Modeling passengers’ motion at high speed railway (HSR) station has been a hot topic in the field of pedestrian flow theory. However, little effort has been made to explore the passengers’ boarding behaviors at the platform of HSR station. This study proposes a cellular automaton (CA) model to study the passengers’ boarding behavior at the platform of HSR station. Some numerical tests are conducted to explore the passengers’ movements and the complex traffic phenomena (e.g., each passenger’s trajectory, congestion, and travel time) which occur during the boarding process. The numerical results illustrate that the passengers’ inflow rate and entrance choice behavior have significant impacts on the boarding efficiency. These results can help managers to understand the passengers’ boarding behavior and to improve the boarding efficiency.
With the rapid development of urbanization, overcrowding occurs in many stations, stadiums, and other public places [
High speed railway (HSR) has been considered as a significant technological breakthrough of transportation tool in the 20th century [
However, the studies [
However, the scenarios in [
During the boarding process at HSR station, platform and hall are two important scenarios. To study this topic, Tang et al. [
At the platform of HSR stations, pedestrian movements are different from those at the platforms of other stations due to the platform layout and passenger management. Currently, each HSR platform is equipped with two entrances. Also, the entrances are regarded as obstacles for those who move at the platform. Passenger seats are allocated beforehand; thus the destination carriage is allocated as well. In terms of pedestrian flow, the density is relatively low at HSR platform. Pedestrian flow in an origin HSR station is unidirectional flow and correspondingly boarding behavior is the significant pedestrian characteristic. The comparison of railway, subway, and HSR station platform in terms of layout, management, and pedestrian characteristics is summarized in Table
Comparison of railway, subway and HSR station platform.
Layout | Management | Pedestrian characteristic | ||||
---|---|---|---|---|---|---|
Entrance | Obstacle | Seat/carriage allocation | Density | Direction | Boarding∖alighting behavior | |
Railway station | One entrance (see Figure |
No obstacle | Beforehand allocated | Relatively low | Bidirectional or unidirectional | Boarding or alighting |
Metro station | Two or more entrances (see Figure |
The entrances are obstacles | Self-determined options | Relatively high | Bidirectional | Boarding and alighting simultaneously |
HSR station | Two entrances (see Figure |
The entrances are obstacles | Beforehand allocated | Relatively low | Unidirectional | Boarding |
Specifically, the pedestrian movements at the platform of HSR stations have the following three attributes: (1) the pedestrian flow on a HSR platform is usually of low density and is close to a free flow since the platform size of HSR station is greater than that of other stations (i.e., the length is usually several hundred meters and the width is more than ten meters), that is, the congestion only occurs around the entrance and near the carriage’s door. (2) The HSR platform is always equipped with two entrances (see Figure
Architectural structure of platform of different stations.
Layout of platform of railway station in [
Layout of platform of metro station in [
Layout of platform of HSR station
Pedestrian flow models can roughly be sorted into macroscopic ones and microscopic ones. The macroscopic models explore the macroscopic features of pedestrian flow (e.g., speed, density, and flow), where the fluid dynamic model [
In this paper, a CA model is used to study the passengers’ movements at the platform of HSR station, where the scenario is equally divided into cells and the Moore neighborhood is used to update each passenger’s movement at each time step. Each pedestrian at cell
The scheme of Moore’s neighborhood.
Since
For simplicity, (
Based on the above discussion, the passengers’ motion update rules at each time step are summarized in the flow chart shown in Figure
The flow chart of update rules at each time step.
This model is developed from the basic CA model. And it is possible that the simulation results of this model can be realized by other models.
In this section, the proposed model is used to explore each passenger’s boarding behavior at the platform of HSR station. To display the feature of each passenger’s movement, it is necessary to introduce the scenario of the platform at HSR station and give some basic assumptions in advance.
At the platform of HSR station, passengers’ movements can simply be formulated as follows.
(1) Passengers enter the platform from two entrances and will choose the entrance that is close to their target carriage.
(2) The density near each entrance at the platform is relatively high. The two entrances are located in the middle of the platform, so the passenger flow can be divided into two parts, where some passengers go ahead and others go back. At this time, the passenger flow in this area may be somewhat chaotic.
(3) After leaving the high-density area, most passengers move in free flow and walk in a straight line along the carriage until they arrive at the door of their target carriage.
(4) When reaching the target carriage, passengers immediately enter the carriage since the ticket checking is always ignored at the platform of the HSR station.
Before simulation, we should give the following assumptions based on field observations.
(1) The platform is defined as a rectangle with 208 m length and 12 m width (see Figure
The simplified sketch of the HRS platform.
(2) The platform is uniformly divided into
(3) Each passenger’s initial position lies at the right hand of square A or the left hand of square B (here, A and B denote two entrances and their sizes are
(4) The number of passengers is 640; each passenger’s desired speed is 1 m/s; each carriage contains 80 passengers; the time step is 0.4 s.
