Experiment, theory, and simulation of the evacuation of a room without visibility

We study the evacuation process from a smoky room by means of experiments and simulations. People in a dark or smoky room are mimicked by “blind” students wearing eye masks. The evacuation of the disoriented students from the room is observed by video cameras, and the escape time of each student is measured. We find that the disoriented students exhibit a distinctly different behavior compared to a situation in which people can see their environment. Our experimental results are related to a theoretical approach and reproduced by an extended lattice gas model taking into account the empirically observed behavior. Our particular focus is on the mean value and distribution of escape times. For a large number of people in the room, the escape time distribution is wide because of jamming. Surprisingly, adding more exits does not improve the situation in the expected way, since most people use the exit that is discovered first, which may be viewed as a kind of herding effect based on nonlocal, but direct acoustic interactions. Moreover, the average escape time becomes minimal for a certain finite number of people in the dark or smoky room. These nonlinear effects have practical implications for emergency evacuation and the planning of safer buildings.

Figure 1

Schematic illustration of the classroom of width $W=4.2\mathrm{m}$ and length $L=5.5\mathrm{m}$, in which desks, chairs, and other obstacles have been moved aside. There is only one exit in the front of the classroom, the width of which is $0.5\mathrm{m}$. Two video cameras 1 and 2 were located within and in front of the classroom to record the motion of all test persons. In our experiments with ten persons, everyone started in the central area indicated by the dashed line. White circles represent the initial (off-lattice) positions of the test persons, while the simulation model approximates their motion with a lattice gas model in which particles hop between the discrete sites of a square-diagonal lattice with $W=11$ sites in the $x$ direction and $L=14$ sites in the $y$ direction (see also Figs. 6, 9, 10). The possible directions of motion are indicated by the solid lines (see Fig. 6), while the elementary cells are $W\times L$ squares. When the site next to the exit is reached, the corresponding walker is removed immediately in analogy to our experimental observations.

Figure 2

Four typical trajectories of students until they successfully escape from the room. Their face direction at the initial position is indicated by an arrow. Below each trajectory, the escape time obtained from the experiment is indicated.

Figure 3

Photo of the evacuation of students from the room at $t=16\sec$.

Figure 4

Time evolution of the evacuation process of ten students without visibility of the exit. The patterns (a)–(d) were obtained at $t=0\sec$, $5\sec$, $10\sec$, and $15\sec$. Numbered circles represent ten disoriented students with eye masks, whose face directions are indicated by arrows.

Figure 5

Time evolution of the evacuation process for ten students in a room with normal visibility. The patterns (a)–(d) were obtained at $t=0\sec$, $1\sec$, $3\sec$, and $5\sec$. Their face directions are indicated by arrows.

Figure 6

Illustration of the variables occuring in the theoretical approach to our evacuation experiment from a smoky room (see text for details).

Figure 7

Two of all possible configurations of a biased-random walker on the square-diagonal lattice, where bias is applied to the upward direction. Configuration (a) shows the situation of being able to move to all the nearest-neighbor and next-nearest-neighbor sites. The arrows indicate the possible directions in which the walker can move. Configuration (b) shows the situation in which another walker occupies one of the nearest-neighbor sites, which is indicated by a cross.

Figure 8

Representative trajectories obtained from the simulation when there is only one walker. The escape times obtained are shown below the trajectories.

Figure 9

Plot of the probability density of the simulated escape time for a single walker.

Figure 10

Simulated time evolution of the evacuation process of ten persons. The patterns (a)–(d) were obtained at $t=0\sec$, $5\sec$, $10\sec$, and $15\sec$. Solid circles represent ten students, whose face directions are indicated by arrows.

Figure 11

Simulated time evolution of the evacuation of 20 persons. The patterns (a)–(d) were obtained at $t=0\sec$, $5\sec$, $10\sec$, and $\mathrm{20}\sec$.

Figure 12

Plots of the probability densities of the simulated escape times for (a) 5, (b) 10, (c) 15, and (d) 20 persons. In each figure, the probability density distributions are shown for the 1st, 5th, 10th, 15th, 20th, and all persons.

Figure 13

Probability density distributions of the simulated escape times for all persons in the case of 1, 5, 10, 15, and 20 walkers.

Figure 14

Plot of the mean escape time of the first escaped walker as a function of the overall number of walkers who are initially present in the room.

Figure 15

Plot of the average escape time as a function of the initial number of walkers. Circles represent the results for one single exit. In the two-exit simulation, the average escape time is only reduced a little, as walkers orient towards the exit which has been discovered first, which produces jamming at one door (scenario A, see the squares). The expected significant reduction in the average escape time is only found, if walkers do not react to the discovery of a door by other walkers (scenario B, see the triangles).

Figure 16

Plot of the overall evacuation time of all walkers as a function of the initial number of persons. A second exit reduces the overall evacuation time with respect to the situation with one exit (circles), but it does not reduce it by a factor of 2. If people orient towards the first discovered door (scenario A), the overall escape time is mainly reduced by the earlier discovery of an exit (squares). However, the overall escape time is normally much higher than in the hypothetical scenario B, for which we assume that the discovery of an exit by other people is not recognized or ignored, and both exits are equally used (triangles).