The pedestrian choice behavior between escalator and stairway is a complex process and can be influenced by individual characteristics, pedestrian flow conditions and facilities conditions.^[27–29] Pedestrian individual characteristics mainly include gender, age, luggage, walking speed, etc. Pedestrian flow conditions mainly include the difference between queuing pedestrians, the degree of crowdedness, etc. Facilities conditions mainly include the interlayer height, the width of stairway, the width of escalator, the speed of escalator, etc. Different pedestrians have different decision-making psychologies, for example, the pedestrian who carries a large amount of luggage tends to choose the escalator, the older pedestrian tends to choose the escalator, and the pedestrian in a hurry tends to choose the stairway.

Because the factors that have an influence on the pedestrian choice behavior between escalator and stairway are multiple and there may be collinearity and interdependence among these factors, it is necessary to select the key influence factors.^[2]

Based on the relevant research,^[1–7] the pedestrian flow data of the transfer passage are gathered. Four main factors which include the interlayer height, luggage, the difference between queuing pedestrians, and walking speed, are selected by the method of Regression Analysis Stepwise (RAS) and are added into the choice model as characteristic variables. The model variables are listed in Table 1.

Table 1.

Table 1.

Table 1. Introduction of model variables. . Type Characteristic variable Characteristic value Independent variable Interlayer height The actual value Luggage 1: without luggage or a little amount2: a moderate amount of luggage3: a large amount of luggage The difference between queuing pedestrians The difference in the number between queuing pedestrians in front of escalator and stairway Walking speed 1: low speed: v ≤ 1.3 m/s2: moderate speed: 1.3 m/s < v ≤ 1.7 m/s3: high speed: v > 1.7 m/s Dependent variable Vertical walking facilities −1: escalator 1: Stairway

Table 1. Introduction of model variables. .

As the relationship among influencing factors of pedestrian choice behavior is nonlinear, so the problem of pedestrian choice of vertical walking facilities in a transfer station is regarded as a nonlinear classification problem. The support vector machine has the ability to solve the problems of a small sample and nonlinear classification.^[30–32] So, the support vector machine is used to build the pedestrian choice model.

According to the analysis results of influence factors for pedestrian choice behavior, interlayer height, luggage, the difference between queuing pedestrians, and walking speed are the key influence factors. The pedestrian characteristic vector is described as follows:

The pedestrian sample set can be described as follows:

The problem of pedestrian choice of vertical walking facilities in a transfer station is regarded as a nonlinear classification problem, and pedestrian samples cannot be separated linearly. So, it needs to map the samples into the high dimensional feature space through the mapping function ϕ(x), and the nonlinear classification problem can be transformed into a linear separable problem.

In the support vector machine, as for the linear binary classification problem, the purpose of model optimization is to find a hyperplane to separate two kinds of samples. The hyperplane is described as follows:

According to the structural risk minimization principle, the minimum risk is achieved when the classification interval becomes largest during the separation. And according to the relevant research, the problem of searching for the optimal hyperplane is transformed into the problem of optimization, which is described as follows:

The Lagrange multiplier method is used to solve the problem of optimization. The optimal classification decision function is obtained as follows:

To overcome the curse of dimensionality, according to the Mercer theorem, the kernel function K(x,x_i) is used to replace ϕ (x) · ϕ (x_i), namely K (x,x_i) = ϕ (x) · ϕ (x_i). Radial basis function (RBF) is selected as a kernel function, and the formula is given as follows:

The pedestrian samples data of Changchun light-rail transfer station and Beijing Xizhimen transfer station were collected by recording videos on August 16, 2015 and August 17, 2015, respectively. According to Table 1, we transfer the video data into pedestrian sample data by artificial means. 880 pedestrian samples for each of the upward and downward directions are selected out, randomly. Each pedestrian sample contains the real situation of the interlayer height, luggage, the difference between queuing pedestrians, walking speed, and the choice result.

The prediction process of pedestrian choice behavior is as follows:

Step 1 Data preprocessing

According to Table 1, we should transform the pedestrian samples which contain the real situation of the interlayer height, luggage, the difference between queuing pedestrians, walking speed, and the choice result into the corresponding characteristic values. For example, if the pedestrian carries no luggage or a little amount, we set the characteristic value of luggage to 1; if the walking speed of the pedestrian is 1.5 m/s, we set the characteristic value of the pedestrian walking speed to 2.

