Train dwell time estimation is a critical issue in both scheduling and rescheduling phases. In a previous paper, the authors proposed a novel dwell time estimation model at short stops which did not require the passenger data. This model shows promising results when applied to Dutch railway stations. This paper focuses on testing and improving the generality of the model by two steps: first, the model is tested by applying more independent datasets from another city and comparing the estimation accuracy with the previous Dutch case; second, the model’s generality is tested by a theoretical approach through the analysis of individual model parameters, variables, model scenarios, and model structure as well as work conditions. The validation results during peak hours show that the MAPE of the model is 11.4%, which is slightly better than the results for the Dutch railway stations. A more generalized predictor called “dwell time at the associated station” is used to replace the square root term in the original model. The improved model can estimate train dwell time in all the investigated stations during both peak and offpeak periods. We conclude that the proposed train dwell time estimation model is generic in the given condition.
Train dwell time estimation is a critical issue for both the scheduling and rescheduling phases. In the scheduling phase, accurate estimation of the train dwell time provides necessary inputs to the timetable and allows the timetable to match the passenger demand. In the rescheduling phase, the estimation results of the train dwell time can be used to predict potential conflicts between train lines.
To estimate dwell time accurately, the development of a dwell time estimation model is necessary. One of the most critical issues for broad applications of the train dwell time estimation model is its generality. The generality of a model can be defined as a model that is generic rather than a more specific or detailed one [
To test the generality of a train dwell time estimation model, there are two possible approaches. One intuitive methodology is to apply the model to more or a wider range of independent cases; if the accuracies under these different cases are acceptable, then the model can be classified as a relatively general model. This approach is called a comparison approach. However, comparison approaches may face problems like how many cases they should cover and what the wider range means. Another methodology is to analyze the parameters and variables of the model theoretically to prove its generality [
The main methodology of this paper is as follows: first, a train dwell time estimation model is selected; second, the generality of the selected model is analyzed by using both comparison and theoretical approaches. In the comparison approach, an independent dataset is applied, and the estimation result is compared with the previous one. In the theoretical approach, the model is analyzed from four aspects: variable analysis, parameter analysis, scenario analysis, and structure and condition analysis. Finally, based on the testing of generality, an improvement is made to the model.
The remainder of this paper is organized as follows. In Section
In the literature, many types of train dwell time estimation models have been proposed. The existing models can be classified according to different criteria such as passenger traffic dependency, modeling methodology, validation, railway mode, and type of station, all of which are listed in Table
Main features of existing dwell time estimation models.
Source  Passenger traffic dependency  Model methodology  Validation  Railway mode  Station type  

Stations and lines  Country  
Lam, 1988  Pr  Lr  3S on 3L  HKG  Subway  Ich 
Lin, 1992  Pr  NLr  2S on 1L  USA  Light rail  — 
Puong, 2000  Pr  NLr  2S on 1L  USA  Subway  Ich and Ime 
Buchmueller et al., 2008 [ 
Pr  Di  —  SWE  Hsr  — 
Zhang et al., 2008 [ 
Pr  Mi  3S on 3L  CHN  Subway  Ich and Ime 
Hansen, 2010  Pd  Lr  2S on 1L  NED  Hsr  Ime 
Jong, 2011  Pr  Lr  1S on 1L  TPE  Hsr  Ich 
Sourd, 2011  Pr  Mi  1S on 1L  FRA  Hsr  — 
Yamamura, 2013  Pr  Mi  —  JPN  Subway  — 
Kecman, 2015  Pd  Lr  —  NED  Hsr  Ich and Ime 
Seriani, 2015  Pr  Mi  —  —  Subway  — 
Hänseler et al., 2015 [ 
Pr  Mi  1S on 1L  SWE  Hsr  Ich 
Li, 2016  Pd  NLr  1S on 1L  NED  Cr  Ime 


