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Forecasting for short-term ridership is the foundation of metro operation and management. A prediction model is necessary to seize the weekly periodicity and nonlinearity characteristics of short-term ridership in real-time. First, this research captures the inherent periodicity of ridership via seasonal autoregressive integrated moving average model (SARIMA) and proposes a support vector machine overall online model (SVMOOL) which insets the weekly periodic characteristics and trains the updated data day by day. Then, this research captures the nonlinear characteristics of the ridership via successive ridership value inputs and proposes a support vector machine partial online model (SVMPOL) which insets the nonlinear characteristics and trains the updated data of the predicted day by time interval (such as 5-min). Afterwards, to avoid the drawbacks and to take advantages of the strengths of the two individual online models, this research takes the average predicted values of two models as the final predicted values, which are called support vector machine combined online model (SVMCOL). Finally, this research uses the 5-min ridership at Zhujianglu and Sanshanjie Stations of Nanjing Metro to compare the SVMCOL model with three well-known prediction models including SARIMA, back-propagation neural network (BPNN), and SVM models. The resultant performance comparisons suggest that SARIMA is superior for the stable weekday ridership to other models. Yet the SVMCOL model is the best performer for the unstable weekend ridership and holiday ridership. It shows that for metro operation manager that gear toward timely response to real-world unstable and abnormal situations, the SVMCOL may be a better tool than the three well-known models.

Short-term ridership forecasting is a vital component of metro operation and management. Accurate predictions can reflect real-time changes in ridership. The prediction results can become important inputs for decision-making in evaluating rail transit service level and system operating status and provide an important basis for station passenger crowd regulation and emergency response. In addition, short-term ridership forecasting is the key to the success of revenue management for railway operators [

In the last two decades, traditional metro ridership forecasting is based on travel demand forecasting models including the steps of trip generation, trip distribution, mode choice, and assignment [

Though the spatial-temporal characteristics of metro ridership are not completely the same as those for vehicle traffic flow [

Whether it is traffic flow or passenger, time series model has become one of the classic models of short-term flow prediction [

Neural networks are among the most widely used nonlinear models. A neural network trains neurons based on historical data, maps the complicated nonlinear relation between input and output data, and uses the relationship for predictions for given inputs. Neural network algorithms have the adaptive and learning advantages and are flexible without the need to construct detailed and explicit models like other methods. Vlahogianni et al. [

Compared with neural network algorithm, support vector machine (SVM) model can strike a compromise between prediction accuracy and generalization ability based on the structural risk minimization principle. With the help of intelligent use of kernel function, SVM can solve the problems of small sample, nonlinearity and the curse of dimensionality, overfitting, and local minima. Zhang and Xie [

The research of short-term metro ridership forecasting is a rather new undertaking. Tsai et al. [

The reliability and the operability of the models play a crucial role in the accuracy and real-time implementation of the prediction, so the choice of the model is very important in a practical application. Since the characteristics of metro ridership are quite different from those in other transportation systems, most of forecasting models provide unsatisfactory prediction effectiveness. After comparing time series model, neural network model, and SVM model, this paper selects SVM model as the base short-term prediction model, considering capturing in real-time the periodicity and nonlinearity characteristics of short-term ridership as mentioned previously. With this base model, this paper proposes a support vector machine overall online (SVMOOL) model, which extracts input features via SARIMA model, trains the updated data by day, and optimizes the parameters by a particle swarm optimization (PSO) algorithm, to capture the periodicity of ridership in real-time. This paper also proposes a support vector machine partial online (SVMPOL) model, which extracts input features based on the temporal continuity of ridership model, trains the updated data by time intervals (such as 5-min), and also optimizes the parameters by a PSO algorithm to capture the nonlinearity of ridership. Afterwards, the support vector machine combined online (SVMCOL) model is proposed by combining the SVMOOL model and the SVMPOL model.

The main contributions of this paper are as follows.

