Short-Term Metro Daily Passenger Flow Prediction Using Machine

Learning

Leyang Liu

School of Science, Renmin University of China, Beijing, China

Keywords: Time Series Analysis, Machine Learning, Passenger Flow Prediction.

Abstract: The prediction of daily passenger flow in the metro would be meaningful to the construction and operation of

urban rail transit, which is common in megacities of China. The study takes the daily passenger flow of the

Beijing metro as an example and tries to make a short-term prediction of it based on its historical data. Since

the data volume is relatively small, resulting in an overfitting problem when applying mainstream time series

models like Recurrent Neural Network (RNN) and Long Short Term Memory (LSTM), four selected machine

learning models are applied to this topic. Their prediction performance is compared by not only the common

indicator like Mean Squared Error (MSE) and their comprehensive performance. The result shows that the

machine learning models considering both seasonality and holiday factors perform best and have the strongest

interpretability. For future research, it’s possible that the combination of multiple machine learning models

would achieve better results or with stronger interpretability in this topic.

1 INTRODUCTION

With the acceleration of urbanization in China, many

people are flooding into megacities. A common

solution to transport such a large volume of passengers

is establishing a transportation system based on rapid

rail transit, with conventional public transportation and

multiple transportation modes coordinating, where

urban rail transit is the top priority. Passenger flow is

the basis of the planning, design, construction, and

operation of urban rail transit. Therefore, passenger

flow prediction is an important link in the construction

and operation of urban rail transit, which to a

considerable extent determines the form and cost of the

line, the selection of operating vehicle models, and the

size of train stations. With the improvement of the

urban rail transit network and the increasing intensity

of passenger flow, it is particularly important to grasp

the trend of passenger flow changes in the short term

in the future. Since the total length of metro lines

accounted for 77.8% of the total length of urban rail

lines, the metro passenger flow prediction is a vital part

of the urban rail passenger flow prediction and an

emerging research field that triggers significant social

attention.

The study will use the Beijing metro as an example

to predict the daily overall metro passenger flow, a

typical time series prediction problem. The passenger

flow will be influenced by historical data, holidays,

and other factors (Zheng et al 2021). The basic idea is

to divide the dataset into the training set and the test

set, using the training set data to train the model and

capture periodic and holiday features in the data, then

compare and analyze the predicted passenger flow by

the model and the true value in the test set. The study

hopes to provide a reasonable method to predict daily

passenger flow according to historical data and

holiday information.

2 DATA SOURCE AND

COLLECTION

The study used the daily passenger flow of the Beijing

Metro from February 13 to August 10, 2023, for

approximately half a year. Due to the COVID-19

epidemic, Beijing was in a state of long-term

lockdown from the beginning of 2020 to December

2022, with subway passenger flow at a low level in the

past three years; from December 2022 to January

2023, despite the unblocking of China, nearly 90% of

the people are infected with COVID-19, which means

the metro passenger flow was at an even lower level.

The data during that period is of limited reference

significance since the public has a stronger confidence

to travel and stronger resistance toward COVID-19.

Although the passenger flow before the epidemic

faced a similar social situation and public travel

confidence, the reference value of passenger flow

Liu, L.

Short-Ter m Metro Daily Passenger Flow Prediction Using Machine Learning.

DOI: 10.5220/0012809800003885

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 1st International Conference on Data Analysis and Machine Learning (DAML 2023), pages 349-355

ISBN: 978-989-758-705-4

Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.

349

before the epidemic was not significant due to the

opening of some new metro lines in Beijing during the

epidemic period. The study only selected metro

passenger flow data from February 2023 onwards.

Since long-term prediction may be affected by subway

construction planning and has little application value,

the study aims at short-term prediction. Therefore the

six-month dataset should be sufficient.

Figure 1: Daily passenger flow of Beijing metro

(2023.2.13-2023.8.10) (Original).

The data is collected from the official Weibo

account of Beijing Metro. Daily traffic data is filtered

and stored in an Excel file by crawling down all posts

on the official Weibo account. The format of the data

is presented in Table 1 and the data is visualized in

Figure 1.

Table 1: Example of the Passenger Flow Data.

