (modified FF model)
246 247 248 249 250 251 252 253 254
8
9
10
145.68
146.06
145.30
144.90
{0.340,1}
{0.320,1}
{0.317,1}
{0.308,1}
44.70
44.13
40.28
39.96
The evacuation area (ID=7) is taken for example to interpret this phenomenon. As is shown in Fig. 3, in original FF model, pedestrians are divided almost evenly into two sub-areas according to the distribution of sub-static floor field (see Fig. 4 (a) and (b)) at 9 s. But the evacuation capability of exit 2 (width: 1 cell) is much lower than exit 1 (width: 7 cells) obviously, which means that the number of pedestrians in front of exit 2 far exceeds its evacuation capability. Therefore, serious congestion occurs in front of exit 2 at 30s (see Fig. 3 (b)), while exit 1 has already finished evacuation and undergone a long period that is not in use during evacuation, which reduces evacuation efficiency critically. However, in modified model, the sub-static floor field and sub-area are redistributed by employing exit weight coefficient (see Fig. 4 (c) and (d)). The imbalanced evacuation is relieved, and the number of pedestrians in sub-area k is in coincidence with the evacuation capacity of exit k. Therefore, exit 1 and exit 2 can be fully utilized and finish evacuation as simultaneously as possible. (see Fig. 3 (c) and (d)).
(a) 9 s
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7
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Evacuation time (s)
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of
ID
(b) 30 s
original FF model 256
original FF model
(c) 9 s modified FF model
(d) 30 s modified FF model
Fig. 3 Snapshot of evacuation process at 9 s and 30 s in the double-exit evacuation area (ID=7)
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(a) original FF model
(c) modified FF model
(d) modified FF model
Fig. 4 Schematic diagram of sub-area and sub-static floor field in the double-exit evacuation area
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(b) original FF model
(ID=7)
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(a) Simulating by original FF model
(b) Simulating by modified FF model
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Fig. 5 Simulation curves of evacuation time against the number of pedestrians in ten types of
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evacuation areas
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To further investigate the function of exit weight coefficient, simulation curves of evacuation time against the number of pedestrians in these ten types of evacuation areas are acquired(see Fig. 5). With the increment of pedestrian quantity, evacuation time increases almost linearly. In Fig. 5 (a), it is illogical that the evacuation time in different types of evacuation areas has little difference when the number of pedestrians is identified. Generally, with the increment of the width of exit, the evacuation time usually becomes shorter. In the modified model shown in Fig. 5 (b), by employing exit weight coefficient, it is obvious that the evacuation time is decreased with the increment of the width of exits, when the number of pedestrians is identified. And the effect of exit weight coefficient on evacuation time is enhanced when a large number of pedestrians inside. In the building evacuation system, simulation results in the evacuation simulation sub-system are transferred to the emergency evacuation guiding sub-system, which can give guiding information for each pedestrian, so the evacuation time also depends on individual acceptance degree of guiding information. The relationship between the value of individual acceptance coefficient and evacuation time is researched as is shown in Fig. 6 and Fig. 7. Fig. 6 shows the simulation curves of evacuation time against the width of exit 1 with different acceptance coefficients when 500 pedestrians distributed uniformly. Evacuation time decreases obviously when , and there is a negative exponential relation between the evacuation time
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and individual acceptance coefficient after . Meanwhile, the impact of exit weight coefficient will be lessened as the number of pedestrians decreases in the enclosure as is shown in Fig. 7, when 100 pedestrians are distributed in the evacuation room at the beginning, no fluctuation emerges in the evacuation time as alters. This is because crowd density is so small that available exits are enough for pedestrians to escape from the enclosure without overcrowding. While the crowd amount increases to 800, the simulation curve exhibits considerable variation, the gradient of which is higher than any other case, and evacuation time decreases almost linearly. If pedestrians can accept and comply with the guiding information absolutely, i.e. , most pedestrians can get a reasonable evacuation route without serious congestion to leave the evacuation room and not be bothered by the exit selection, which can eliminate evacuation imbalance and improve evacuation efficiency.
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Fig. 6. Relationship between evacuation time and exit width
Fig. 7. Relationship between evacuation time and
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individual acceptance coefficient
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Fig. 8. Simulation curves of the percentage of sub-area 2 against acceptance coefficient
The attraction of exits to pedestrians varies with the altering of the layout of exits and
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individual acceptance coefficient, which is interpreted by the variation of percentage of sub-area 2 in Fig. 8. The percentage of sub-area 2 shows a linear downward trend with individual acceptance coefficient increasing, which means that the attraction of exit 1 to crowd becomes stronger, and more pedestrians choose the exit with larger evacuation capacity to escape. Because the distribution of pedestrians is random and uniform in these cases, so crowd density has little impact on the value of exit weight coefficient and the percentage of sub-area. It is different from that in [21], where had a critical density in the curves of sub-area against crowd density. 3.2 Simulation in four-exit evacuation areas The evacuation time depends not only on the layout of exits but also on the distribution of pedestrians in an enclosure. 256 pedestrians are distributed in a four-exit evacuation area in two ways as shown in Fig. 9. Three scenarios are researched and the variation of static floor field is shown in Table 5, which is adjusted by exit weight coefficients that are obtained from the simulation program.