(5) The average check-time of passengers at each ticker barrier is set as 12 time steps based on [
First, this study explores each passenger’s trajectory at the platform of HSR station during the boarding process. If a one-dimensional curve is used to describe each passenger’s trajectory at the platform during the boarding process, some prominent features of the trajectory curves cannot be summarized since the curves are relatively chaotic. Therefore, each passenger’s trajectory is placed in the
Definition of
Figure
Each pedestrian’s trajectory, where (a) is the
(1) In the
(2) The passengers who have the same target carriages have similar trajectories in the
(3) Most curves in curves I, II, IV, V, VI, and VIII are approximately smooth straight lines; that is, most passengers’ speeds in the
(4) In the
Figure
According to (
(1) Frequently occupied cells are placed near each entrance and spread to the door of each carriage along the correspond route, so
(2) The passengers with the same carriage select the routes near the path to this carriage door, so
(3) During the boarding process, some passengers occur below A or B; that is, their
The cumulative density of cells can quantitatively reflect the spatial distribution of passengers during the boarding process. The total inflow rate decides the density around the path. Thus how the inflow rate affects the spatial distribution is to be studied. Table
The relationships between the number of cells with high cumulative density and total inflow rate.
Total inflow rate |
|
|
|
---|---|---|---|
4500 | 275.5 | 172.9 | 93.9 |
6000 | 274 | 167.3 | 90.7 |
9000 | 264.3 | 163.5 | 81.6 |
(1) The number of cells with high cumulative density drops with the increase of the total inflow rate. The reasons are as follows: (a) the higher total inflow rate means that more passengers appear at the platform simultaneously, and an individual has to occupy the space of 0.4 m
(2) When the cumulative density increases, the number of cells with high cumulative density prominently drops, where the reason is obvious.
Table
The relationships between
(1)
(2)
Each passenger’s travel time at the platform is an important factor of boarding efficiency, so it is needed to study it. Here, each passenger’s travel time at the platform is defined as the difference between the time that he leaves the platform and the time that he enters the platform. To eliminate the randomness, the average travel time of passengers is defined; that is,
The passengers with different carriages have different route and the distances between their origins and destinations are different and directly affect
The relationships between
(1)
(2) The quantitative relationship between
To better understand the distribution features of
The relationship between
(1) There are no prominent relationships between
(2) The relationships between
The passenger’s travel time can be used to qualitatively evaluate the boarding efficiency, but it is not intuitionistic and cannot provide his real route. The passenger’s real route may be longer than the distance between his initial position and target carriage during the boarding process, so the passenger’s real route can be used to evaluate the boarding efficiency. An index is defined to study the boarding efficiency; that is,
Equation (
The passengers’ average movement efficiency of each carriage.
(1) The routes from A (B) to C1 (C5) are similar to a straight line. At this time, the passengers whose target carriage is C1 (C5) move along the straight lane, so the passengers’ average movement efficiency is very high. As for the passengers whose destinations are other carriages, they have to make a turn when they enter the platform, so the real routes may deviate from the shortest route between their initial positions and target carriages; that is, the passengers’ average movement efficiency is relatively low.
(2) The trajectories of the passengers whose destination is C1 (C5) do not almost interweave with those of other passengers, so the passengers in C1 (C5) are not distributed in a wide area during the boarding process. This is another reason that makes the average movement efficiency of the passengers in C1 (C5).
In the above numerical tests, all passengers are assumed to select the entrance close to their carriage. However, some passengers may select the entrance far away from their carriage, where the passengers’ percentage is set as
The boarding time under different
From Figure
(1) When
(2) When
(3) BT drops with the increase of
From Figure
(1) Some interweaving between passengers occurs at the middle of the platform.
(2) The amount of interweaving increases with
In this paper, a CA model is used to study each passenger’s movement at the platform of HSR station during the boarding process. In this CA model, the static floor field potential and dynamic potential are calculated to update passenger movements. The simulation results display several indexes (i.e., trajectories, congestion, travel time, and movement efficiency), which shows that the proposed model can perfectly describe each passenger’s movement at the platform during the boarding process. Finally, the numerical results show that the parameter
Comparing with the existing studies, this study has the following new insights: (1) the simulation results show that passenger movements at platform are significantly influenced by their destination carriage; (2) passengers’ entrance choice behavior (which rarely draws researchers’ attention) is studied and the results show that the improper choice will not only produce bidirectional flow, but also prolong boarding time.
However, this paper still has the following limitations:
(1) Only the parameter
(2) The simulation results are not testified by experimental or video data.
(3) The simulation conditions used in this paper are not calibrated by the pedestrians’ attributes at the platform.
Therefore, experimental/empirical data are going to be used to propose a more realistic boarding model for HSR station and study various complex phenomena occurring during the HSR boarding process.
The authors declare that they have no conflicts of interest.
This work was supported by the National Natural Science Foundation of China (71771005, 71422001, and 71371128) and the Foundation of MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology in Beijing Jiaotong University.