Date

Passenger Flow(ten thousand people)

2023-2-13

851.06

2023-2-14

885.72

2023-2-15

856.93

2023-2-16

855.13

2023-2-17

897.63

2023-2-18

514.52

2023-2-19

524.49

3 ANALYTICAL METHODS

Zeng (2021) indicates that because historical

passenger flow data can reflect future passenger flow

trends, time series models are widely used in

passenger flow prediction (Zeng et al 2021).

Meanwhile, in megacities like Beijing, the metro is the

first commuting choice for many office workers.

Therefore, commuter passenger flow is an important

component of metro passenger flow, which endows

daily subway passenger flow with significant

periodicity, that is, the passenger flow on weekdays is

significantly greater than that on weekends, and the

cycle is one week (7 days). It should also be noted that

metro passenger flow is significantly affected by

holidays, especially during large and long holidays

such as summer vacations.

Based on the above considerations, the selected

time series model should be suitable for periodic data.

Limited by the data volume, some mainstream, more

complex passenger flow prediction models, such as

Long Short Term Memory (LSTM) and Transformer

neural networks, risk overfitting and weak

interpretability (Haimin et al 2019, Yuanhong et al

2023 & Yun 2022). Thus the study selected the

following four more explanatory models for

comparative analysis.

3.1 SARIMA

The basic idea of the ARIMA (Auto Regressive

Integrated Moving Average) model is to use the

historical information of the data itself to predict the

future. It extracts the patterns of time series hidden

behind the data through autocorrelation and

differentiation and then uses these patterns to predict

future data, which can better capture the trend changes

of the data (Taylor and Letham 2021, Triebe et al 2021

& Qingmei and Xiping 2020). The formula is as

follows.

φ

φ

θ

θ

. Where Y is the time

series under consideration, φ

the parameters

of the AR (Auto Regressive) model, describing the

correlation between the current value and the values

of p past ttimepoints; θ

are the

parameters of the MA (Moving Average) model,

describing the correlation between the current value

and the error at q past time points. C is the constant

term and ε

is the error term. Y should be a stationary

sequence, and when the data is a non-stationary

sequence, it can be transformed into a stationary

sequence through differentiation.

SARIMA (Seasonal Auto Regressive Integrated

Moving Average) is a seasonal time series prediction

model based on the ARIMA model (Hahn 2023,

Tiwari et al 2022 & Chatterjee et al 2021). It first

performs seasonal differentiation, which removes

seasonal components from the time series.

Specifically, a n-order differentiation is performed

when the seasonal period is n. Then the ARIMA

model is fitted with the differential sequence. Due to

the significant periodicity of metro passenger flow

data, the study adopted the SARIMA model.

DAML 2023 - International Conference on Data Analysis and Machine Learning

350

3.2 Holt-Winters

Holt Winters is an optimization of the MA (Moving

Average) method, which uses the cubic exponential

smoothing method to input historical time series data

into three recursive sequences, then calculate the

predicted data values from the recursive values of the

three sequences (Chatterjee et al 2021). This method

can effectively predict non-stationary sequences with

linear trends and periodic waves. A "cumulative"

exponential smoothing will be used for subway

passenger flow data. The formula is as follows.

(1)

(2)

(3)

(4)

(5)

(6)

Where is the data smoothing factor and ;

is the trend smoothing factor and ; is

the seasonal change smoothing factor and

. m is the length of time that needs to be predicted and

L is the length of the cycle.

3.3 Prophet

Prophet is a Facebook open-source time series model

that takes trend lines, seasonality, periodicity, and

exogenous variables into account during the modeling

process. It has good predictive performance and

significant advantages over traditional time series

models. The formula of the model is as follows.

(7)

Where g(t) is the trend term, s(t) is the seasonal or

periodic term and h(t) is the holiday term or mutation

caused by the big event. The trend term includes linear

growth models and logistic growth models. For

periodic changes, the model uses the Fourier series to

simulate.

(8)

The values of N and P vary depending on the

period. The paper recommends using P=7 and N=3 for

weekly seasonality (Taylor and Letham 2021). The

combination of seasonal and trend terms includes

addition and multiplication. For the collected data,

after testing, it is better to use linear trend terms and

additive combinations.