This paper attempts to develop an online hybrid model to improve the forecasting performance of metro ridership. The rest of this paper is organized in the following manner. A brief theoretical background of the SVM model is presented first, followed by detailed description on SVMOOL model, SVMPOL model, and SVMCOL model. After that, a brief description of the data source and the implementation of the models are given. Finally, results analysis and conclusions are presented.

To introduce the SVMOOL, SVMPOL, and SVMCOL models, SVM model is illustrated here first.

A detailed description of SVM algorithm is given in Vapnik [

Ultimately, the decision function given by (

Identifying input features is crucial step in SVM modeling. Metro ridership has significant characteristics of periodicity and nonlinearity. Abe [

Parameter optimization is to obtain better forecasting accuracy of the SVM model. The parameters optimized are mainly the penalty coefficient, the insensitive loss coefficient, and the corresponding parameters of kernel function. The LibSVM package [

Support vector machine overall online (SVMOOL) model is based on the theory of SVM, to extract input features, to train the batched updated training data, to use intelligent algorithms, to find the optimal parameters, and to get time-varying prediction function to realize the short-term forecasting.

Due to apparent periodicity feature of the rail transit ridership, SARIMA model is used to extract input features because SARIMA model is able to capture the periodicity of time series. A time series

Considering the computation time of the training data and the real-time demand of the one-step prediction, the SVMOOL model is constructed by updating the training data day by day. That is to say, the training data is updated by adding the ridership data of the most recent day, and the time-varying prediction function is then constructed. Stating in simpler words, assume that

The process of constructing SVMOOL model.

Support vector machine partial online (SVMPOL) model is also based on the theory of SVM, to extract input features, to train the real-time updated testing data, to use intelligent algorithm, to find the optimal parameters, and to get real-time prediction function to realize the short-term forecasting.

According to the input feature extraction approaches mentioned previously and considering the temporal continuity of the real-time data, SVMPOL model extracts input features from successive actual values before the prediction time to capture nonlinear features of the ridership. In addition, parameters are also optimized by PSO.

The SVMPOL model makes full use of the temporal continuity of ridership data and takes advantage of SVM’s capability of addressing small samples. The testing data is updated by adding the ridership value of every time interval of the prediction day at same time deleting the earliest value. The real-time forecast function is obtained by training updated data and optimizing parameters in real-time to predict the value in the next time until the end of the prediction day. Stating in simpler words, assume that

The process of constructing SVMPOL model.

As described previously, this paper proposes a SVMOOL model to address the periodicity of ridership and a SVMPOL model to address the nonlinearity of ridership. But the SVMOOL model updates the training data day by day and cannot capture the real-time local variations of ridership on the day being predicted. And considering the computation time of the testing data and the real-time demand of the one-step prediction, the testing data contains one-day data at most for constructing the SVMPOL model and the internal mechanism of metro ridership to study is insufficient. To avoid the drawbacks and to take advantages of the strengths of the two individual online models, the average predicted values of two models are the final results, which are called support vector combined online (SVMCOL) model.

At present, Automatic Fare Collection (AFC) System has been able to realize real-time data collection of metro passengers in and out station records [

A ridership dataset of metro is collected to investigate the validity of the proposed SVMOOL, SVMPOL, and SVMCOL model for forecasting short-term ridership. The dataset is collected from the entrance transaction records of Nanjing Metro’s Automatic Fare Collection (AFC) Systems. In general, short-term forecasting represents prediction for a specific time interval, such as 5 min, 10 min, and 15 min. For metro ridership, 5-min interval will be more useful for metro operation and management because the departure interval of the metro vehicle is really short. Taking the operation time of Nanjing Metro into consideration, the time period of data collection for each day is from 6:00 AM to 11:00 PM. There are 204 observations collected with a 5-min interval every day. The collected data is divided into two sets of training data plus testing data. In addition, it is obvious that ridership during workdays is different from that on weekends or holidays. As discussed by [

The dataset is collected from the entrance transaction records of the Sanshanjie station during the period from November 5 to December 2, 2012, so there are 5712 observations in total for these 28 days. The first training data set is data collected from November 5 to November 25, and the first testing data set contains the remaining seven days’ ridership values, or 1428 observations, as shown in Figure

The origin entrance ridership time series at Sanshanjie Station of Nanjing Metro from November 5 to December 2, 2012.