This paper  Pd  NLr  1S on 1L 
NED 
Cr 
Ich and Ime 
From Table
In the passenger regarded model, the dwell time is estimated based on the alighting and boarding time of the passengers. The numbers of boarding and alighting passengers are the key inputs of this kind of model. The approaches of the passenger regarded train dwell time estimation mainly include two types: a microscopic simulation model and a regression model.
Among the microscopic simulation models, these studies focused on the microlevel movement during alighting and boarding processes by simulation modeling. Most of the microscopic simulation studies are based on field data collected in test stations and lines. They are used to explain the effect of the uncertainties of passenger behaviors on dwell times. Zhang et al. [
Among the passenger regarded regression models, the train dwell times have usually been estimated using a linear or nonlinear function of the number of alighting and boarding passengers. Lam et al. [
Among the passenger disregarded models, the dwell time was estimated using many variables that were not related to passenger demand. To the best of our knowledge, so far, regression is the only approach that has been used in passenger disregarded models. Hansen et al. [
With regard to the validation of the existing models, most of the former studies included only a few stations belonging to one railway (as shown in Table
To select a possible generic train dwell time estimation model, both the input data availability and model characteristics should be considered. We noticed that all the passenger regarded models could not be selected because the data, such as the number of boarding and alighting passengers, were usually not available, especially in real time. However, the generality of the passenger disregarded model, especially the model proposed by Li et al., is worthy of discussion because the variables considered in Li et al.’s model do not depend on specific types of rolling stocks and traffic conditions [
Li et al.’s model studied the dwell time estimation problem particularly for short stops without passenger demand by means of a statistical analysis of track occupation data from Netherlands. In their paper, the factors of influence on dwell time are classified into five categories: passenger, rolling stock, station, operation, and external factors. The five categories include the majority of influencing factors. Then, with the analysis of these factors, 10 potential predictors, including time variation, length of target train, length of preceding train, departure delay at previous station, dwell time of target train at previous station, second previous station, dwell time of preceding train at target and previous station, and dwell time of the same train during the last week, are selected. Various combinations (including linear items and nonlinear items) are tried to establish 10 different parametric regression models. With the correlation analysis and experimental testing, the model shown in formula (
The reason why this model can work well in practice lies in the selected predictors. Unlike other models, Li et al.’s model does not consider the station layout, rolling stock configuration, or passenger behavior directly because these factors are involved in independent variables in the model and act on the dependent variable indirectly. For example, the predictors of the model are mainly the dwell time of the preceding train
To test the generality of the model, in the following two sections, two different approaches are used. First, a Beijing dataset is applied to the model that was established based on the Dutch railway station, and the estimation accuracy is analyzed by comparing the two results. Because the two datasets are independent in both time and space, it can be inferred that the validated result reflects the generality of the model to some extent. Second, the quantitative generality of the model is analyzed by a theoretical approach.
The original dataset for Li et al.’s model development is from Dutch railway stations. To test whether it is still applicable for a totally independent case, a new dataset, which is dependent on the original validated case, is selected from the Beijing urban railway. First, an empirical study is conducted by analyzing the difference between the scheduled and actual dwell time in the Beijing urban rail transit, while the distributions of the actual dwell time are also analyzed. Then, these results are compared with the results from Netherlands. Second, the dataset of the Beijing urban rail stations is used to regress the original model that was previously validated for a station in the Dutch railway system, and the regression parameters and the accuracy of the results are compared with the proposed model. In this way, the generality of the proposed model is analyzed.
To study the generality of the model by a comparison approach, datasets from China are carefully selected. To obtain precise datasets from the Beijing railway stations, a line that has been operating for a relatively long amount of time is selected so that the passenger demand is stable. Thus, line four of the Beijing urban rail transit is selected for this empirical study; the stations of this line are shown in Figure
Stations of line four of the Beijing urban rail transit system.
This line opened in 2009, has a length of 50 km, and comprises 35 stations; all trains stop at every station, and no train overtaking occurs at any station. In this railway, Anheqiao North is the first station, and Tiangongyuan is the last station, where the trains are able to turn around. The interchange stations are Haidianhuangzhuang, National Library, Xizhimen, Ping'anli, Xidan, Xuanwumen, Caishikou, Beijing South Railway Station, and Jiaomen West, where passengers can transfer to another line; however, passenger connections are not considered in the timetable, so we neglect the “adhere to schedule effect” which may exist in some transfer stations in other cases. The remaining stations are intermediate stations.
In this paper, four intermediate stations and three interchange stations are selected, and all of the selected stations are consecutive. The selected stations are listed in Table
The selected stations and their classifications.
Number  Target station  Classification 