Step 2 Parameters optimization

With the increasing of the value of C, the empirical risk decreases and generalizing ability weakens. So, under the premise of high accuracy, a smaller C is needed. With the increasing of the value of g, the empirical risk increases, and the empirical risk increases and the generalizing ability strengthens. So, a suitable g is needed. The optimal parameters of C and g are achieved through a genetic algorithm, and the processes are shown in Figs. 1 and 2. In the upward direction, the optimal value C_up is equal to 2.531 and g_up is equal to 0.359. In the downward direction, the optimal value C_down is equal to 4.055 and g_down is equal to 0.392.

Fig. 1.

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	Fig. 1. Parameters optimizing process in the upward direction.

Fig. 2.

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	Fig. 2. Parameters optimizing process in the downward direction.

Step 3 Prediction and accuracy analysis

Based on the survey data, we select 800 pedestrian samples for each of the upward and downward directions randomly as the training set. On the platform of the Libsvm toolbox in MATLAB software, with the training set and the optimal parameters C_up, C_down, g_up, and g_down, the Svmtrain function is used to solve the optimization problem of formula (4). And the pedestrian choice results of the remaining 80 pedestrian samples for each of the upward and downward directions are predicted by the Svmpredict function. The prediction results are shown in Table 2.

Table 2.

Table 2.

Table 2. Predicted results of pedestrian choice behavior. . Upward Downward Number of samples 80 80 Prediction accuracy/% 91.25 87.50 Mean prediction accuracy/% 89.38

Table 2. Predicted results of pedestrian choice behavior. .

From Table 2, it is noted that the prediction accuracies of pedestrian choice behavior in upward and downward directions are respectively 91.25% and 87.50%. The prediction results of pedestrian choice behavior are good.

There are five assumptions in the process of pedestrian simulation.

Assumption 1 There is no sojourn time when pedestrians make a decision in front of the escalator and stairway.

Assumption 2 All pedestrians make their decision of choosing escalator or stairway in the choice zone.

Assumption 3 All prediction results of the pedestrian choice model of vertical walking facilities are correct.

Assumption 4 The expectation speeds of all pedestrians are the same.

Assumption 5 The different forms of movements on stairs and escalators are not considered.

Scenario A The transfer passage of Changchun light-rail transfer station is selected as a research object. We set the size of a cell to be 0.4 m × 0.4 m, which is the typical space occupied by a pedestrian.^[33] With the actual measurement, the simplified simulation scenario is shown in Fig. 3. In Fig. 3, the length of the passage is 118 cells and the widths of both entrance and exit are all 9 cells; the width of the upward escalator is 2 cells; the width of the downward escalator is 2 cells; the widths of upward and downward stairways are both 5 cells; the lengths of escalator and stairway are both 46 cells. The upward and downward escalators are on the same side of the passage.

Fig. 3.

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	Fig. 3. Scenario A.

Scenario B Generally, the number of pedestrians choosing the escalator is more than choosing stairway, and the escalator is narrower than the stairway. Therefore, the density of pedestrian flow is larger and there always appears the phenomenon of queuing in front of the escalator. As the actual observation, the upward and downward escalators on the same side would lead to more conflicts and increase the pedestrian delay time. In order to reduce the conflicts between pedestrians coming from opposite directions, the upward and downward escalators are set separately on both sides of the passage and the stairway is set in the middle with the same size as shown in Fig. 4. Scenario B is the improved Scenario A.

Fig. 4.

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	Fig. 4. Scenario B.

In the process of calculation of the floor field, when pedestrians can only walk in the horizontal and vertical directions, the minimum step between cell (i,j) and exit m is denoted by . When pedestrians walk in horizontal, vertical, and diagonal directions, the minimum step between cell(i,j) and exit m is denoted by . The weighted distance to the exit m is denoted by .

The detailed generation process of static floor field is described as follows.^[33,34]

Step 1 Initialize and . For arbitrary cell(i, j), set and if the cell(i, j) is wall or barrier, and and otherwise.

Step 2 Set k = 1; calculate the distance to the exit in four directions (horizontal and vertical).

Step 2.1 Check grids in four directions around the exits, namely, front, rear, left, and right, denoted by (i′, j′); if , then set ;

Step 2.2 For an arbitrary cell where , check cells in four directions around it, namely, front, rear, left, and right, denoted by (i′, j′); if , then set , k = k + 1;

Step 2.3 If ∃i, j, , repeat Step 2.2; otherwise, go to Step 3.

Step 3 Set k = 1; calculate the distance to the exit in eight directions (horizontal, vertical and diagonal).

Step 3.1 Check the cells around the exit in eight directions, denoted by (i′, j′); if , then set ;

Step 3.2 For an arbitrary cell where , check (i′, j′) around it in eight directions; if , then set , k = k + 1;

Step 3.3 If ∃ i, j, , repeat Step 3.2; otherwise, go to Step 4.