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(a) Case 1: concentrated distribution
(b) Case 2: random distribution
Fig. 9 Distribution of pedestrian
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Table 5 The variation of static floor field and exit weight coefficient for three evacuation scenarios Scenario 2
Scenario 3
{0.881, 0.282, 0.489, 1}
{1, 0.290, 0.340, 0.385}
{1, 0.323, 0.323, 1}
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Evacuation scenario
Scenario 1
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Static floor field
in original FF model
Case
Weight
1
coefficient
Journal Pre-proof Static floor field in modified FF model Weight
Case
Static floor
2
field
{1, 0.480, 0.485, 0.492}
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in modified FF
Scenario 1
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Fig. 10 shows the evacuation time of each exit in three scenarios. It is obvious that the most imbalanced evacuation always occurs in scenarios with a concentrated distribution of pedestrians in original FF model, some exits in which are even not in use at all during the evacuation process, which results in a low evacuation efficiency. Evacuation time decreases obviously in scenarios with
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Scenario 3
Fig. 10 Evacuation time of each exit in three scenarios
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Scenario 2
uniform distribution of pedestrian compared with that of case 1, no exit is at free condition during the evacuation process despite the imbalanced evacuation process, so pedestrian's concentrated distribution has an advert impact on evacuation in this paper. Red and pink bars in Fig. 10 represent evacuation time in the modified FF model with pedestrian distributed concentrated and randomly, respectively. It is found that evacuation time decreases a lot compared with that in original FF model, and the unbalanced evacuation process is reduced. Both four exits finish evacuation almost at the same time, which is in line with the simulation result in ref [21]. The variation of sub-area in different scenarios shown in Fig. 11 could be used to interpret the simulation results in Fig. 10. In scenario 1, when pedestrians are distributed concentrated at the top-left corner in the enclosure, most people choose exit 1, 3 and 4 to evacuate from the room according to the shortest distance from the exit, nobody goes to exit 2. Therefore, it is necessary to amplify the sub-area 2 to attract more people to evacuate via exit 2. When pedestrians are distributed uniformly, more pedestrians escape from the room via exit 2 due to the asymmetrical
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{1, 1, 1, 1}
of
{0.684, 1, 0.609, 0.503}
coefficient
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layout of exits. Therefore, sub-area 2 is lessened in the modified FF model. In scenario 2, sub-area 1 accounts for the largest part in the enclosure, so exit 1 bears most of the pedestrians to evacuate while other exits are not fully used, so sub-area 2, 3, and 4 are broadened to various degrees. Scenario 3 has a symmetrical layout of exits with no imbalanced evacuation process when pedestrians are distributed uniformly. However, it is necessary to adjust sub-area 2 and 3 in case 1 where all pedestrians evacuate via exit 1 and 2 in original FF model.
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Scenario 3
Fig. 11 Percentage of sub-area of each exit in case 1 and case 2
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Fig. 12 The relationship between evacuation time and
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Scenario 2
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Scenario 1
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in different cases and scenarios
Fig. 12 depicts the relationship between evacuation time and personal acceptance coefficient in two cases and three scenarios. Evacuation time shows a downward trend except scenario 3 with the random distribution of pedestrians due to its symmetrical property. It is exceptional that evacuation time decreases only after in scenario 3 with the concentrated distribution of pedestrians. The reason is that crowd in the top right corner of the enclosure is far from exit 2 and 3, so only when pedestrians perceive the guide information strongly, i.e. , they will choose a faster route to escape via these two exits.
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4. Case study—evacuation from a library In order to extend the application of this simplified method and prove the availability of the modified FF model, the paper takes a more complex evacuation building in the real-world for example as shown in Fig. 13, which is the first floor of a university library that is used for studying and reading. The size of the library is . There are plenty of facilities, like desks, bookshelves, helpdesk, retrieval computers, etc. that pedestrians cannot pass through during evacuation process. 160 pedestrians are distributed in the library, most of them are in the self-study area and reading area, and some staffs are in the helpdesk and office. There are three exits—main exit (exit 1), secondary exit (exit 2), and emergency exit (exit 3)—in this library, the size of which is marked in Fig. 13. Fig. 14 depicts evacuation time of each exit in the library. It cost much more time for the emergency exit than the other two exits to finish the evacuation because the exit bears many more pedestrians to evacuate from library in original FF model. By employing the simulation program, proper exit weight coefficients are acquired: , which is applied to the modified FF model. Total evacuation time is 20.52 s, which is much smaller than that in original FF model (32.62 s). The difference between the evacuation time of three exits reduces a lot and all exits can finish evacuation synchronously almost (see Fig. 14 (b)) when compared with Fig. 14 (a).
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Fig. 13 The geometry of the library
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Fig. 14 Evacuation time of each exit (the symbol and bar represents the mean value and standard
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(b) in modified FF model deviation, respectively)
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It is further evident that standard deviation of evacuation time of the secondary exit is too small to observe in both two models in Fig. 14. The reason for that mainly refers to the conflicts between pedestrians. Fig. 15 describes snapshots of pedestrians evacuated via different exits that are marked in different colors, pretty of pedestrians are gathering in front of exit 3 in both original and modified FF models, the probability of conflict between these people increases a lot, which result in a higher uncertainty of evacuation time of exit 3, so the standard deviation of this item is higher than other exits. Pedestrians evacuated via the secondary exit are distributed scattered, so nearly no conflicts occur in front of the exit 2 and evacuation time of the exit in 50 simulation runs experiences little fluctuation. It is obvious that most pedestrians are clogging at exit 3 while exit 1 and exit 2 are free relatively in original FF model, which leads to an imbalanced evacuation and a lower evacuation efficiency. However, in modified model, the serious congestions are dispersed to each exit rather only around exit 3. Pedestrians are allocated to a rational exit without serious jams, and the utilization rate of exits is improved. Fig. 16 shows the simulation curve of evacuation time against individual acceptance coefficient in the library. With the increment of , evacuation time shows a downward trend. When pedestrians can comply with the evacuation guidance absolutely in the evacuation system, the evacuation efficiency will be improved a lot and the imbalanced evacuation process can be reduced.