1  Renmin University  Intermediate station 
2  Weigongcun  Intermediate station 
3  National Library  Interchange station 
4  Beijing Zoo  Intermediate station 
5  Xizhimen  Interchange station 
6  Xinjiekou  Intermediate station 
7  Ping'anli  Interchange station 
There are two different ways to obtain the dwell time for the two cases. In the Dutch case, almost three months of data were used to analyze the distribution of the actual dwell time in different periods. The dwell times at the selected stops and trains were estimated based on the track occupation data. In Netherlands, track occupation data were collected using a train describer system (TROTS), which provided the exact time of occupation and clearance of track sections [
The original recorded datasets of the investigated stations in Beijing are processed and analyzed, and we find that the actual and scheduled dwell times are significantly different, whether by more or less time. The analysis results are shown in Table
Comparison of the actual and scheduled dwell times of the investigated stations.
Stations  Max dwell time  Min dwell time  Average actual dwell time  Scheduled dwell time  Average absolute error  Average relative error  Root mean square error  Max absolute error 

Renmin University  69 s  25 s  34.76 s  30/35 s  5.51 s  17.69%  9.31 s  39 s 
Weigongcun  67 s  25 s  35.76 s  30/35 s  6.2 s  19.94%  10.42 s  37 s 
National Library  69 s  29 s  46.55 s  35 s  12.59 s  35.98%  15.5 s  34 s 
Beijing Zoo  65 s  24 s  43.37 s  40 s  8.55 s  21.37%  10.65 s  25 s 
Xizhimen  67 s  33 s  46.62 s  45 s  6.38 s  14.18%  8.36 s  22 s 
Xinjiekou  70 s  27 s  38.68 s  35 s  6.1 s  17.42%  11.62 s  35 s 
Ping'anli  95 s  24 s  45.45 s  35 s  11.77 s  33.64%  16.72 s  60 s 
In this section, the datasets from two countries are compared. At first, the two datasets are statistically described; and then the dwell time distributions and the differences between the actual and scheduled dwell times of the two cases are analyzed.
Comparison between Dutch and Beijing datasets.
Dataset  Average  Minimum  Maximum  SD  Variance  KS test 

D_peak  52.67 s  40 s  71 s  10.28 s  105.75  0.375 
B_peak  47.68 s  29 s  65 s  8.99 s  80.84  