Meanwhile, the Prophet model allows for the

inclusion of holiday terms, so holiday changes in metro

passenger flow caused by summer vacation are

considered based on trends and periodic changes.

Particularly, two columns of Boolean variables are

added to the Data Frame of the original data to

determine whether it is in the summer season. The

judgment criteria are that when the months are July and

August, it is considered to be in the summer season.

Table 2: Example of the Data Format after Adding Boolean

Variables that Determine whether It Is in the Summer

Holiday.

Date

Passenger

Flow

On

Summer

Holiday

Off

Summer

Holiday

2023-2-13

851.06

False

True

2023-2-14

885.72

False

True

2023-8-9

915.99

True

False

2023-8-10

916.31

True

False

3.4 Neural Prophet

Neural Prophet is a decomposable time series model

just like Prophet (Triebe et al 2021). Compared to the

previous version of the Prophet model, it has similar

components such as trend, seasonality, and special

events. The difference lies in the introduction of auto-

regression terms, future regression terms, and lagged

regression terms. The trend is modeled by a linear or

combined model of multiple linear trends that includes

various change points. Seasonality is modeled using

Fourier terms, and autoregression terms are processed

using AR Net, an autoregression feed-forward neural

network used for time series. Lagged regression terms

are also modeled using a single feed-forward neural

network. Future regression terms and special events

are both covariant of the model.

For a classic AR model, the modeling process

p-order autoregression can be understood as a linear

combination of several past data.

(9)

When modeling autoregression terms using AR

Net, Neural Prophet directly imitates the expression of

Classic AR in the first layer, adding several hidden

layers to achieve more accurate predictions. The

learning process still uses MSE as the loss function,

also to maintain consistency with Classic AR.

For the prediction of subway passenger flow, the

settings of trend, season, and holiday items will be

Short-Term Metro Daily Passenger Flow Prediction Using Machine Learning

351

Figure 2: Result of the ADF test after removing seasonality (Original).

consistent with Prophet. Based on this, a lagged

regression term will be added as a comparison.

4 RESULT ANALYSIS

Since the Prophet and Neural Prophet need to consider

the effects of summer vacation, a part of the data on

summer holidays needs to be included in the training

set. Therefore, the data from the last 20 days is divided

into the test set, and the remaining data is divided into

the training set. Use the trained model to predict the

passenger flow of the validation set for the 20th day

and compare it with real data, using MSE as the

evaluation indicator.

4.1 SARIMA

After removing seasonality, an ADF test was

conducted on the data, as shown in Figure 2. The

sequence is relatively stable, thus the ARIMA model

can be applied to the sequence.

After establishing the ARIMA model, the predicted

results are shown in Figure 3. It’s clear that the model

reflects a cyclical trend within a week. Still, the

predicted values are significantly lower than the true

values in weekday data. Considering that all the test set

data are within the summer vacation, it is reasonable to

speculate that the model did not consider the rise of

passenger flow in summer vacation.

Figure 3: Performance of SARIMA model on the test set

(Original).

4.2 Holt-Winters

The prediction result of the Holt-Winters model is

shown in Figure 4. Compared to the SARIMA model,

Holt-Winters not only reflects periodic changes but

also fits better with the original data. Notably, there are

two days when the true values are significantly lower

than predicted. Considering the rainstorm in Beijing

from July 30 to August 1, 2023, a reasonable

explanation is that people's travel was blocked in the

heavy rain, and the passenger flow was significantly

reduced, which is an accidental incident. Overall, the

model has good prediction performance.

Figure 4: Performance of Holt-Winters on the test set.