Step 4 Calculate the weighted distance .

Step 5 Calculate the static floor field value .

In the choice zone, simulate the pedestrian choice behavior by switching the floor field, and set the weight coefficient ε to be 0.4. Before choosing escalator or stairway, the LP (Pedestrians generated on the left side of the passage) have the probabilities to walk on the downward escalator or stairway, but they cannot walk on the upward escalator. So, we can set the upward escalator as the barrier.

Figure 5 shows the floor field for LP without choosing vertical walking facilities in Scenario B. With choosing the downward escalator, the LP only has the probability of walking on the downward escalator. So, we can set the upward escalator and stairway as the barrier.

Fig. 5.

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	Fig. 5. Floor field for LP without choosing escalator or stairway in Scenario B.

Figure 6 shows the floor field for LP with choosing the escalator in Scenario B. In the same case, for the LP with choosing the stairway, we set the upward and downward escalator as the barrier. Figure 7 shows the floor field for LP with choosing the stairway in Scenario B. The white cell represents the exit of the passage, and the dull-red cell refers to wall or barrier.

Fig. 6.

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	Fig. 6. Floor field for LP with choosing escalator in Scenario B.

Fig. 7.

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	Fig. 7. Floor field for LP with choosing stairway in Scenario B.

In general, cellular automata Moore motion rule is widely used.^[35] In Fig. 8, including the position occupied by himself, there are nine positions for a pedestrian to go. The transition probability of a pedestrian to each position is shown in Fig. 9.

Fig. 8.

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	Fig. 8. Moore motion rule.

Fig. 9.

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	Fig. 9. Transition probability.

With the cellular automata Moore motion rule,^[36] the transition probability of a pedestrian is calculated as follows:

The k_S and k_D have a remarkable influence on the distribution of the floor field values. In the process of simulation, k_D reflects the following trend of pedestrians. Since the scenario discussed in this paper is the transfer passage of the station, we can treat pedestrians as people who have a specific aim. There is no need to consider the aimless following phenomenon. So, we set the coefficient of dynamic floor field k_D to be zero. If k_D is set to be a fixed value, when k_S increases gradually, the pedestrian motion time would decrease in a nonlinear way.^[37] When the coefficient of static floor field k_S is equal to 3, the pedestrian motion time is a well acceptable value and the walking features of the pedestrians would appear in the simulation, for example, pedestrians gather in front of the narrow exit and present an arched shape close to the narrow exit. So, we set the coefficient of the static floor field k_S to be 3.

According to the actual observation, the capacity is larger at the position where the passage becomes wider, and the change of pedestrian flow state gives a ‘message’ to each pedestrian. Most pedestrians make a choice between escalator and stairway at the position where the passage becomes wider. According to the actual observation, we set the width of the choice zone to be 2 cells and the probabilities of pedestrian choice behavior occurring in 2 cells are equal. The choice zone of Scenario B is shown in Fig. 10.

Fig. 10.

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	Fig. 10. Choice zone in Scenario B.

There are two rows of cells in the choice zone, so we set the probabilities of pedestrian choice behavior in the first and second row cells as both 0.5. When a pedestrian arrives at the first row cells of the choice zone, a random number R(R ∈ [0, 1]) is generated. If 0 ≤ R ≤ 0.5, the pedestrian chooses to take the escalator or take the stairway according to the pedestrian choice model in the first row cells of the choice zone. If 0.5 < R ≤ 1 , the pedestrian chooses to take the escalator or take the stairway according to the pedestrian choice model in the second row cells of the choice zone. In this way, the pedestrian choice model of vertical walking facilities is added into the pedestrian simulation model and the pedestrian choice behavior is simulated.

Pedestrians are generated on both sides of the passage, and walk towards the escalator and stairway. When pedestrians arrive at the choice zone, the real-time characteristics of height, luggage, the difference between queuing pedestrians, and walking speed are extracted. Based on these four influence factors, the pedestrian choice model is used to make the choice between escalator and stairway, and the pedestrian choice behavior is simulated by switching the floor field.

Pedestrians generated on the left side of the passage are marked as LP. Pedestrians generated on the right side of the passage are denoted as RP.

Taking the LP in Scenario B for example, the transition probability calculation of LP is dependent on the floor field which is described in Fig. 5 at the beginning. When they arrive at the choice zone, they choose to take the escalator or take the stairway according to the pedestrian choice model of the downward direction. If the pedestrian chooses the escalator, the transition probability calculation of the pedestrian is dependent on the floor field described in Fig. 6. If the pedestrian chooses the stairway, the transition probability calculation of the pedestrian is dependent on the floor field described in Fig. 7.