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(a) 0 s, original FF model
(b) 0 s, modified FF model
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(c) 9s, original FF model
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Fig. 15 Snapshot of pedestrians evacuation process via each exit: Pink grids: pedestrians evacuated via
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exit 1; Blue grids: pedestrians evacuated via exit 2; Brown grids: pedestrians evacuated via exit 3
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5. Conclusion This paper proposes a simplified method to provide evacuation guidance in a multi-exit building by employing an evacuation system. The modified model reduces the imbalanced evacuation by adopting exit weight coefficients, which translates pedestrians' congestions around exits into a simplified weight coefficient. It can redistribute static floor field and prevent evacuation procedures and efficiency from being affected by the asymmetrical layout of exits or pedestrians. Then the simulation results of the modified model are transferred to the emergency evacuation guiding sub-system, which can provide guiding information to individual. The individual acceptance coefficient is introduced to describe the acceptance degree of guiding information from guidance equipment.
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Fig. 16. Simulation curve of evacuation time against individual acceptance coefficient
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Through the analysis and comparison of the simulation results, it is proved the effectiveness of the modified FF model in reducing evacuation time and improving the utilization rate of exits in a multi-exit building. It indicates that the evacuation time depends on the layout of pedestrians and exits in an evacuation area and pedestrian's acceptance degree. The unbalanced evacuation
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procedure could be relieved effectively with proper exit weight coefficients, and evacuation time could be reduced with the increment of the value of individual acceptance coefficient. This work considers the effect of congestion in advance rather than during the evacuation process. The simplified method can help to disperse the congestion to each exit in a multi-exit building rather than let pedestrians congest in front of only one or some exits, which improves the utilization rate of exits. This method can be applied to the evacuation system in crowded multi-exit buildings to reduce the evacuation imbalance. The most ideal condition is that it only takes several seconds to calculate the exit weight coefficient of the building according to the real position of pedestrians, which has a high demand for computational effectiveness. The exit weight coefficients can also be calculated by the simulation program ahead of time according to the probable distribution of pedestrians in the building, which can be a referenced evacuation scheme in real-time as well. When pedestrians in the evacuation system evacuate according to the guidance, the evacuation procedure and efficiency can be optimized. However, pedestrians' behavior of following the guidance usually alters during evacuation, so they need to be trained in daily drills. In future work, we will conduct more research about pedestrians' complex behavior in the simulation model.
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(MIIT No. [2016]546). The authors deeply appreciate their supports.
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Journal Pre-proof *Declaration of Interest Statement
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
PII: DOI: Reference:
S0378-4371(19)31980-6 https://doi.org/10.1016/j.physa.2019.123554 PHYSA 123554
To appear in:
Physica A
Received date : 28 December 2018 Revised date : 31 October 2019 Please cite this article as: J. Gao, J. He and J. Gong, A simplified method to provide evacuation guidance in a multi-exit building under emergency, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123554. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
*Highlights (for review)
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Highlights: Propose a modified model by considering asymmetrical layout of exits or pedestrians Employ exit weight coefficient to redistribute static floor field Evacuation time decreases with individual acceptance coefficient increasing Evacuation imbalance is reduced and exits are fully utilized in modified model
*Manuscript Click here to view linked References
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A simplified method to provide evacuation guidance in a multi-exit building
2
under emergency
3 4 5
Jin Gao, Jun He, Jinghai Gong (School of Naval Architecture, Ocean & Civil Engineering, civil engineering, Shanghai Jiao Tong University, Shanghai 200240, China) Abstract:
7
This paper introduces a simplified method to provide evacuation guidance under emergency by employing an evacuation system, which intends to develop an effective evacuation scheme in
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Keywords: exit weight coefficient; static floor field; evacuation system; asymmetrical layout
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1. Introduction In recent years, public safety accidents occur frequently in various countries, which attracts extensive attention from governments and societies. Public buildings, such as airports, hospitals, railway stations, libraries, etc., usually have the characteristics of high crowd density and heavy traffic, so it is essential to develop evacuation plans in advance that can guide pedestrians to exits safely and rapidly under emergency. In order to generate an effective emergency evacuation scheme, a growing amount of simulation models, including macroscopic and microscopic, have been developed and applied until now. The macroscopic models, like fluid-dynamic model[1,2], human movement resembles a fluid flow and is described through differential equations, while microscopic models mainly consist of floor field cellular automata model [3,4], social force model [5,6], lattice gas model[7,8], dynamic parameters model [9,10] and queueing network model [11,12], etc., which are able to create individual behavior and interactions. Microscopic models are widely used in the researches of pedestrian evacuation dynamics
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advance to prevent overcrowding in front of exits caused by the asymmetrical layout of exits or pedestrians in a multi-exit building. A modified cellular automata model based on Floor Field theory is proposed to solve this problem. Two coefficients: exit weight coefficient and individual acceptance coefficient are put forward, which are used to redistribute the static floor field and represent personal acceptance degree of the guiding information respectively. The effectiveness of the modified model is validated by simulating a series of double-exit and four-exit evacuation areas, with uniform and concentrated distributed of pedestrian respectively. A more complex and real evacuation building is investigated to further prove the validity of the modified model. Simulation results demonstrate that proper exit weight coefficients can reduce the imbalance during evacuation procedures effectively and help to reach a higher evacuation efficiency, which can be transferred to the emergency evacuation guiding sub-system to guide pedestrians to a rational exit in the evacuation system. With the increment of individual acceptance coefficient, the evacuation time shows a downward trend. It is also found the concentrated distribution of pedestrians has an advert effect on evacuation time when compared with pedestrians' uniform distribution in four-exit evacuation areas. By this simplified method, most pedestrians are given a faster route to leave the evacuation area and not bothered by the exit selection.