D_offpeak  41.67 s  17 s  77 s  16.46 s  271.06  0.505 
B_offpeak  38.68 s  24 s  65 s  9.38 s  88.04 
Distribution of the actual and scheduled dwell times in the Dutch railway stations.
Distribution of the actual and scheduled dwell times in the Beijing urban railway stations.
In the Dutch case, as shown in Figure
In the Beijing case, the dwell time is collected manually by investigators. The distribution of the dwell time is analyzed for two typical types of stations during both peak and offpeak hours. The National Library interchange station and the Beijing Zoo intermediate station are selected. The result is shown in Figure
In summary, the distributions of the actual dwell time in the Dutch railway stations and in the Beijing urban rail transit have some common characteristics: regarding the maximum frequency value, the actual dwell time during the peak period is longer than that during the offpeak period. Meanwhile, the maximum frequency values in the two cases are similar. For example, during the peak period, the maximum value of the actual dwell time is 47–51 s at the Beijing Zoo station and 52–56 s at the National Library station, which is similar to the dwell time of 50–54 s during the morning peak period in the Dutch railway stations.
The time period is separated into the peak period and the offpeak period: the peak period lasts from 7:30 to 9:00 am, and the offpeak period lasts from 9:00 to 10:30 am. Two typical stations, the National Library interchange station and the Beijing Zoo intermediate station, are selected to analyze the differences between the scheduled and actual dwell times during the peak and offpeak hours, respectively.
Figure
Comparison of the actual and scheduled dwell times in the Dutch railway stations.
Figure
Comparison of the actual and scheduled dwell times in the Beijing railway stations.
In summary, the differences between the actual and scheduled dwell times in the Beijing urban rail transit system and in the Dutch railway stations have common characteristics: most of the actual dwell times are longer than the scheduled dwell times during the peak period. The actual and the scheduled dwell times are closer during the offpeak period, and the actual dwell time is likely to increase during the peak period.
In this section, the generality of the selected train dwell time estimation model is analyzed by the comparison approach. The collected data are separated into two parts, the first of which is used to calibrate the model. The other part is used to validate and measure the error of the model. Ten records are selected randomly from the data as the validation set, and the remainder are used as the learning sample in the calibration part. In other words, the model is validated by applying the model to the Beijing urban railway dataset; the results are compared with the original values. Accordingly, this method verifies whether the model can cover wider scenarios.
First, we consider the predictors that are used in the original model [
Second, a simple correlation analysis is performed between the selected predictors and the dwell times at different stations. The result in Table
The correlations between the input variables and the dwell time.
Stations  Periods  

Peak  Offpeak  







Renmin University  —  —  —  —  —  0.36 
Weigongcun  0.41  0.84  —  —  0.53  — 
National Library  0.54  0.54  0.35  0.54  0.36  — 
Beijing Zoo  0.46  0.55  —  0.46  0.77  0.56 
Xizhimen  0.47  0.49  0.34  —  0.51  — 
Xinjiekou  0.73  0.68  0.60  —  0.43  0.48 
Ping'anli  0.35  0.59  0.44  —  0.36  — 
Third, the dataset of the Beijing railway stations is used to calibrate the parameters in formula (
Three indicators are introduced to evaluate the estimation accuracy of the results: the adjusted coefficient of determination (adj
Performance measures.
Indicators  Peak period  Offpeak period 

Adj 
0.594  0.162 
RMSE  7.21 s  6.21 s 
MAPE  11.4%  13.1% 
Table
The parameters of the model that which based on the two datasets are shown in Table
Model parameters in the different datasets.
Parameters  Dutch dataset  Beijing dataset  

Peak period  Peak period  SD  Offpeak period  SD  


−0.83 (0.00)  0.23  7.02 (0.00)  0.37 

—  —  —  —  — 

1.60 (0.00)  1.60 (—)  —  1.60 (—)  — 

0.03 (—)  0.76 (0.00)  0.04  0.30 (0.00)  0.06 

1.11 (0.00)  0.04 (0.00)  0.05  0.24 (0.00)  0.07 
The
Residuals analysis by ACF and PACF.
ACF
PACF
In addition, the model fails during the offpeak hours for the Dutch case but is still applicable during the offpeak hours for the Beijing case. One possible reason for this is that the scheduled headway is large during the offpeak hours in the Dutch case, which tends to decorrelate the dwell times. Another reason is that the passenger demand in the Dutch case during the offpeak period is so small that the random factors play a key role in the dwell time. However, the headway (Figure
The accuracy of the parametric model based on the Beijing dataset is compared with those of existing models reported in literature (see Table
Comparison of the regression results for different datasets.
Indicators  Puong [ 
Hansen et al. [ 
Kecman (2014)  Dutch dataset  Beijing dataset  

