In many countries, staircase is the only way to evacuate from a multi-story building when a fire or other emergency occurs.^[1] All the upper stories share the lower stairs, which leads to a natural merging behavior in the stair landing and the sharply increasing density will slower the evacuees’ velocity and the flow rate. Understanding the rules of merging will help improve the high-rise buildings’ evacuation strategies. In recent years, more and more scholars have paid attention to the merging behavior and conducted many valuable researches.

Pedestrian merging behavior can be divided into two parts, merging on the ground or merging along the vertical direction. Craesmeyer and Schadschneider developed a floor field model to describe the dynamics at T-junctions and compared the fundamental diagram with experiments.^[2] Cuesta et al. have built an experimental data-set about the passing time cost in various combinations of door weight, corridor weight, and the height differential at the junction.^[3] Aghabayk et al. have done some real merging experiments to compare the flow rates among the cases of different merging angles (60°, 90°, and 120°) at different walking velocities (1.5 m/s and 3 m/s).^[4] Analogously, Shi et al. conducted a series of controlled experiments considering symmetrical 60°, 90°, 180° merging angles and found that as the merging angle increases, mean velocity and mean flow in the measuring region decrease.^[5] Lian et al. analyzed a university-students’ experiment and studied the relationship between branch width and the flow rate.^[6] Chen et al. built a bidirectional pedestrian flow merging model based on social force model to simulate the merging behavior at a T-junction.^[7]

As for the merging behavior in stairs, as early as 2008, Galea et al. developed a C++ software including Occupant, Movement, Behavior, Toxicity, and Hazard sub-models. Conflict behavior was introduced to describe the merging behavior.^[9] Ding et al. investigated a computer simulation model to describe the merging behavior at the floor–stair interface and four different door positions were discussed. The results show that the door which is on the opposite side of the landing to the incoming stair is the best situation.^[10] Boyce et al. analyzed three evacuation drills in university and health center and the people’s merging behavior was described in detail.^[11] Xu and Song modeled the staircase evacuation with multi-grid CA model considering the turning behavior, and compared the simulation results with an egress drill.^[8] Huo et al. extended the original lattice gas model by considering inner-side walk preference, turning behavior, and different desired speeds. The simulation results had the same tendency as the empirical data.^[12] After that, Huo et al. conducted two different experimental scenarios. The speed of participants walking through two adjacent floors and the space–time distribution were discussed.^[13] Sano et al. put forward a simplified mathematical model for calculating the evacuation time from a multi-story building. In this model, the merging rate is continuous and the merging ratio is equal for all the stories. The result was compared with a simulation model using SimTread.^[14]

Summarizing the current models, it can be found that when the people come into the landing, the merging behavior occurs naturally. However, in our real life, when the pedestrian faces a crowded staircase, he prefers to await for a certain amount of time to avoid congestion rather than to walk into the landing directly. To describe the procession of stair evacuation, the waiting time and policy should be considered in the models. As a consequence, a series of low-density merging experiments are conducted in this paper. Waiting policy considering the influence of crowd density is involved in the improved cellular automaton model to simulate the merging behavior on stairs.

The rest of this paper is organized as follows. In Section 2, the experimental procedure is introduced. In Section 3 the change of the model is presented. The drills and simulations are compared in Section 4 and expansion simulation is conducted in Section 5. Finally, the conclusions and disscusion about the experiments and the model are given in Section 6 and Section 7 respectively.

The experiments were conducted in the 4-story simulation building. The structures of the building stairs are shown in Fig. 1. All the participants were college students from two classes of the same department. There were 33 students in class one and 29 students in class two. Besides, there are 2 guide students in each experiment. The students starting from floor 3 were regarded to wear blue hat and those from floor 2 wore red hats, so it was easy for us to distinguish the different crowds in merging areas.

Fig. 1.

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	Fig. 1. Structures of building stairs: (a) structure of the stairs between the 3rd floor and the 1st floor; (b) stereogram of stairs; (c) stair tread.

At the beginning of the drills, the participants were divided into 2 parts randomly. They were arranged in a single line behind the door on floor 2 and floor 3 respectively. The two guide students were assigned to be the heads of the two lines respectively. The participants in the two lines were required to “try to merge into one line when going downstairs”. After hearing the order “Go!”, the guide student on floor 3 began to walk into the stair landing and went downstairs first. Other students on floor 3 followedthe guide. To extend the merging time period, the students on floor 2 were regarded as starting to participate in the experiment after the first floor 3 student had come into the downward staircase of floor 2. The drills ended after all the students had passed through the door of floor 1. The same procedure was repeated separately by class one, class two and the two class together. Figure 2 shows the beginning lines and figure 3 shows the merging behavior and leaving behavior.

Fig. 2.

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	Fig. 2. Lines of students on (a) floor 2 and (b) floor 3 about to start experiment.

Fig. 3.

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	Fig. 3. (a) Merging on floor-2 landing, where the red hat tries to merge into the two blue hats, and (b) leaving on floor 1.

