When urban rail transit is faced with a large number of commuter passengers during peak periods, passengers are often waiting for the next train because the subway is running at full load, which causes delays to the overall travel time of passengers. The calculation and prediction of the congestion delay in subway stations can guide the operation department and passengers to make better planning and selection. In this paper, we use a new method based on deep learning technology to evaluate the congestion delay of subway stations. Firstly, we use automatic fare collection (AFC) system data to evaluate the congestion delays of stations. Then, we use a convolutional long short-term memory (Conv-LSTM) network to extract spatial and temporal characteristics to solve the short-term prediction problem of the subway congestion delay in the network structure. The spatiotemporal variables include inbound passenger flow, outbound passenger flow, number of passengers delayed, and average delay time. As a spatiotemporal sequence, the input and prediction targets are both spatiotemporal three-dimensional tensors in the end-to-end training model. The effectiveness of the method is verified by a case study of the Chongqing Rail Transit. Experimental results show that Conv-LSTM is better than the benchmark models in capturing spatial and temporal correlation.
With the rapid development of the national economy and the continuous improvement of the urbanization level, the number of passenger trips and construction projects of urban rail transit is also increasing rapidly. By the end of 2019, 40 cities in mainland China had opened urban rail transit, with annual passenger quantity up to 23 billion 710 million times. Moreover, there are still 65 cities whose urban rail transit plans have been approved, and China’s urban rail transit is in a period of great development and construction.
Although the subway has the characteristics of large passenger capacity, the imbalance of traffic supply and demand often occurs in the peak periods [
Subway congestion usually refers to the crowd in carriages. When passengers cannot get on the crowded subway car, it will reduce the comfort and increase the travel time [
The main contributions of this paper are as follows: (1) based on the calculation of passenger travel time using AFC data, we use the idea of control variables to eliminate interference factors and use the difference between the real travel time in the peak period and normal travel time in the off-peak period to evaluate passenger congestion delay. (2) The congestion delay of subway passenger flow in the whole network is represented by the image and time series. Among them, the image contains the spatial propagation of congestion delay between adjacent stations, and the time series contains the time dependence of subway station congestion delay. (3) We extend the traditional fully connected long short-term memory (FC-LSTM) network idea to the convolutional long short-term memory (Conv-LSTM) network, which has a convolution structure in both input-to-state and state-to-state transitions and can effectively capture spatiotemporal correlations of congestion delay. (4) The congestion delay of the whole Chongqing Metro network is calculated and predicted, and the effectiveness of the method is verified by the operation data. This is different from the traditional passenger flow forecast research, which is often limited to station or route-level forecasting.
The rest of this paper is organized as follows. Section
In the research field of the subway congestion delay problem, there is no complete and effective calculation and prediction method. However, in recent years, big data processing technology and artificial intelligence have developed rapidly, which provides us with new ideas and methods to study the subway congestion delay problem.
In the research field of subway passenger congestion delay, the existing literature mainly focuses on the evaluation and optimization of passenger travel time or waiting time. As early as 2009, Vansteenwegen [
In recent years, machine learning has made great progress in various practical applications [
In conclusion, by reviewing the existing results, we found that the inbound passenger flow at subway stations is generally influenced by the travel habits of passengers and the weather, so better prediction results can be obtained by using LSTM and its improved model [
Passenger flow congestion means that the movement of passengers is limited by other passengers and the state of the environment, increasing travel costs (travel time, physical consumption). The passenger congestion in the station shows that the limited space (station space, train residual capacity) and equipment capacity cannot meet the needs of passengers, thus gradually forming congestion. Compared with other periods, the passenger volume in the peak period is significantly higher, and a large number of passengers gather in a short time in the local space, which easily leads to passenger congestion. If we cannot achieve early warning and effective management, it will bring security risks to the subway operation. However, there are many reasons for passenger delays. For example, passenger flow congestion, train delay, signal failure, and other objective factors will cause an increase in passenger travel time. When the passenger travel time exceeds a certain threshold, it means that the passenger travel is different from the usual, and it is likely that there is a delay. Due to the congestion of passenger flow during the peak period, passengers are hindered by objective factors such as other passengers or control measures, resulting in extra time loss in the process of travel. Rather, the delay is expressed as the difference between the real travel time and the normal travel time.
Among them, the increase of travel time caused by passenger congestion is called congestion delay, which is the main research object of this paper. Congestion delay is mainly composed of walking delay and waiting delay. (1) The main reasons for walking delay include slow travel caused by passenger flow congestion, queuing caused by equipment capacity limitation, and increased travel distance caused by passenger flow organization adjustment in the station. (2) The main reason for the waiting delay is that passengers cannot get on the train in time due to the high full load rate. Therefore, this paper adopts the idea of control variables, selects specific dates to eliminate the interference of other factors (train delay and signal failure), and focuses on the impact of passenger flow congestion on travel time delay.