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time-based strategies in a simulation were analyzed and fused to construct a mixed strategy of exit selection through a cognitive coefficient in Ref. [21], which shows the effectiveness of reducing the evacuation imbalance. Meanwhile, some experiments are executed as well to further explore exit choice in a multi-exit building. S. Liu et al [22] researched the impact of occupant density around exits on human behavior by conducting an experiment in a classroom with obstacles and simulating the evacuation by a modified cellular automaton model. To further investigate the influence of neighbor egress behavior and exit familiarity on exit choice, M. Kinateder et al. [23] performed the first experimental test of exit familiarity hypothesis and researched how it interacts with social influence to determine exit choice during evacuation. These models mentioned above mainly focused on personal behavior and congestion around exits during the evacuation, most of which can reproduce exit selection behavior in real-time evacuation and reduce evacuation imbalance effectively. However, it is difficult for pedestrians to estimating the moving and queuing time in front of exits during evacuation process in real-time evacuation. Sometimes these methods may lead to a waste of individual evacuation time under emergency, some pedestrians may even fall into the dilemma of the selection of evacuation route. Therefore, it is necessary to use some simplified schemata to come up with an exit choice. This paper introduces a simplified method to provide evacuation guidance under emergency by
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because personal characteristics and moving processes can be described in detail, which helps to improve the reliability of simulation results. Considering the complexity of evacuation scenarios and individual behaviors in reality, some classical models are extended to approximate pedestrian dynamics and simulate the self-organization of pedestrian flow. During the simulation, evacuation time is a significant factor in access evacuation efficiency, which is determined by many factors, including the distribution of pedestrians, the layout of internal obstacles and exits, etc. When emergency occurs in a multi-exit building, asymmetrical layout of exits or pedestrians can lead to imbalanced evacuation process, so it is essential to conduct an evacuation scheme to help pedestrians to formulate proper exit choice and reduce the imbalanced evacuation, which is still an open problem and has been studied by many scholars frequently. A growing number of methods were proposed to solve this problem, including game theory-based exit selection model [13], logit-based discrete choice [14], reserve capacity of exit [15], dynamic background field[16,17] and artificial intelligence (AI) [18], etc. Y. Hao et al. had done a series of researches in solving evacuation imbalance in a multi-exit room [19–21]. They pointed out that the evacuation imbalance is caused by the asymmetry of exit layout in [10] and presented the “max-min” selection of actual and imaginary distance to reduce the evacuation imbalance in Ref. [19]. The impact of asymmetrical pedestrian layout on evacuation was studied in [20], which introduces the waiting distance and the imbalance coefficient from the viewpoint of the utilization of exits. Finally, distance-based and
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employing an evacuation system. The system intends to develop an effective evacuation scheme to guide evacuees to choose a faster route and reduce evacuation imbalance, which helps to prevent the overcrowding in front of exits ahead of time. To balance the evacuation process in multi-exit building, a modified cellular automata model
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2. Methodology 2.1 Introduction of evacuation system The evacuation system plays a significant role in modern buildings when an emergency occurs, which consists of three sub-systems as shown in Fig. 1. Information acquisition sub-system is used to gather the position of pedestrians, as well as the internal layout of the evacuation building, including the distribution of obstacles and exits, which are input variables in the system. Evacuation simulation sub-system is the hard-core part, which is used to build evacuation model and calculate a rational route for individual as quickly as possible. An evacuation scheme is developed according to the simulation results in evacuation simulation sub-system, which is transferred to the emergency evacuation guiding sub-system. The function of emergency evacuation guiding sub-system is to provide pedestrians with faster evacuation route identification by using luminous type indicators, ground continuous oriented indicators, individual mobile guidance equipment and so on. The evacuation system in this paper intends to formulate an effective evacuation scheme in advance according to the information obtained from the information acquisition sub-system, which can reduce imbalanced evacuation and improve evacuation efficiency in a multi-exit building.
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based on Floor Field theory considering the asymmetrical layout of exits or pedestrians is proposed in this paper. The simulation program is embedded in the evacuation system and simulation results can be transferred to the emergency evacuation guiding sub-system, which can guide pedestrians to a more reasonable exit automatically. The concept of sub-area and sub-static floor field are proposed to dominate personal movement. Exit weight coefficient and individual acceptance coefficient are put forward, which are used to redistribute the static floor field and represent individual acceptance degree of the guiding information respectively. The imbalanced evacuation procedure in multi-exit buildings, the relationship between evacuation time and the number of pedestrians and individual acceptance degree are researched by a series of simulations. The paper is organized as follows: in section 2, a brief description of the evacuation system is provided, the pedestrian evacuation model and simulation update procedures are described. The simulation scenario, results, and further comparison and discussions are presented in Section 3. In order to test and verify the modified model, section 4 simulates and analyses pedestrian evacuation in a more complex real building. The final section is a conclusion.
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Fig. 1 Composition of an evacuation system
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2.2 Modified evacuation model In order to achieve the quick calculation of the hard-core part of the evacuation system—evacuation simulation sub-system, this paper proposes a modified evacuation model, which allows for an efficient implementation for large computer simulations. The model is based on the Floor Field model (FF model), which is widely used in pedestrian evacuation researches [24–27]. FF model usually uses static floor field
and dynamic floor field
to calculate the
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transition probability
of each pedestrian. The static floor field is used to specify regions of
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space which are more attractive and not evolve with time, the value of which is inversely proportional to the distance from to an exit cell. Dynamic floor field represents attractive interaction between pedestrians, which is modified by the presence of pedestrians. And it has its own dynamics namely diffusion and decay. Pedestrians can move to a neighbor cell or stay at original cell in each time step according to the transition probability calculated by Eq.(1).
