In the microscopic evacuation model, the desired direction of the pedestrian is consistent with the minimum-distance direction. However, the minimum-distance route may not same as the minimum-time route. The evacuation time is made up with the movement time to the exit and waiting time at the exit. The movement time is determined by the exit location, while the waiting time is determined by pedestrian distribution and exit width. The microscopic model usually solves the exit choice based on the distance, and other constraints are rarely taken into account. However, in some cases, the shortest distance does not necessarily guarantee the minimum evacuation time. For example, when there is a high occupant density around the nearest exit, the pedestrian will spend a lot of waiting time if he chooses the nearest exit. Instead, if he changes his option to select a farther exit, he may leave more quickly if there is a low occupant density around the exit. Moreover, suppose there are two optional exits, one of which has a shorter distance and smaller width, the other has a longer distance and larger exit width. Choosing the nearer exit rather than the farther one may spend more time because the exit width is too small to let the crowd pass quickly. The key of solving this issue is to help the pedestrian know how long he will wait at the exit. The waiting time is related to the pedestrian distribution and exit width. Thus, the individual evacuation time is not only related to the distance but also the pedestrian distribution and exit width. When choosing the exit, not only the exit position (evacuation distance) should be considered in estimating the evacuation time, but also the pedestrian distribution and exit width.
In this paper, the optimal exit choice algorithm is presented based on the microscopic model. The algorithm aims at the shortest individual evacuation time which is calculated in iterative method. The factors such as pedestrian distribution, exit position and exit width are all involved in the time evaluation function in the algorithm. Taking a room with multiple exits as an example, the cellular automata model is applied to simulate the evacuation process, and the evacuation time with optimized and non-optimized exit choice are compared and analyzed.
To be noticed, for the reason that during the evacuation process, nervous and herding might influence the exit chosen behavior, the occupants might not change their decision as long as the exit they chose is available. As a consequence, in the present article we do not intend to introduce dynamical method to determine the exit option of the occupants. What is more, frequently changing signal of exit signs could induce potential crowd disaster when occupants follow these signals and change their moving directions from time to time. As a result, the optimal exit selection method is a statistic algorithm.
The exit choice for each pedestrian is visually displayed by the exit selection zoning map. The zones occupied by pedestrians with different colors are associated with different exits. Each zone covered with the same color corresponds to one exit.
The results show that under the influence of the optimized exit choice, some people no longer choose the nearest exit but the exit with larger width or with lower occupant density around. The algorithm solves the problems of uneven and inadequate utilization of the exit in the evacuation.
As the exit choice changed, the evacuation time through each exit changed accordingly. The overall evacuation time, namely the maximum value, is the time when all the pedestrians leave the room. It is found that the overall evacuation time drops from the 850s to 564s for the optimized exit choice, which indicates that the evacuation efficiency increases by 33.64%.
The standard deviation of the evacuation time can reflect the uniformity of the exit utilization. The higher the value of the standard deviation is, the greater the difference of exit utilization is. The results show that the standard deviation of the evacuation time for the original exit choice is 195s, while the value for the optimized exit choice is 145s. It indicates that adopting the optimized exit choice realized the diversion of the crowd flow during the evacuation, and the waiting time was distributed approximately evenly.
Idle time of an exit is defined as the difference between the overall evacuation time and the evacuation time of the exit. It is found that compared to the original exit choice, the idle time for all exits with optimized exit choice decreases greatly. For the original choice, the average idle time is 520s and the maximum idle time is 781s. When taking optimized choice, the average idle time reduces to 226s and the maximum idle time 454s. The average idle time drops by 56.54%, which demonstrates that taking optimized exit choice effectively reduces the vacancy rate of the exit and enhances the utilization greatly.
The optimal algorithm gives the exit selection zone map which can provide reference for planning evacuation. As one evacuee cannot get global information of all evacuees in the room, they may choose the nearest exit but need to wait for a long time. Thus, it is necessary to guide evacuees to the most proper exits from the global perspective. The dividing line between different exit selection zones is the key to allocate evacuees. In case of emergency, the executor should assign some guiders near the dividing line to conduct evacuees to an optimal exit according to the zone map. In fact, the exit selection zone map from the results provides the placement of guiders and the guiding direction to the designer.