For the passengers who need to transfer in the process of travel, we can only know the location of the passengers in and out of the station through AFC data and cannot determine where the passengers’ transfer. Moreover, when passengers’ travel time increases due to passenger congestion, we cannot judge whether the increased travel time occurs at the origin station or the transfer station. Therefore, when we evaluate the degree of station congestion, we take nontransfer passengers as the research object. If this part of passengers has a congestion delay, it can also be judged that nontransfer passengers entering the station during the same period will also face the same congestion situation.
We assume that, during the off-peak period, passengers will not stay on board due to passenger congestion in the carriages or platforms. In this case, the waiting time of passengers is an approximately uniform distribution
Since the passengers’ walking speed is approximately normal [
Some researchers consider that, for the same station, the path of entering and leaving the platform is the same, so they set the walking time to enter and leave the station to the same value. However, through the investigation, we found that some stations have different routes for passengers to enter and leave the platform, passengers have different directions on the stairs when entering and leaving the platform, and the capacity of the stairs is also different. Therefore, we calculate and analyze the walking time to enter and leave the platform, respectively. For station
Taking the no transfer route (
According to the independence of each travel time element, the mean and variance of travel time can be given by
For line
Congestion delay refers to the additional part of travel time caused by passenger flow congestion in the stations and carriages. It mainly includes the extra walking time caused by the passenger flow congestion in the walking link and the extra waiting time caused by the passenger flow congestion in the waiting link.
For the same station at the same time point, due to different up and down directions, the waiting situation of passengers is also different. As shown in Figure
Numbering diagram of the platform in up and down directions.
Taking the no transfer route (
According to the independence of each travel time element, the mean and variance of travel time can be given by
Using the walking time
The time range of the station congestion study is divided into
If passengers arrive at the platform evenly, the average waiting time is equal to half of the departure interval. In other words, even if there is no congestion at the platform, half of the passengers’ waiting time is longer than half of the departure interval.
Therefore, for a specific passenger, even if
For station
For station
Passenger congestion delay has complex characteristics in spatial and temporal dimensions. The passenger congestion delay of a station at a certain time can be explained from two aspects. From the perspective of the temporal dimension, the passenger congestion delay of the next period can be regarded as the continuation of the passenger congestion delay of the previous period. From the perspective of the spatial dimension, the passenger congestion delay of a station is affected by the congestion delay of adjacent stations, and the congestion delay of adjacent stations has a certain spatial correlation. Therefore, we apply Conv-LSTM to deal with the spatial dependence, temporal dependencies, and the network topology properties of the subway passengers’ congestion delay. In this section, we will briefly review the traditional FC-LSTM structure and then explain the deep learning architecture and advantages of Conv-LSTM.
LSTM is a special form of the RNN structure, which is mainly used to solve the problems of gradient vanishing and gradient explosion in the process of long sequence training. In most RNNs, the hidden layer function
The main innovation of LSTM is that its storage unit is the accumulator of state information. Whenever there is a new input, if the input gate
The inner structure of an FC-LSTM layer.
Because the internal gate of FC-LSTM is calculated by a similar feedforward neural network, this structure can deal with the time-series data well, but for spatial data, it will bring redundancy. The reason is that spatial data have strong local characteristics, but FC-LSTM cannot describe these local characteristics.
To obtain a better spatiotemporal relationship of the model, we extend the traditional FC-LSTM idea to Conv-LSTM. The method is to replace input-to-state and state-to-state of FC-LSTM with convolution instead of feedforward calculation [
Comparison of (a) FC-LSTM and (b) Conv-LSTM.
As we defined, the grid of the subway congestion delay system in a spatial region is composed of
All the inputs
In this part, we can take Conv-LSTM as a model to deal with the eigenvectors in 2D meshes. We can predict the characteristics of the central grid according to the characteristics of the surrounding points in the grid. Therefore, we can make a short-term prediction of the subway congestion delay system under the spatiotemporal variables.
The training steps of Conv-LSTM are as follows (Algorithm
Record on the number of inbound passenger flow Record on the number of outbound passenger flow Record on the number of delay rate Record on the number of average congestion delay time Look-back window: Conv-LSTM with learned parameters Initialize a null set: For all defined time slice t do A training observation Initialize all the weighted and intercept parameters A batch of samples are randomly selected from The parameters are estimated by minimizing the objective function in Convergence criterion met
This paper takes the Chongqing subway network as an example to verify the model. In the Chongqing subway system, passengers need to input smart card information on the automatic fare collection system of each subway station. The AFC system records the entrance and exit information of each passenger (e.g., transaction time and station ID). An example of card data is shown in Table
An example of card data.