Peak  Offpeak  Peak  Offpeak  
Adj 
—  —  —  0.577  —  0.594  0.162 
RMSE  4.04 s  16.6 s  —  6.2 s–8.8 s  8.49 s  7.21 s  6.21 s 
MAPE  14.55%  —  15%  11.5%–14.2%  19.9%  11.4%  13.1% 
The results from the comparison of the author’s model in the different cases are discussed in further detail. First, adj
The comparison approach in the previous section performed well with regard to the generality of the model. However, this approach may face problems such as how many cases should be covered, although it is usually impossible to cover all cases for a model in practice. To solve this problem, the following section shows that the generality of the model is tested using a theoretical approach. The theoretical approach includes four aspects. These aspects include variable analysis, parameter analysis, scenario analysis, and model structure and condition analysis.
First of all, the generality of the model is discussed based on the variables.
Under the premise that the parameters are fixed, the range of the values of the variables (definition domain) should be within a certain trusted value domain. In other words, it has a lower bound and an upper bound.
Based on Assumption
For the length of the train, literature [
The distribution of the worldwide subway dwell time.
City  Station  Date  Dwell time  Flow/dwell  Passenger  Average headway 

San Francisco  Montgomery  pm peak  30 s–60 s  38%  586  153 s 
New York  Grand Central  am peak  35 s–120 s  64%  1143  160 s 
Toronto  Commission King  am peak  25 s–45 s  31%  428  168 s 
British Columbia  SkyTrain Burrard  am peak  20 s–30 s  40%  562  151 s 
Next, we discuss the result of the model when the variables change within the domain. The domain variables are introduced into the model which is regressed by the Beijing datasets to obtain the results. Figure
The results from changing the variables in the Beijing railway stations.
The results from changing the variables in the Dutch railway stations.
The headway of two cases.
In this section, the value ranges of the parameters are discussed. The values of the parameters can be inferred from both the structure of the model and the domain of the definition of the variables.
At first, there are two contributors, and the results are for the dwell time in the model. If the trains’ length does not change in the modeling scenario, the value of the dwell time at the target station can be calculated approximately as a weighted average of the dwell times of the preceding train, at the previous station and the second previous station. Thus, we consider that the values of
It can be deduced from the meaning of the parameter that the value of
Finally, the parameters concerning the train lengths are discussed. Although the ranges of the other parameters and variables are already limited, nonetheless we can still obtain the ranges of
In summary, when the parameters are in their established ranges, the results can be trusted, and the ranges of the parameters are within the model scope of the application.
The scenario is usually defined by several indicators, such as headway, type of station, and train speed. The scenario is one of the most important factors of influence when we discuss the generality of a model.
The model is general if it can apply to more scenarios.
To study whether the model can be applied to different scenarios, it is important to discuss the effect of these scenario indicators on the model.
First, the effect of headway is twofold. On one hand, the headway influences the relationship between the dwell time of the target train at the target station
However, the headways in Figure
Second, the effect of different types of stations is also an indicator for determining which scenario is relevant. At intermediate stations, where a train cannot overtake another, the dwell time is mainly determined by the dwell time of the previous train, the minimum headway, and the passengers. At interchange stations, the previous train’s dwell time is one of the most significant influencing factors. Moreover, whenever the train timetable is required for synchronization between two lines, the connections for transfer passengers should be considered. That is, the dwell time of the target train is related to the departure and arrival times of other trains in the interchange station. At the terminal station, the dwell time is mainly determined by the time when the train turns back. The turn back time is related to the train’s length and turn back technique. The shorter the train and the higher its efficiency in turning back, the shorter the dwell time.
The average headway, minimum headways, train length, and dwell time (the target and previous train at the target and previous station) can all be used to describe different scenarios. The model is applicable to those scenarios, if the indicators that determine the scenarios are considered in the model. Based on our analysis, the model is applicable to more scenarios because the correlation between the headway and dwell time is high, and we can also determine from formula (
In the selected model, passenger demand is disregarded because passenger demand can be reflected by the substitute variables such as the dwell time of the preceding train and the dwell time at the previous station, so its assumption is not proven to be true. To demonstrate the generality of the model, it is necessary to know to what extent this assumption holds. To answer this question, the dwell time variables of the model can be replaced by an equation for the other variables that have already been proven to be relevant from formulations in previous research. Then, we can establish a new model with new variables and discuss the applicability of the new model. If the new model is plausible, then the assumption is proven.
In previous research, Puong [
We enter formula (
In this formula, apparently
The comparison of the values of the left part and right part in formula (
From the generality testing, it can be seen that the relationships between passenger demand at different stations and trains significantly impact the estimation result. However, such a relationship is not necessarily based on consecutive stations or consecutive trains. Based on this inference, we introduce a more generalized predictor to improve the generality of the proposed model, and the results of the improved model are compared with the results of the proposed model in this section.
The generality of our model can still be improved. Past research analyzed the relationships among the dwell times of three consecutive stations in the Dutch railway lines. Because of the data consistency problem, some data were missing due to incorrect track identifiers resulting from track changes after maintenance. However, the Beijing dataset includes the dwell times of all the stations on the selected line, which inspires our refinement of the model.
We can analyze the relationships between the dwell times of the target station and previous stations. The correlation of dwell time between the target station and previous stations in peak and offpeak periods is analyzed and the result is shown in Tables
Correlation coefficients of the dwell time in peak periods.
Stations  Pervious stations  