4.3 Prophet

After considering the impact of summer vacation on

passenger flow, the result is shown in Figure 5, the

contribution of each component to the passenger flow

is shown in Figure 6, and the performance on the test

set is shown in Figure 7. It can be seen that the trend

term went upwards generally. Considering that with

the loose of epidemic policies, public confidence in

travel significantly increased, and China's economic

development is gradually stabilizing, the overall

growth trend can be expected. As for the periodic

change term, there is a clear periodic feature that

passenger flow stays relatively high on weekdays and

relatively low at weekends in both summer and

nonsummer seasons, which truly reflects the impact of

commuting passenger flow. Another noteworthy

feature is the greater fluctuation in passenger flow on

summer vacation. One possible explanation is that

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352

during the summer vacation, due to increased ecdemic

tourists, local people in Beijing travel less on

weekends. These people contribute to the total

passenger flow on weekends off summer vacation, but

do not contribute to passenger flow on weekends on

summer vacation; During the summer vacation, the

passenger flow on weekdays is jointly contributed by

commuters and ecdemic tourists, while during

nonsummer vacation, there are almost no ecdemic

tourists on weekdays. In conclusion, the delta of

passenger flow between weekdays and weekends on

summer vacation mainly results from the commuters.

In contrast, off summer vacation, the delta needs to

consider the decrease of commuting passenger flow

and the increase of local tourists. Therefore, there’s

an Increased fluctuation in passenger flow on summer

vacation.

Figure 5: The results of the model fitting the data after

considering the impact of summer vacation (Original).

Figure 6: The contribution of different components in the

Prophet (Original).

Figure 7: Performance of Prophet on the test set (Original).

4.4 Neural Prophet

After making corresponding settings, the performance

of the model on the test set is shown in Figure 8, the

contribution of trend term on the train set is shown in

Figure 9, the contribution of trend term on the test set

is shown in Figure 10, and the comparison between the

test set and the true value is shown in Figure 11. It can

be seen that although the predicted values on the test

set are more in line with the true values and capture

periodic features in the data, the fluctuation of the trend

term is very severe and weird, and it seems to be overly

affected by the fluctuation of the data. Even on the test

set, the trend term saw an unusual downward trend,

significantly different from the actual situation. It is

inferred that the model has been overfitting.

Figure 8: Result of Neural Prophet fitting the data (Original).

Figure 9: Contribution of trend term on train set (Original).

Figure 10: Contribution of trend term on test set.

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353

Figure 11: Performance of Neural Prophet on test set

(Original).

4.5 Overall Comparison

The MSE of the four models on the test set is shown

in Table 3.

Table 3: MSE of Four Models on the Test Set.

Model

SARIMA

Holt-

Winters

Prophet

Neural

Prophet

MSE

7912.78

10120.70

6489.86

5616.15

Due to the influence of the outliers resulting from

the rainstorm from July 30 to August 1, the MSE of

each model is relatively large and is seriously affected

by the outliers, which cannot be directly used as the

standard for judging the quality. Overall, the best-

performing model is Prophet, followed by Holt-

Winters and SARIMA, while Neural Prophet exhibits

significant overfitting when the autoregressive term is

included.

5 CONCLUSION

The traditional SARIMA and Holt-Winters models

capture the periodic characteristics of Beijing subway

passenger flow within a week. Still, it is difficult to

reflect the impact of holidays or other big events.

Therefore, prediction accuracy, especially during

holidays, is relatively low; The Prophet model takes

holidays into account and can customize the start and

end dates of holidays. It achieves good results

regardless of whether the predicted period is during

holidays or not, with higher prediction accuracy. The

Neural Prophet model incorporates the autoregressive

term. Judging from the MSE, it performs best on the

test set, but from the component decomposition

graphs, it is clear that the model overfits the data.

Currently, some mainstream passenger flow

prediction models have adopted relatively complex

combination neural networks. However, from the

results, for daily passenger flow prediction, due to the

complexity of the data, complex models are not the

most suitable models. Instead, simple machine

learning models are sufficient to capture important

features in the data of daily passenger flow. As shown

in the results, the models that consider holiday factors

perform better than those that only consider cyclical

and seasonal features.

The study has provided a general daily passenger

flow prediction method and shown the result of some

single machine learning models. It’s still worth

exploring whether combining multiple machine

learning models would achieve better results or

stronger interpretability in this topic. Another

direction worth exploring is how to reduce the

problem of overfitting complex models like neural

networks and enhance their interpretability in this

topic. Also, an important factor that is widely

overlooked is weather. It would be advisable to take

the weather into account. For example, when the

weather is very hot, people are likely to choose the

subway as a means of transportation due to the cooling

effect of the air conditioning in the subway and the

comfortable environment.

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