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Here,
124
. represents the condition of pedestrian or obstacle while
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, indicates
indicates is occupied by a is empty. This paper assumes that
pedestrians are familiar with the layout of evacuation area and will not follow the evacuation trace left by others, so , . The simulation model is built on two-dimensional grids, each grid is a cell with three situations: empty, occupied by one pedestrian or obstacle. Assuming the size of each cell is according to personal size in reality and the Moore neighborhood is adopted (see Fig. 2), pedestrians can only move to one empty cell of the eight neighbor cells or stay at the central cell in each time
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(2)
is a normalization factor to guarantee
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,
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(1)
133
step. To get the static floor field in a building with n exits, n is the number of exits, we use the
134
algorithm as follows:
135
(a) Assuming
136
exit, k is the serial number of the exit among n exits. If
137 138
to be the shortest distance from
to the cells that occupied by the
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is occupied by exits,
;
(b) Adopting
algorithm, let the exit cell be the start node. Each cell occupied by exits
139
has a number: 1, 2, 3… .
140
occupied by the
is the shortest distance from
exit. For each cell, a distance sequence is given. If
to the
cell that
is calculated, then
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of all cells have been obtained;
(c) After traversing all cells occupied by the sequence of
as
，
values of
146
the shortest distance from
to exits in a building.
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,
(4)
of all the cells.
(5)
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to be the maximum value of
Finally, static floor field is formed that reflects the shortest distance from a cell to exit. The value of the static floor field becomes largest in exits. With the increment of the distance from to exits, the value of static floor field becomes smaller, which is zero for the cells that occupied by obstacles and walls.
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(e) Let
of other exits. Finally, each cell has n
. Comparing these n distance values of each cell, choose the smallest one as
， 147
(3)
(d) Repeating the procedure (b) and (c), get
145
in the
. ，
144
exit, choose the smallest
of
142
put it into this sequence, until
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(a)
(b)
Fig. 2 Floor field cellular automata model (a) Moore neighborhood (b) Probability matrix of move target
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The static floor field is divided into n parts in an enclosure according to the number of exits in the computational process, which is called sub-static floor filed in the paper. The projected area on the horizontal plane of sub-static floor filed is called sub-area (see Fig. 4). To calculate sub-floor
157
field and sub-area, in step (d), if the value of
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sub-area k and sub-static floor field k. According to Eq.(1), if a pedestrian in sub-area k, the transition probability will be calculated by the sub-static floor field k, so the pedestrian usually escapes from the building via the exit. When original FF model is adopted in a multi-exit
155
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is equal to
, then
is belong to
building with asymmetrical layout of exits or pedestrians, the evacuation process will suffer imbalance, i.e. overcrowding will appear in front of the nearest exit to pedestrians while the farthest exit is not fully utilized. According to Ref. [20], the balance evacuation can be achieved by adjusting the width of exits or altering the number of people belonging to the sub-area under the
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situation with an asymmetrical pedestrian layout. In a real building, it is almost impossible to change the position or width of exits, so changing individual evacuation routes by altering the static
167
floor field is an effective way. In order to solve this problem, static floor filed
and sub-area
168
are
coefficient . acts on
165
redistributed
in
modified FF model by employing exit according to the layout of exits and pedestrians,
169 170
the
weight
exit as is shown in Eq. (6).
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Proper exit weight coefficients can redistribute sub-static floor field and sub-area reasonably, the crowd in which can evacuate from the enclosure without serious congestion, so all exits can finish evacuation as simultaneous as possible, which can lead to a shorter evacuation time and higher evacuation efficiency. This paper uses c% to represent the evacuation time difference between the evacuation time of the exit that finishes evacuation firstly and the total evacuation time. Table 2 illustrates the algorithm of calculating the exit weight coefficient. The important nomenclatures in the algorithm are summarized in Table 1. and in the algorithm are calculated by the algorithm in Table 3.
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of
(6)
Table 1 Summary of notations
181 Symbol
Description
Symbol
The total number of exits in a building,
.
The serial number of an exit, i.e. the
Total simulation runs in the algorithm.
simulation run.
The
al
The evacuation time of the
exit in the
Evacuation time of the first exit to finish evacuation in the
urn
Description exit,
simulation run in the algorithm,
Total evacuation time in the
.
run: .
Vector of exit weight coefficients:
simulation run:
Vector of temporary exit weight coefficients in the simulation run,
={
,
…
…
The evacuation time difference between
in the
}
and
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The temporary exit weight coefficient that is a little smaller than
s
182 183 184 185
in the
Temporary exit weight coefficient that acts on the
step (see
exit
simulation run
Exit weight coefficient that acts on the
exit
The temporary exit weight coefficient that is a little bigger than
in the
step (see
Table 3).
Table 3).
The serial number of the exit whose temporary weight
The serial number of the last exit that finishes evacuation in
coefficient is changed in the
the first simulation run.
simulation run.
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Table 2 Algorithm for calculating exit weight coefficient =1, initialize exit weight coefficients: =1, do the first simulation run, get the results: {
and
2: While
}. , do:
3:
If:
=1,
4:
Then: find the exit
Else: find the exit
12:
If:
13:
Else：
14:
End if
15: with
,
,
18:
,
Else:
7:
End if
.
End if
=
19:
,s)
={
,
…
…
}in Eq. (6),
,
}.
.
20: Wend
If: there is an exit
with
,
;
21:
) runs:
al
2: For all temporary exit weight coefficients in first (
and smaller than lb
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If: a temporary exit weight coefficient is bigger than
Then:
(
apply
,
Table 3 Algorithm for calculating
4:
,
.
{
193
3:
,
and obtain a new solution:
.
Else:
1: initialize
with , Then：
Pr e-
6:
with
.
16： End if
find the exit
192
194
11:
17:
If:
9:
Then：calculate
which is fixed in the following calculation.