1  2  3  4  5  6  7  8  9  10  11  
Renmin University  0.22 

0.44  0.16  0.12  —  —  —  —  —  — 
Weigongcun  0.22  0.42  0.29  0.27  0.41 

—  —  —  —  — 
National Library 







—  —  —  — 
Beijing Zoo 






0.16 

—  —  — 
Xizhimen 






0.12  0.44 

—  — 
Xinjiekou 






0.08  0.28  0.59 

— 
Ping'anli 






0.02  0.07  0.24  0.33 

Correlation coefficients of the dwell time in offpeak periods.
Stations  Pervious stations  

1  2  3  4  5  6  7  8  9  10  11  
Renmin University  0.33  0.12 

0.06  0.12  —  —  —  —  —  — 
Weigongcun 

0.06  0.14  0.12  0.06  0.23  —  —  —  —  — 
National Library 




0.15  0.22  0.12  —  —  —  — 
Beijing Zoo 







0.03  —  —  — 
Xizhimen 







0.1  0.2  —  — 
Xinjiekou 










— 
Ping'anli  0.08  0.1  0.13  0.15  0.1  0.16  0.09  0.12  0.08  0.1 

To test the above idea, the correlation coefficients between the dwell time at the target station and the dwell time at the associated stations are obtained and are compared with the square root term used in the original model. The results from the Beijing dataset are shown in Table
Correlation coefficients of the predictors.
Stations  Peak periods  Offpeak periods  









Renmin University  0.20  0.14 

0.12  0.08 

Weigongcun 



0.15  0.12 

National Library 




0.16 

Beijing Zoo 



0.07  0.15 

Xizhimen 



0.23  0.14 

Xinjiekou 



0.02 


Ping'anli  0.28 


0.07  0.13  0.17 


All stations 




0.27 

Table
Based on this improvement, a more generalized model is obtained, as shown in the following formula:
The Beijing dataset is used to calibrate formula (
To test the performance of the improved model and compare the estimation accuracy of the improved model with that of the original model, adj
Comparison with the improved parametric model.
Dataset  Dutch  Beijing  