The dataset is collected from the entrance transaction records of the Zhujinglu station during the period from March 12 to May 6, 2012, so there are 11424 observations in total for these 56 days. The second training data set is data collected from March 12 to April 1, and the third training data set is data collected from April 9 to April 29. Both two training data sets contain three weeks’ ridership values, or 4284 observations. Both two testing data sets contain the remaining seven days’ ridership values, respectively, or 1428 observations, as shown in Figures

The origin entrance ridership time series at Zhujianglu Station of Nanjing Metro from March 12 to April 8, 2012.

The origin entrance ridership time series at Zhujianglu Station of Nanjing Metro from April 9 to May 6, 2012.

Usually, normalizing raw input data can improve the convergence rate and performance of an SVM model. A common practice of data normalization was used to transform the raw data into a range

The mean absolute error (MAE), the mean absolute percent error (MAPE), and the root mean square error (RMSE) are commonly used criteria to evaluate the forecasting model. Generally, the smaller the MAE, MAPE and RMSE values, the better the prediction performance. The three performance criteria are, respectively, defined as

In this section, specific applications of the SVMOOL, the SVMPOL, and the SVMCOL models described previously are addressed.

In the methodology section, several methods of choosing the appropriate input features are introduced. The SVMOOL model’s input features are extracted using the SARIMA model. The SARIMA model is formulated with statistical software SAS. The model forms generated from the three training data sets are all SARIMA(1,0,1)(0,1,1)_{1428}. For example, the specific equation is shown as the following, which constructs by the second training data set at Zhujianglu station:

Therefore, for the prediction at time

The optimal parameter sets of the second training data set at Zhujianglu station.

Training Data Set | | | |
---|---|---|---|

Data From March 12 to April 1 | 597.69 | 0.42 | 0.57 |

Data From March 12 to April 2 | 870.02 | 0.77 | 0.76 |

Data From March 12 to April 3 | 996.26 | 0.32 | 0.57 |

Data From March 12 to April 4 | 1001.00 | 0.28 | 0.76 |

Data From March 12 to April 5 | 577.02 | 0.46 | 0.48 |

Data From March 12 to April 6 | 797.80 | 0.47 | 0.90 |

Data From March 12 to April 7 | 1001.00 | 0.07 | 1.00 |

The SVMOOL model updates training data set day by day. For example, using the second training data set from March 12 to April 1, predictions of ridership for every time interval on April 2 are made, then actual observed values of April 2 are added to the initial training data set to produce an updated training data set. Then the updated training data set from March 12 to April 2 is used to forecast the ridership of every interval on April 3 and the process repeats.

For the SVMPOL model, the testing data is updated by time interval (i.e., 5-min) for the day being predicted, and the number of input features extracted via continuity, or

For the combined model, after the values from SVMOOL and SVMPOL models are calculated, the final prediction value is the average prediction of the previous two models.

After the SVMOOL, SVMPOL, and SVMCOL models are implemented with the data sets, this research selects SARIMA, SVM, and BPNN models (i.e., back-propagation neural network) as the benchmark for one-step prediction are shown in Tables

Weekday and weekend performance comparison for one-step prediction.