Car ID | Transaction date | Transaction time | Ticket type | Type | Station ID |
---|---|---|---|---|---|
020877757 | 20181021 | 17:44:29 | General card | Entry | 0321 |
020884738 | 20181021 | 17:44:09 | General card | Exit | 0316 |
020910814 | 20181021 | 17:43:55 | General card | Exit | 0325 |
020940911 | 20181021 | 17:44:10 | General card | Exit | 0318 |
We need to divide the subway network diagram into many small units and ensure that each small unit contains at most one subway station. Therefore, we take the row and column values of subway network cells as 64. Besides, the dataset will be divided into two parts: the first part is the training data (35 days), and the second part is the test data (5 days). We will test the Conv-LSTM model with different layers to determine the best structure. The future delay rate is predicted by using historical observation data such as the number of passengers entering or leaving the station, the delay rate, and the average delay time.
In this paper, root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (
Predictive performance comparison.
Model | RMSE | MAE | |
---|---|---|---|
ARIMA | 0.0409 | 0.0200 | 0.774 |
ANN | 0.0383 | 0.0209 | 0.790 |
CNN | 0.0354 | 0.0179 | 0.769 |
LSTM | 0.0381 | 0.0196 | 0.791 |
FC-LSTM | 0.0373 | 0.0188 | 0.796 |
Conv-LSTM | 0.0331 | 0.0165 | 0.806 |
Figure
Real delay rate distribution on the map during different time periods. (a) 07:00–08:00. (b) 08:00–09:00. (c) 17:00–18:00. (d) 18:00–19:00.
Predicted delay rate distribution on the map during different time periods. (a) 07:00–08:00. (b) 08:00–09:00. (c) 17:00–18:00. (d) 18:00–19:00.
Besides, we found some rules in the training and prediction of the model. First of all, the stations with the highest congestion delay are mainly concentrated in the subway stations at the intersection of line 1 and line 3 and the stations in the surrounding areas. This is mainly because line 3, as the longest straddle-type monorail transit line in the world, has its limited capacity. Moreover, line 3 passes through several important areas and transfer stations in Chongqing, attracting a large number of passengers. During the peak period, it is even necessary to wait for 5 trains to get on the train. Secondly, the peak of congestion in the morning peak occurs between 7:30 and 8:30, and that in the evening peak occurs between 17:30 and 18:30, which is consistent with the commuter rule of passengers. Thirdly, we also find that congestion mainly occurs in areas within the inner ring, while the possibility of congestion outside the inner ring is relatively small. This is related to the layout of the subway network created by the special terrain of Chongqing. There are relatively few routes to the central city, which make it easy for passengers to gather in the urban area, which will lead to congestion.
The method of combining passenger congestion delay distribution with visualization is helpful for the subway operation department to detect and forecast station congestion and provide a more reasonable basis for subsequent work plan arrangement and even subway network planning. At the same time, it can also provide a reference for passenger travel route planning.
Based on the analysis of the reasons for the delay of subway travel time, this paper uses the idea of control variables to propose the calculation method of passenger congestion delay at the subway network level. Considering that the passenger flow congestion between stations is communicable, the congestion of stations is not only related to the historical congestion of the station but also related to the congestion of adjacent stations. Therefore, combined with the temporal and spatial characteristics of passenger congestion, we use the improved deep learning method Conv-LSTM based on CNN and FC-LSTM to make a short-term prediction of subway station congestion delay. Conv-LSTM not only retains the advantages of FC-LSTM but also is suitable for spatiotemporal data because of its unique convolution structure. We use a variety of benchmark models to evaluate the performance of the proposed model. The test results show that Conv-LSTM is satisfactory in solving the passenger congestion delay prediction problem of the subway station.
In this paper, an end-to-end deep learning structure based on spatiotemporal variables is used to realize the short-term prediction of the passenger congestion delay distribution, which can real-time grasp the congestion situation in the subway network. On the one hand, it can help the operation management department to develop better management and planning schemes. On the other hand, it can help passengers grasp the congestion situation of subway stations and make better travel plans and choices. However, this paper also has corresponding shortcomings, such as transfer passengers will face twice or more waiting time, and we cannot accurately determine the specific time and place of congestion delay. In future work, we will discuss how to judge and calculate the congestion delay of transfer passengers and add it to the prediction model.
Access to data is restricted. The survey data source has certain confidentiality.
The authors declare that they have no conflicts of interest.
The authors thank Chongqing Rail Transit (Group) Co., Ltd., for providing the necessary data. This research was supported by the National Key Research and Development Program of China (2017YFB1200702).