Model  PM  NPM  PM  IPM  
Period  Peak  Offpeak  Peak  Offpeak  Peak  Offpeak 
Indicators  
Adj 
0.577  —  0.594  0.162  0.860  0.455 
RMSE  6.2 s–8.8 s  8.49 s  7.21 s  6.21 s  4.19 s  4.14 s 
MAPE  11.5%–14.2%  19.9%  11.4%  13.1%  7.8%  9.9% 
In the IPM, adj
Due to the data consistency problem in the Dutch railway, the associated stations are not analyzed further. The square root term can be a special case of the associated station; therefore, it can be deduced that using the associated station item would not reduce the model’s accuracy.
Based on the test datasets in this paper, it is worth noting that the generality of the estimation model indicates that the model with the same parameters and predictors can fit for all railway lines, regardless of whether the line is a subway or commuter rail or other railway types. Certain conditions must be satisfied to use the model.
The original model is specifically designed for short stops. Short stops are stops on the open track where sidings are usually not available and where trains dwell only for alighting and boarding, after which they immediately continue their journey. In both cases, all stations are short stops without sidings, and whether the model fits stations with sidings and large stations with passenger connections remains unclear.
The estimation model with the same predictors can regress the dwell time of different stations on different lines even in different countries, and the result is valid. However, the values can be different in different cases. In other words, the model followed the specific cases, and the parameters vary from case to case. The main reason is that the influence level of the predictors may differ in different cases. Therefore, when applying the model to a new case, the parameters should still be regressed. Accordingly, it is better to use the model at rescheduling phase where the train system is running and necessary datasets such as previous dwell times and train length are available.
In summary, the approach in this paper is convincing. However, it is difficult to establish a model that can fit all scenarios.
The dataset should follow several constraints when studying specific cases. To improve the model’s performance, the following principles should be considered.
The first issue concerns the data investigation site:
Another issue is measurement. The measurements in the two cases are different, which could cause bias. The dwell time is estimated from track occupation data in the Dutch case; in that case, the train dwell time is estimated by an algorithm according to the stop sign of a train and the timedependent occupation states of a track [
Station dwell times are the major component of headways at close train frequencies. The existing literature suggests that the best achievable headways under these circumstances are in the range of 110 to 125 seconds [
The main contribution of this paper is to propose a systematic approach for testing the generality of a train dwell time estimation model and improving the model performance by introducing a more generalized predictor.
The generality of the model is tested by using two approaches, namely, a comparison approach and a theoretical approach. In the comparison approach, a dwell time estimation is selected and applied to a completely new independent test bed. The test results from two datasets from two different countries show relatively high accuracy and equivalent effectiveness. The regression parameters are compared using the dataset of line four in the Beijing urban rail transit system. The parameters are regressed using the datasets of these two cases. In the theoretical approach, the train dwell time estimation model is analyzed by four steps: variable analysis, parameter analysis, scenario analysis, and model structure and condition analysis. We conclude that the test model is general in the given condition, namely, short stops with a headway less than 15 min.
Furthermore, a more generalized predictor, dwell times at the associated station, is introduced to improve the performance of the model. The performance indicators show that the result of the improved model is better than the result of the original model. Thus, the associated station would be relevant for estimating train delays during operation, and using the associated station item would improve the generality of the results.
Usually, generality and accuracy are two contrary indicators for a model. If the accuracy of the model is higher, the range of the model’s applicability is narrower, meaning that the model can be applicable only in certain scenarios. In contrast, if the model is applicable to many different scenarios, in other words, it is more general, it is difficult to maintain high accuracy at the same time as generality. The estimation error of the model we test is acceptable. Meanwhile, it is proven that the model is relatively general; therefore, the model can balance the tradeoff between generality and accuracy well.
The focus of future research should be on two directions. On one hand, more datasets from different cases can be tested to verify the model. On the other hand, the accuracy and the generality of the model should be improved, particularly for long headways. Randomness and the weak relationship between the dwell time and passenger demand under this condition make dwell time estimation more difficult. To improve the accuracy of the model, other nonparameter methods, such as kernel regression and the nearest neighbors method, which do not require a significant amount of data, can be tested. More influencing factors, such as the transfer rule, weather, and accident, could also be considered if such data can be collected by using sensors. These factors will be extensively studied in the near future.
The authors declare that they have no conflicts of interest.
This research is supported by the National Natural Science Foundation of China (U1434207), the Fundamental Research Funds for the Central Universities of China (2016JBM030), the National Key Research and Development Plan (2016YFE0201700), and the Beijing Chaoyang District Science and Technology Commission (CYXC1607). The authors wish to acknowledge these agencies.