Evacuation time is a significant safety coefficient for Urban Metro Hubs (UMHs). Usually, a reasonable model for evacuation time will effectively promote the safety for pedestrian when emergency incidents occur in UMHs. In this paper, we propose a pedestrian evacuation time model for UMHs to improve the accuracy and reliability of its evacuation time. Firstly, we design an experiment survey based on the multiple video sequences to analyze the characteristics of pedestrian flow. Then, we decompose the evacuation process on the basis of the parameters, which involve the evacuation characteristics, the speed-density variation law, the pedestrian drop-off time, the platform evacuation time, and the channel evacuation time. Finally, we take the Bei Da-jie metro hub in Xi’an as an example, and verify the feasibility of the proposed pedestrian evacuation time model. The results show that the relative error for the evacuation time between the experiment result and the actual data is only 1.90%, where the experiment time is 169.87 s and the actual time is 166.64 s. Moreover, the proposed model strictly follows the Code for Design of Metro (GB 50157-003) and hence it can provide a good theoretical guidance for innovating the evacuation efficiency and the design reasonability of UMHs.
Transport plays an important role in enhancing the quality of our living environment. The Urban Metro Hubs (UMHs), known as a key node of the integrated transport system, are the distribution center of passenger flow and play a crucial role in providing multimodal access to people and services in a manner that is convenient, safe, affordable, sustainable, efficient, and enjoyable. With the steady and rapid growth of passenger flow as well as the intensive transit, the closed environment space, and the complex transfer networks, the UMHs have become places vulnerable to extreme events, such as fire, stampede, and delay. Therefore, a time model for pedestrian evacuation is vital, for one thing, it can improve the efficiency of pedestrian evacuation, for another, it also ensure the passengers’ life with a reasonable evacuation strategy.
In recent years, the pedestrian evacuation dynamics theory has become a hot topic in the academic field; they focus their attention on the passenger distribution characteristics and traffic behavior. It has made considerable progress since the 1980s; the researchers observed the characteristics of pedestrian movement regularity. With the deepening of the research on the regularity in the pedestrian movement, some also put physiological and psychological characteristics of pedestrians as a factor into consideration and set up a large amount of pedestrian simulation models, which is considered to be a powerful tool for evaluating pedestrian flows in facilities. These models can be classified as macroscopic and microscopic models. These scholars who study macroscopic models believe that pedestrian movement behavior is similar to the flow of gas or liquid [
In China, the study of pedestrian and evacuation dynamics theory is in early stages, which is mainly focused on pedestrian traffic characteristics in urban traffic environment and the crowd evacuation in large public places or buildings (e.g., a theatre, a stadium, or a shopping mall). In the first part, [
Through analyzing the current research on pedestrian, this paper maintains that the study of pedestrians and evacuation dynamics is more focused on a building (e.g., a theatre, a stadium, or a shopping mall), rather than the UMH. What is more, these models do not consider the queuing delay caused by limite dcapacity in stairs or escalator, gate and China’s pedestrian characteristics are ignored. On the basis of summarizing traditional evacuation time models, this paper proposes to do research, respectively, on the character of the UMHs structure and Chinese pedestrian traffic characteristics and meanwhile use queuing theory and fluid mechanics simulation theory to establish a pedestrian evacuation time model in UMHs, which includes the pedestrian drop-off time, pedestrian evacuation time in platform, and pedestrian evacuation time in the channel.
Observational station (Bei Da-jie) for pedestrian flow.
The video camera layout drawing in Bei Da-jie hub.
A specific operation is as follows. At the exit: we select the video cameras, which represent the purple circle1, the purple circle2, the purple circle3, the purple circle4, and the purple circle5, to observe the pedestrian flow’s parameters. On the stairs and escalators: we select the video cameras, which represent the blue circle1, the blue circle2, the blue circle3, the blue circle4, the blue circle5, and the blue circle6, to observe the pedestrian flow’s parameters. Where the blue circle1, the blue circle2, and the blue circle3 are used to observe the parameters of down direction of the stairs and escalators, meanwhile, the blue circle4, the blue circle5, and the blue circle6 are used to observe the parameters of up direction of the stairs and escalators. In the TVM: we select the video cameras, which represent the green circle1, the green circle2, the green circle3, and the green circle4 to observe the pedestrian flow’s parameters. In the auto gate: we select the video cameras, which represent the red circle1, the red circle2, the red circle3, and the red circle4 to observe the pedestrian flow’s parameters. In the transfer channel: we select 1 video camera independently to observe the pedestrian flow’s parameters in the transfer channel. On the platform: we select 1 video camera independently to observe the pedestrian flow’s parameters in the platform.
Data collection by the video camera.