The cellular automaton (CA) model has been widely-used in many fields, such as pedestrian simulation in buildings,^[15–23] crossing streets,^[24] choosing exits,^[25–27] the interaction among pedestrians and vehicles,^[28,29] the self-organized phenomenon,^[30] etc. Especially, because the space in a CA model is discrete and the same as that in a staircase, it is also used to simulate the pedestrian flow in stairs or escalators.^[21,31,32]

This improved CA model is based on the one considering evacuee’s walk preferences of Ding et al.^[33,34] The cell size in the landing is 0.5 m × 0.5 m and that in the steps is 0.5 m × 0.28 m. From the experiment video data, it is found that there is one or two evacuees’ lines in the step because the number of evacuees is not so large, which means that the extra 20-cm step width has no influence on the model. That is to say, the 1.2-m width step can be replaced with 2 cells. In the experiment, evacuees are regarded as leaving the door in a single line, so the door can be represented by one cell but not two cells. The landing and the staircase are divided into 6 parts just as shown in Fig. 4. The moving direction depends on the location area. On the red line, the pedestrian transfers to another floor in the model.

Fig. 4.

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	Fig. 4. Model area setting and moving direction.

Fig. 5.

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	Fig. 5. Video snapshot of experiment, showing (a) 1-step distance in higher density; (b) 2-step distance in lower density.

3.1. Walk preference

In the Ding’s model^[34] evacuees’ desiring to keep distance with others is introduced and the neighborhood around a pedestrian with two situations is defined. In this experiment, some new characteristics are found.

When the evacuees are in lower density situation, for example, only the students from floor 3 walking on the treads, the distance between two pedestrians is 2 steps. After students from floor 2 come into the stream, the distance becomes 1 step. As the evacuees on the treads accumulate, the distance turns into 0 step. The distance between the evacuees in the experiment video snapshot is shown in Fig. 3. As a result, the neighborhood of a pedestrian on the step is changed as shown in Fig. 6, while the neighborhood types on the landings are consistent with each other.

Fig. 6.

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	Fig. 6. Neighborhoods in different condition for (a) low step density, (b) medium step density, (c) high step density, and (d) landing neighborhood with no change.

3.2. Merging policy

While the pedestrians on the upper floor walk through the front landing, the students will make a decision about whether to merge into the flow considering the landing density and their own patience of waiting. If the landing density is considered as being high by the pedestrian, he/she will await for a moment until the density becomes bearable. With the waiting time accumulating, the endurance to high landing density increases and the desired density advances, too.

What is more, if a large number of people come into the landing in a few seconds, that is to say, the landing density is foreseen to be higher, the endurance will increase.

According to the experiment videos, the desired landing density in the new model is divided into three states: low density (landing people number is less than 3), medium density (landing people number is between 4 and 6), high density (landing people number is more than 6). At the beginning of the experiment, the desired density is low density. The desired density will increase one level after every 4-s waiting (it takes 4 s for someone to walk through half the floor staircase in the experiments). Meanwhile, if the number of people on the last 3 steps of the upward stairs is more than 5, the desired density will also increase one level. In one computation step, the desired density is changed as shown in Table 1.

Table 1.

Table 1.

Table 1. Desired density changing situation. . Original state Waiting time Upper number Summary Final state Low < 4 s < 5.5 +0 low >5.5 +1 medium 4 s < 8 s < 5.5 +1 > 5.5 +2 high > 8 s < 5.5 +2 > 5.5 +3

Table 1. Desired density changing situation. .

3.3. Right priority

The right preference is considered by several models.^[8,33] In Ding’s model, high probability rightward is considered, which may cause an unreasonable phenomenon during evacuation simulation. For example, when someone occupies a landing cell next to the staircase, it is possible that the pedestrian walks back to the tread in the simulation. Consequently, the right preference is changed at the particular positions. For pedestrians in the landing cells next to the staircase, the staircase side is not considered no matter wherher the cell is occupied. An example is demonstrated in Fig. 7.

Fig. 7.

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	Fig. 7. Special neighborhood.

It should be noted that participants are all college students aged from 20 to 24. Consequently, the features in this paper cannot represent the general characteristics of old people or children. Moreover, the floor number involved in the experiment is limited and the fatigue is not considered in the model. Besides, the experiments and the simulations are all for normal environment. It will be very different in emergency due to panic emotion. However, the model introduces high landing density endurance (in Subsection 3.2) to describe the merging decision. High endurance may be useful for panic evacuation simulation, which needs further research.

In this work, an improved CA model describing the merging behavior in the stairwell landings is presented and validated experimentally. This paper focuses on studying the factors influencing the evacuation from high-rise building, such as the floor number, evacuee number, and door location. The results show that the door located next to the downward staircase leads to fastest evacuation and the total time ascends linearly with the floor number increasing. Additionally, the pedestrians on upper floors have a negative influence on evacuation flow rate.

In conclusion, the improved CA model is good for describing the merging behavior and can extend to other high-rise building staircase evacuation scenarios.