5:
8:
10:
of
1:
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= the temporary exit weight coefficient
( =1,2…n),
and
5:
End if
6:
If: a temporary exit weight coefficient is smaller than
,
and bigger than ls 7:
Then:
8:
End if
= the temporary exit weight coefficient
9: End for
Given the stochastic nature of the modified model, in Table 2, step 1 and 18 can be carried out
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several times to get the mean value of simulation results { and , } if the exit weight coefficient does not converge for in this program, which can improve the convergence, though it may reduce the computation efficiency. This model adopts parallel update of evacuation rules. Individual velocity is a function of age according to the data published by Ando et al [28] and A. Poulos et al [29]. Considering pedestrians in the evacuation are adults [30], the mean velocity is 1.34 m/s in the evacuation and each time step is about 0.3s in the paper.
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(1) In every time step, pedestrian selects an target cell based on the transition probability
,
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who will choose a cell randomly from the eight neighbor cells and central cell according to
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(2) When conflict occurs, more than one pedestrian selects the same target cell as moving target, only one of them will be chosen randomly to move to the target cell in a time step according to their
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transition probability
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(3) When a pedestrian moves into exit cells, in the next time step, the pedestrian will leave the evacuation area and will not return to the evacuation area. (4) With the last pedestrian leaving the evacuation area, the simulation procedure is finished. And the evacuation time of the last pedestrian to evacuate is the total evacuation time.
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Simulation results obtained from the evacuation simulation sub-system will be transferred to the emergency evacuation guiding sub-system, which can help pedestrians to choose an evacuation route under emergency. To indicate individual acceptance degree of the guiding information from the emergency evacuation guiding sub-system, an acceptance coefficient is introduced.
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. Others will not move and stay at the original position.
(7)
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Here, . indicates that pedestrians ignore the guide information from guidance equipment completely and they elapse from the evacuation area just according to the shortest
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3. Simulation
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A simple case that pedestrians evacuate from an evacuation area of which size is is researched in this section and the area is defined as the size of , i.e. the size of each cell is . Cells with gray color represent the boundary, like walls and obstacles, black color represents that the cell is occupied by a pedestrian and the other color cells are free
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spaces that pedestrians can move into. This part investigates the imbalanced evacuation caused by the asymmetrical layout of exits or pedestrians in double-exit and four-exit rooms respectively. Because of the probabilistic nature of the evacuation process and the simulation model, 50 different simulations are carried out for each case. Simulation results in the following context adopt the average value from 50 times simulation.
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distance to exits, which means the evacuation model degrades into original FF model. will rise up with individual acceptance degree increasing. represents that pedestrians can select an exit to evacuate from a multi-exit building according to the evacuation guidance absolutely.
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3.1 Simulation of double-exit evacuation areas A double-exit evacuation area is taken for example with two exits locating on the central of opposite walls as shown in Fig. 3. Let the width of exit 1 to be 1, 2, 3, 4……10 cells respectively, the width and position of exit 2 remain unchanged, then ten kinds of evacuation areas are obtained. A series of evacuation models are conducted with 500 pedestrians distributed uniformly, the positions of these pedestrians are identical for each test case. The simulation results are listed in . The proper value of
is found by employing the simulation program, which can guarantee
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both two exits finish the evacuation almost simultaneously. With the increment of the width of exit 1, the evacuation time shows a descendent trend in the modified model while that keeps almost unchanged in the original FF model.
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Table 4 The reasonable value of
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for double-exit evacuation areas
1
2
3
4
5
6
Width of exit 1 (cells)
1
2
3
4
5
6
150.30
150.84
149.96
149.73
149.48
147.24
{1,1}
{0.592,1}
{0.510,1}
{0.429,1}
{0.419,1}
{0.353,1}
150.30
101.74
84.00
62.90
56.29
48.57
(original FF model) Exit weight coefficient Evacuation time (s) (modified FF model)
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8
9
10
145.68
146.06
145.30
144.90
{0.340,1}
{0.320,1}
{0.317,1}
{0.308,1}
44.70
44.13
40.28
39.96
The evacuation area (ID=7) is taken for example to interpret this phenomenon. As is shown in Fig. 3, in original FF model, pedestrians are divided almost evenly into two sub-areas according to the distribution of sub-static floor field (see Fig. 4 (a) and (b)) at 9 s. But the evacuation capability of exit 2 (width: 1 cell) is much lower than exit 1 (width: 7 cells) obviously, which means that the number of pedestrians in front of exit 2 far exceeds its evacuation capability. Therefore, serious congestion occurs in front of exit 2 at 30s (see Fig. 3 (b)), while exit 1 has already finished evacuation and undergone a long period that is not in use during evacuation, which reduces evacuation efficiency critically. However, in modified model, the sub-static floor field and sub-area are redistributed by employing exit weight coefficient (see Fig. 4 (c) and (d)). The imbalanced evacuation is relieved, and the number of pedestrians in sub-area k is in coincidence with the evacuation capacity of exit k. Therefore, exit 1 and exit 2 can be fully utilized and finish evacuation as simultaneously as possible. (see Fig. 3 (c) and (d)).