Video acquisition method, which is one of the widely methods in the investigation. The advantage of the method is convenient for storage and revisit detail information. At the same time, the advantage of the method is almost collects all of the multiple video sequence data in the pedestrian flow characteristics. The observation pedestrian flow is used to the video acquisition method such as speed, and density in the platforms, transfer channels, auto gates, stairs and escalators, exits, and so on.
The pedestrian speed is calculated by the length and time of the observation area in the camera. In the observation, not only record the speed but also the pedestrian density and the corresponding pedestrian flow of the moment, and then put all the multiple video data into the tables, for the purpose of subsequent data analysis. In the process of data analysis, we use the SPSS to fit the curve relationship of pedestrian flow parameters, and we also test the fitting degree using the value of
Through the observation and analysis in Xi’an Bei Da-jie hub, the walking speed and spaces characteristic are different from each other; based on these differences between them, we decompose the evacuation process, and the pedestrian evacuation time (
Decomposition process of safety evacuation in UMHS.
Pedestrian drop-off time refers to the train arriving at the station stably and the time all passengers droping off from the train to the platform. Drop-off time is related to drop-off numbers, get-up numbers, and the width of the train gate door. Here we suppose the pedestrian drop-off time is
Through the analysis, we can conclude that the relationship between the single door drop-off time and the number of passengers is different; it can be power exponent relationship, linear relationship, exponential relationship, and natural logarithm. Among them, the power exponent relationship’s correlation coefficient (
The function curve fitting between passenger number and drop-off time.
In Figure
Safety evacuation time in platform is described in metro design code in China; namely, the width of the exit stairs and evacuation corridor should guarantee the passengers both on the train and the platform and staffs working in the station to escape the fire disaster in 6 minutes. Specific safety evacuation time in platform in metro specification can be seen as follows:
The evacuation time in platform in metro specification above only considers the biggest evacuation capacity of different facilities and thinks little of the pedestrian density and the impact of environment on pedestrian speed, and the influence of guideline information (directional signs, direction signs, radio evacuation command, radio evacuation message, etc.) is also insightful and thinks little about the factors that may affect traffic organization in the transport hub, making the large deviation time between the theoretical calculation result and the actual evacuation. Hence, in the process of channel (stairway, escalators) evacuation, we consider the speed-density change law of the traffic flow, taking wave theory as an example to simulate the pedestrian flow, as well as considering the accumulation and dissipation characteristic of pedestrian, compared to only considering the evacuation capability on the platform which has improved, further to improve the traditional evacuation time model.
Platform evacuation time can be divided into three phases, as shown in Figure
Pedestrian evacuation process.
Here we suppose the safety evacuation time in platform is
Thus the evacuation time in platform
We suppose the time of pedestrian pass channel, stairway (or escalators), is
Create fit curve between speed and density.
According to the fitting functions between the speed and density of pedestrians, we can see that there is a strong correlation between the speed and density of pedestrians in a subway corridor or in the stairway (upward direction and downward direction of the stairs), and they comply with third-degree polynomial curve (
Model summary and parameter estimates.
Equation | Model summary | Parameter estimates | |||||||
---|---|---|---|---|---|---|---|---|---|
|
|
df1 | df2 | Sig. | Constant |
|
|
|
|
Logarithmic | 0.795 | 236.71 | 1 | 61 | 0 | 1.228 | −0.355 | ||
Cubic | 0.934 | 276.576 | 3 | 59 | 0 | 1.651 | −0.229 | −0.113 | 0.022 |
Exponential | 0.894 | 516.655 | 1 | 61 | 0 | 1.836 | −0.349 |
The independent variable: density.
Dependent variable: speed.
Thus the time of pedestrian pass channel can be shown as follows:
Passengers queuing at the auto gate.
In the standard M/M/C and M/M/1/C model, the regulation of characteristics of those models is the same with the standard M/M/1. In addition, specified the auto gates are mutual independent and the average service rates are the same; namely,
Similarly, we find the entire gates idle probability
average number of customers in system average numbers of customer in the queue expected value of stay time in the system
Thus, pedestrian dissipation time on auto gate is
The whole pedestrian evacuation time in the Urban Metro Hub is as follows:
The safety evacuation time of pedestrian is divided into three parts, and with those three parts added up we can get the whole evacuation time. Taking the pedestrian drop-off time, safety evacuation time in platform, time of pedestrian pass channel, and stairway (or escalators) into consideration, the safety evacuation time model in UMHs is established and is shown in what follows:
In this paper, we take the Bei Da-jie metro hub in Xi’an as an example, mainly based on two reasons. On the one hand, the station is a typical “ten” shaped metro interchange station, line 1 and line 2 meet here, line 1 site is side platform, line 2 site is an island platform, and the pedestrians’ walking flow lines are shown in Figure
Pedestrians’ walking flow lines.