Model | RMSE (ridership/5-min) | MAE (ridership/5-min) | MAPE (%) |
---|---|---|---|

November 27, Tuesday, 2012 at Sanshanjie Station | |||

| |||

| | | |

BPNN | 34.84 | 26.82 | 15.99 |

SVM | 34.85 | 26.82 | 15.93 |

SVMOOL | 34.75 | 26.73 | 15.89 |

SVMPOL | 45.29 | 32.82 | 20.48 |

SVMCOL | 36.50 | 26.31 | 16.52 |

| |||

April 5, Thursday, 2012 at Zhujianglu Station | |||

| |||

| | | |

BPNN | 33.84 | 23.53 | 13.89 |

SVM | 33.78 | 23.58 | 13.93 |

SVMOOL | 33.68 | 23.41 | 13.81 |

SVMPOL | 57.75 | 32.86 | 17.90 |

SVMCOL | 41.31 | 25.76 | 14.58 |

| |||

May 3, Thursday, 2012 at Zhujianglu Station | |||

| |||

| | | |

BPNN | 39.05 | 26.99 | 15.09 |

SVM | 39.18 | 27.10 | 15.13 |

SVMOOL | 38.88 | 26.80 | 14.62 |

SVMPOL | 58.45 | 32.02 | 15.92 |

SVMCOL | 40.06 | 27.41 | 15.26 |

weekend performance comparison for one-step prediction.

Model | RMSE (ridership/5-min) | MAE (ridership/5-min) | MAPE (%) |
---|---|---|---|

September 1, Saturday, 2012 at Sanshanjie Station | |||

| |||

SARIMA | 44.17 | 33.50 | 17.07 |

BPNN | 30.99 | 24.35 | 12.60 |

SVM | 30.81 | 24.20 | 12.53 |

SVMOOL | 29.68 | 23.32 | |

SVMPOL | 32.33 | 26.20 | 15.20 |

| | | 12.23 |

| |||

April 7, Saturday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 46.98 | 34.65 | 17.91 |

BPNN | 30.67 | 23.41 | 16.84 |

SVM | 30.66 | 23.43 | 16.85 |

SVMOOL | 30.25 | 23.04 | |

SVMPOL | 32.04 | 25.60 | 21.75 |

| | | 17.56 |

| |||

May 5, Saturday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 52.09 | 33.29 | 18.69 |

BPNN | 30.02 | 22.78 | 15.48 |

SVM | 31.48 | 23.29 | 15.63 |

SVMOOL | 29.71 | 22.53 | |

SVMPOL | 31.88 | 23.83 | 18.87 |

| | | 15.64 |

Ching-Ming Festival and May Day performance comparison for one-step prediction.

Model | RMSE | MAE | MAPE (%) |
---|---|---|---|

April 2, Monday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 103.92 | 62.34 | 34.38 |

BPNN | 29.01 | 22.98 | 14.39 |

SVM | 30.48 | 23.98 | 14.68 |

SVMOOL | 30.48 | 23.98 | 14.68 |

SVMPOL | 31.37 | 25.06 | 14.89 |

| | | |

| |||

April 3, Tuesday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 102.98 | 54.73 | 32.40 |

BPNN | 27.61 | 21.32 | 15.32 |

SVM | 29.53 | 22.55 | 15.78 |

SVMOOL | 27.42 | 21.21 | 15.26 |

SVMPOL | 27.01 | 22.01 | 16.25 |

| | | |

| |||

April 4, Saturday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 121.96 | 69.05 | 51.69 |

BPNN | 24.06 | 18.26 | 15.42 |

SVM | 28.67 | 20.36 | 16.38 |

SVMOOL | 23.88 | 18.08 | |

SVMPOL | 23.74 | 18.70 | 18.07 |

| | | 15.64 |

| |||

April 30, Monday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 106.88 | 60.02 | 38.55 |

BPNN | 28.68 | 22.17 | 15.42 |

SVM | 32.25 | 24.51 | 16.22 |

SVMOOL | 32.25 | 24.51 | 16.22 |

SVMPOL | 28.46 | 22.58 | |

| | | 14.73 |

| |||

May 1, Tuesday, 2012 at Zhujianglu Station | |||

| |||

SARIMA | 117.53 | 65.01 | 53.22 |

BPNN | 24.98 | 19.16 | 16.66 |

SVM | 32.13 | 22.54 | 18.16 |

SVMOOL | 24.28 | 18.80 | 16.34 |

SVMPOL | 26.08 | 20.48 | 19.25 |

| | | |

In addition, the pattern of weekday’s ridership is similar, so Table

The comparison between the real value and the predicted values by 4 different models using origin ridership time series at Sanshanjie Station on November 27, 2012.