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original FF model
(c) 9 s modified FF model
(d) 30 s modified FF model
Fig. 3 Snapshot of evacuation process at 9 s and 30 s in the double-exit evacuation area (ID=7)
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(a) original FF model
(c) modified FF model
(d) modified FF model
Fig. 4 Schematic diagram of sub-area and sub-static floor field in the double-exit evacuation area
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(b) original FF model
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(a) Simulating by original FF model
(b) Simulating by modified FF model
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Fig. 5 Simulation curves of evacuation time against the number of pedestrians in ten types of
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evacuation areas
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To further investigate the function of exit weight coefficient, simulation curves of evacuation time against the number of pedestrians in these ten types of evacuation areas are acquired(see Fig. 5). With the increment of pedestrian quantity, evacuation time increases almost linearly. In Fig. 5 (a), it is illogical that the evacuation time in different types of evacuation areas has little difference when the number of pedestrians is identified. Generally, with the increment of the width of exit, the evacuation time usually becomes shorter. In the modified model shown in Fig. 5 (b), by employing exit weight coefficient, it is obvious that the evacuation time is decreased with the increment of the width of exits, when the number of pedestrians is identified. And the effect of exit weight coefficient on evacuation time is enhanced when a large number of pedestrians inside. In the building evacuation system, simulation results in the evacuation simulation sub-system are transferred to the emergency evacuation guiding sub-system, which can give guiding information for each pedestrian, so the evacuation time also depends on individual acceptance degree of guiding information. The relationship between the value of individual acceptance coefficient and evacuation time is researched as is shown in Fig. 6 and Fig. 7. Fig. 6 shows the simulation curves of evacuation time against the width of exit 1 with different acceptance coefficients when 500 pedestrians distributed uniformly. Evacuation time decreases obviously when , and there is a negative exponential relation between the evacuation time
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and individual acceptance coefficient after . Meanwhile, the impact of exit weight coefficient will be lessened as the number of pedestrians decreases in the enclosure as is shown in Fig. 7, when 100 pedestrians are distributed in the evacuation room at the beginning, no fluctuation emerges in the evacuation time as alters. This is because crowd density is so small that available exits are enough for pedestrians to escape from the enclosure without overcrowding. While the crowd amount increases to 800, the simulation curve exhibits considerable variation, the gradient of which is higher than any other case, and evacuation time decreases almost linearly. If pedestrians can accept and comply with the guiding information absolutely, i.e. , most pedestrians can get a reasonable evacuation route without serious congestion to leave the evacuation room and not be bothered by the exit selection, which can eliminate evacuation imbalance and improve evacuation efficiency.
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Fig. 6. Relationship between evacuation time and exit width
Fig. 7. Relationship between evacuation time and
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individual acceptance coefficient
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Fig. 8. Simulation curves of the percentage of sub-area 2 against acceptance coefficient
The attraction of exits to pedestrians varies with the altering of the layout of exits and
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individual acceptance coefficient, which is interpreted by the variation of percentage of sub-area 2 in Fig. 8. The percentage of sub-area 2 shows a linear downward trend with individual acceptance coefficient increasing, which means that the attraction of exit 1 to crowd becomes stronger, and more pedestrians choose the exit with larger evacuation capacity to escape. Because the distribution of pedestrians is random and uniform in these cases, so crowd density has little impact on the value of exit weight coefficient and the percentage of sub-area. It is different from that in [21], where had a critical density in the curves of sub-area against crowd density. 3.2 Simulation in four-exit evacuation areas The evacuation time depends not only on the layout of exits but also on the distribution of pedestrians in an enclosure. 256 pedestrians are distributed in a four-exit evacuation area in two ways as shown in Fig. 9. Three scenarios are researched and the variation of static floor field is shown in Table 5, which is adjusted by exit weight coefficients that are obtained from the simulation program.
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(a) Case 1: concentrated distribution
(b) Case 2: random distribution
Fig. 9 Distribution of pedestrian
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Table 5 The variation of static floor field and exit weight coefficient for three evacuation scenarios Scenario 2
Scenario 3
{0.881, 0.282, 0.489, 1}
{1, 0.290, 0.340, 0.385}
{1, 0.323, 0.323, 1}
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Scenario 1
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Static floor field
in original FF model
Case
Weight
1
coefficient
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field
{1, 0.480, 0.485, 0.492}
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Fig. 10 shows the evacuation time of each exit in three scenarios. It is obvious that the most imbalanced evacuation always occurs in scenarios with a concentrated distribution of pedestrians in original FF model, some exits in which are even not in use at all during the evacuation process, which results in a low evacuation efficiency. Evacuation time decreases obviously in scenarios with
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Scenario 3
Fig. 10 Evacuation time of each exit in three scenarios
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Scenario 2
uniform distribution of pedestrian compared with that of case 1, no exit is at free condition during the evacuation process despite the imbalanced evacuation process, so pedestrian's concentrated distribution has an advert impact on evacuation in this paper. Red and pink bars in Fig. 10 represent evacuation time in the modified FF model with pedestrian distributed concentrated and randomly, respectively. It is found that evacuation time decreases a lot compared with that in original FF model, and the unbalanced evacuation process is reduced. Both four exits finish evacuation almost at the same time, which is in line with the simulation result in ref [21]. The variation of sub-area in different scenarios shown in Fig. 11 could be used to interpret the simulation results in Fig. 10. In scenario 1, when pedestrians are distributed concentrated at the top-left corner in the enclosure, most people choose exit 1, 3 and 4 to evacuate from the room according to the shortest distance from the exit, nobody goes to exit 2. Therefore, it is necessary to amplify the sub-area 2 to attract more people to evacuate via exit 2. When pedestrians are distributed uniformly, more pedestrians escape from the room via exit 2 due to the asymmetrical
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{1, 1, 1, 1}
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{0.684, 1, 0.609, 0.503}
coefficient
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layout of exits. Therefore, sub-area 2 is lessened in the modified FF model. In scenario 2, sub-area 1 accounts for the largest part in the enclosure, so exit 1 bears most of the pedestrians to evacuate while other exits are not fully used, so sub-area 2, 3, and 4 are broadened to various degrees. Scenario 3 has a symmetrical layout of exits with no imbalanced evacuation process when pedestrians are distributed uniformly. However, it is necessary to adjust sub-area 2 and 3 in case 1 where all pedestrians evacuate via exit 1 and 2 in original FF model.