Before studying the pedestrians’ transfer time model in Xi’an Bei Da-jie station, some parameters are measured, which are shown in Table
Observed values of model parameters in various stages.
Number | Model name | Index name | Observed values | Unit |
---|---|---|---|---|
1 | Pedestrian drop-off time |
|
20 | — |
|
||||
2 | Pedestrian evacuation time in platform |
|
1.495 | (m/s) |
|
1.05 | (m/s) | ||
|
0.93 | (m/s) | ||
|
1.167 | (p/m2) | ||
|
1.193 | (p/m2) | ||
|
2.181 | (p/m2) | ||
|
28.24 | m | ||
|
||||
3 | Pedestrian evacuation time in channel |
|
1.314 | (p/m2) |
|
100 | m | ||
|
6 | — | ||
|
0.5 | (p/min) | ||
|
1.35 | (p/min) |
The observed pedestrian evacuation time in each stage.
Stage name | Observed time (s) |
---|---|
Pedestrian drop-off time | 11.16 |
Pedestrian evacuation time in platform | 44.86 |
Pedestrian evacuation time in channel | 113.85 |
Total time |
|
The calculated pedestrian evacuation time in each stage.
Stage name | Calculated time (s) |
---|---|
Pedestrian drop-off time | 12.23 |
Pedestrian evacuation time in platform | 42.76 |
Pedestrian evacuation time in channel | 111.64 |
Total time |
|
The relative error analysis.
Stage name | Observed time (s) | Calculated time (s) | Relative error |
---|---|---|---|
Pedestrian drop-off time | 11.16 | 12.23 | −9.59% |
Pedestrian evacuation time in platform | 44.86 | 42.76 | 4.68% |
Pedestrian evacuation time in channel | 113.85 | 111.64 | 1.94% |
Total time |
|
|
|
(1) Through calculating the whole evacuation time in Xi’an Bei Da-jie transfer hub, the observed results in the model are 169.87 s, the calculated results in the model are 166.64 s as well, and the relative error between them is 1.90%, where we have the following. (a) The pedestrian drop-off time’s measured value is 11.16 s, the value of calculation is 12.23 s, and the relative error is −9.59%. (b) The value of measure in platform evacuation time is 44.86 s, the value of calculation is 42.76 s, and the relative error is 4.68%. (c) The value of measure in channel evacuation time is 113.85 s, the value of calculation is 111.64 s, and the relative error is 1.94%. Compared to the Code for Design of Metro (GB 50157-003) promulgated by Ministry of Housing and Urban-Rural Construction of the People's Republic of China (MOHURD), the whole time is 166.64 s, less than the 6 min in Code for Design of Metro (GB 50157-003), and the applicability of the pedestrian evacuation time model was verified.
(2) In terms of the pedestrian drop-off time model, through fitting analysis with the multiple video sequence data, the four functions of the relationship are fitted between passengers getting off them through a single door and a number of alighting passengers; the fitting functions are composed of the exponent relationship, linear relationship, exponential relationship, and the natural logarithm relationship. The correlation coefficient of exponent relationship is the largest and the correlation coefficient (
(3) In terms of the channel evacuation time models, the pedestrian evacuation time model has been split into the time that pedestrians pass through the corridor, the auto gate, and stairs or escalators. The research result indicates that there is a strong quartic polynomial relation between pedestrian flow velocity and density of the subway corridor and upward direction and downward direction of the stairs. The time of pedestrians through the auto gate is to meet the standard M/M/C model. The actual evacuation time in the hub corridor can be better reflected while comprehensively considering the time, which consider pedestrians passing through the corridor, the auto gate, and stairs or escalators into the channel evacuation time model.
(4) In addition, as a future work, we only take the Bei Da-jie transfer hub in Xi’an as an example and verify the feasibility of the proposed pedestrian evacuation time model. Next, we should do lots of experiment surveys, such as other Urban Metro Hubs in Xi’an, verify and modified the model. In addition, could the Urban Metro Hubs (UMHs) become a full-time laboratory? What if you could analyze every transaction, capture insights from every passenger interaction, and did not have to wait for months to get data from the field? What if…? Big data are flooding in at rates never seen before—doubling every 18 months. In the future, how to set up the platform for big data, big discovery, and big decision in the UMHs? The answer is technology. Technology for capturing and analyzing big data is widely available at ever-lower price points. With the recent developments of sensing, networking, and computing technologies, more and more UMHs-related big data and computational resources become available.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper has been supported by the National Natural Science Foundation of China (Grant no. 51208051) and the Fundamental Research Funds for the Central Universities (