Table

The comparison between the real value and the predicted values by 4 different models using origin ridership time series at Zhujianglu Station on May 5, 2012.

As shown in Table

The comparison between the real value and the predicted values by 4 different models using origin ridership time series at Zhujianglu Station on April 3, 2012.

The training time and the forecasting time are the keys to real-time implementation. The experiments using LibSVM package on desktop computers indicate that the training time needs about one hour for three weeks’ data (4284 observations) to construct the prediction function and the forecasting time needs less than 1 second for a one-step prediction using SVM. According to the SVMOOL model updating testing data set by day, the SVMOOL model uses the training data sample size from 21 days’ observations to 22 days’ or 27 days’ observations, but the training time only increases 10 min and the forecasting time needs less than 1 s. Because the SVMOOL model is retrained once a day, the obtained forecasting function can be used for one-step predictions for the day, therefore real-time implementation is possible. The SVMPOL model is retained in real-time in 5-min interval. The obtained forecasting function can be used to one-step prediction for the next 5-min. In the process of the implementation experiments, the SVMPOL model needs less than 1 s to construct due to the small data sample and the forecasting time needs less than 1 s for one-step prediction. Therefore, the training time and the forecasting time can meet the real-time demand for the one-step prediction in the implementation as well.

The key to metro operation and management is based on the changes of the ridership to effectively deploy and use the system resources and to timely adjust operation strategy to ensure that metro is safe to complete the transportation service task. The results of short-term ridership forecasting can provide useful information to decision makers of metro system, and the prediction accuracy directly influence the legitimacy and effectiveness of any changes in operations, such as adjustments to headway, train dispatching, and the activation of station passenger crowd regulation plan or emergency response plan.

This paper proposes a novel hybrid model combining the SVMOOL model and the SVMPOL model for short-term ridership forecasting that better captures the periodicity and nonlinearity characteristics by the updated data set. The SVMCOL model takes advantages of the individual strengths of the two models. While the SARIMA model is superior for the stable weekday ridership to other models, experiments results indicate that the SVMOOL model is superior to SARIMA model, BPNN model, or SVM model in terms of MAE and RMSE for the weekend and holiday ridership test. The actual results of 5-min short-term ridership forecasting show the feasibility and effectiveness of the proposed combined model in real-time implementation.

It should be noted that the prediction of ridership under abnormal situations (such as holiday) is evidently more challenging than doing so under normal conditions (such as weekday ridership), and hence, much desired by the operator. Therefore, the proposed SVMCOL model is found to be suitable and useful in real-world operations, particularly in prediction under abnormal conditions. And, further studies need apply the proposed model to other abnormal situations (such as horrible weather, large sports events or emergencies, this study chooses the weekday, weekend, and holiday ridership as the demonstration). In addition, different characteristics (the impact of different meteorological conditions, the number of metro station entrances, etc.) can be considered as the input features in further studies. Jia et al. [

Detailed data are included within the supplementary materials.

An earlier version of this paper has been presented in the Transportation Research Board 92nd Annual Meeting (Washington DC, 2013).

The authors declare that they have no conflicts of interest.

This research has been supported by the Fundamental Research Funds for the Central Universities (no. KYLX16_0270). The authors thank the Nanjing Metro for providing the data used in this research. Thanks are due to Chih-Chung Chang and Chih-Jen Lin for permission to use the LibSVM package in this research.

APPENDIX Table 1: the origin 5-min entrance ridership data at Sanshanjie Station of Nanjing Metro from November 5 to December 2, 2012. APPENDIX Table 2: the origin 5-min entrance ridership data at Zhujianglu Station of Nanjing Metro from March 12 to April 8, 2012. APPENDIX Table 3: the origin 5-min entrance ridership data at Zhujianglu Station of Nanjing Metro from April 9 to May 6, 2012.