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Fig. 11 Percentage of sub-area of each exit in case 1 and case 2
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Fig. 12 The relationship between evacuation time and
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Scenario 2
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in different cases and scenarios
Fig. 12 depicts the relationship between evacuation time and personal acceptance coefficient in two cases and three scenarios. Evacuation time shows a downward trend except scenario 3 with the random distribution of pedestrians due to its symmetrical property. It is exceptional that evacuation time decreases only after in scenario 3 with the concentrated distribution of pedestrians. The reason is that crowd in the top right corner of the enclosure is far from exit 2 and 3, so only when pedestrians perceive the guide information strongly, i.e. , they will choose a faster route to escape via these two exits.
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4. Case study—evacuation from a library In order to extend the application of this simplified method and prove the availability of the modified FF model, the paper takes a more complex evacuation building in the real-world for example as shown in Fig. 13, which is the first floor of a university library that is used for studying and reading. The size of the library is . There are plenty of facilities, like desks, bookshelves, helpdesk, retrieval computers, etc. that pedestrians cannot pass through during evacuation process. 160 pedestrians are distributed in the library, most of them are in the self-study area and reading area, and some staffs are in the helpdesk and office. There are three exits—main exit (exit 1), secondary exit (exit 2), and emergency exit (exit 3)—in this library, the size of which is marked in Fig. 13. Fig. 14 depicts evacuation time of each exit in the library. It cost much more time for the emergency exit than the other two exits to finish the evacuation because the exit bears many more pedestrians to evacuate from library in original FF model. By employing the simulation program, proper exit weight coefficients are acquired: , which is applied to the modified FF model. Total evacuation time is 20.52 s, which is much smaller than that in original FF model (32.62 s). The difference between the evacuation time of three exits reduces a lot and all exits can finish evacuation synchronously almost (see Fig. 14 (b)) when compared with Fig. 14 (a).
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Fig. 13 The geometry of the library
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Fig. 14 Evacuation time of each exit (the symbol and bar represents the mean value and standard
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(b) in modified FF model deviation, respectively)
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It is further evident that standard deviation of evacuation time of the secondary exit is too small to observe in both two models in Fig. 14. The reason for that mainly refers to the conflicts between pedestrians. Fig. 15 describes snapshots of pedestrians evacuated via different exits that are marked in different colors, pretty of pedestrians are gathering in front of exit 3 in both original and modified FF models, the probability of conflict between these people increases a lot, which result in a higher uncertainty of evacuation time of exit 3, so the standard deviation of this item is higher than other exits. Pedestrians evacuated via the secondary exit are distributed scattered, so nearly no conflicts occur in front of the exit 2 and evacuation time of the exit in 50 simulation runs experiences little fluctuation. It is obvious that most pedestrians are clogging at exit 3 while exit 1 and exit 2 are free relatively in original FF model, which leads to an imbalanced evacuation and a lower evacuation efficiency. However, in modified model, the serious congestions are dispersed to each exit rather only around exit 3. Pedestrians are allocated to a rational exit without serious jams, and the utilization rate of exits is improved. Fig. 16 shows the simulation curve of evacuation time against individual acceptance coefficient in the library. With the increment of , evacuation time shows a downward trend. When pedestrians can comply with the evacuation guidance absolutely in the evacuation system, the evacuation efficiency will be improved a lot and the imbalanced evacuation process can be reduced.
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Fig. 15 Snapshot of pedestrians evacuation process via each exit: Pink grids: pedestrians evacuated via
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exit 1; Blue grids: pedestrians evacuated via exit 2; Brown grids: pedestrians evacuated via exit 3
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5. Conclusion This paper proposes a simplified method to provide evacuation guidance in a multi-exit building by employing an evacuation system. The modified model reduces the imbalanced evacuation by adopting exit weight coefficients, which translates pedestrians' congestions around exits into a simplified weight coefficient. It can redistribute static floor field and prevent evacuation procedures and efficiency from being affected by the asymmetrical layout of exits or pedestrians. Then the simulation results of the modified model are transferred to the emergency evacuation guiding sub-system, which can provide guiding information to individual. The individual acceptance coefficient is introduced to describe the acceptance degree of guiding information from guidance equipment.
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Fig. 16. Simulation curve of evacuation time against individual acceptance coefficient
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Through the analysis and comparison of the simulation results, it is proved the effectiveness of the modified FF model in reducing evacuation time and improving the utilization rate of exits in a multi-exit building. It indicates that the evacuation time depends on the layout of pedestrians and exits in an evacuation area and pedestrian's acceptance degree. The unbalanced evacuation
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procedure could be relieved effectively with proper exit weight coefficients, and evacuation time could be reduced with the increment of the value of individual acceptance coefficient. This work considers the effect of congestion in advance rather than during the evacuation process. The simplified method can help to disperse the congestion to each exit in a multi-exit building rather than let pedestrians congest in front of only one or some exits, which improves the utilization rate of exits. This method can be applied to the evacuation system in crowded multi-exit buildings to reduce the evacuation imbalance. The most ideal condition is that it only takes several seconds to calculate the exit weight coefficient of the building according to the real position of pedestrians, which has a high demand for computational effectiveness. The exit weight coefficients can also be calculated by the simulation program ahead of time according to the probable distribution of pedestrians in the building, which can be a referenced evacuation scheme in real-time as well. When pedestrians in the evacuation system evacuate according to the guidance, the evacuation procedure and efficiency can be optimized. However, pedestrians' behavior of following the guidance usually alters during evacuation, so they need to be trained in daily drills. In future work, we will conduct more research about pedestrians' complex behavior in the simulation model.
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(MIIT No. [2016]546). The authors deeply appreciate their supports.
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Acknowledgments This work is supported by the Ministry of Industry and Information Technology project “Research on Emergency and Escape Technology for Large Living Quarters of Offshore Platforms”
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Journal Pre-proof *Declaration of Interest Statement
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: