Time prediction model of subway transfer
 Yuyang Zhou^{1}Email author,
 Lin Yao^{1},
 Yi Gong^{1} and
 Yanyan Chen^{1}
Received: 30 September 2015
Accepted: 6 January 2016
Published: 19 January 2016
Abstract
Walking time prediction aims to deduce waiting time and travel time for passengers and provide a quantitative basis for the subway schedule management. This model is founded based on transfer passenger flow and type of pedestrian facilities. Chaoyangmen station in Beijing was taken as the learning set to obtain the relationship between transfer walking speed and passenger volume. The sectional passenger volume of different facilities was calculated related to the transfer passage classification. Model parameters were computed by curve fitting with respect to various pedestrian facilities. The testing set contained four transfer stations with large passenger volume. It is validated that the established model is effective and practical. The proposed model offers a realtime prediction method with good applicability. It can provide transfer scheme reference for passengers, meanwhile, improve the scheduling and management of the subway operation.
Keywords
Time prediction Subway transfer Passenger flow Pedestrian facilitiesBackground
As an indispensable transportation system of big cities, subway has the merit of time reliability and vast capacity. With the development of urban subway system, passenger flow has increased significantly on peak time. The great concentration of passenger flow in transfer station has put enormous pressure on the subway system. Not only the underground network design decision, but also a huge range of consequential information service for passengers including transfer waiting time, travel time, reliability and even mode choice depend on the assumption about how long passengers will spent on walking from one subway line to the other.
It is shown from the literature about the subway interchange that Virkler and Elayadath (1994) established a relationship for speedflowdensity based on Transport and Traffic survey. Feng et al. (2009) drew the relation curve of speed and passenger flow density at the subway loading areas and upstairs in Beijing. Lu et al. (2002) founded the dynamical equation of evacuation speed for personnel. Fang et al. (2007) verified the dynamical equation of evacuation speed and the parameters in the equation. Kirchner and Schadschneder (2002) used a bionicsinspired cellular automaton model to analyze the pedestrian dynamics. Sarkar and Janardhan (1997) reported different speed relationships built for different pedestrian facilities. In the previous research, transfer time prediction was found regionspecific. Bookbinder and Désilets (1992) developed its own emphasis on the evaluation of transfer time cost. Osorio and Bierlaire (2009) analyzed the capacity of the queuing network model which could capture the propagation of congestion and predict the travel time. Chen et al. (2008) analyzed the evacuation capacity and the level of the service for passengers at Metro station. Xuejun (2006) studied the characteristics of the transfer behavior from different transfer stations design. In the congestion situation, Singh and Srivastava (2008) proposed a traffic flow model which were applied to elevator configuration based on Markov network queuing theory. A new elevatordispatching method was deduced theoretically using queuing theory by Zong et al. (2005). According to the survey on pedestrian walking characteristics, Blue and Adler (2001) established the cellular automata (CA) model based on the ant colony algorithms. Cao et al. (2009) put forward the update rules that could embody the walking characteristics of pedestrian counter flow.
Although the above researches cover most contents of the transfer behavior, there is less study for the walking time prediction by pedestrian facilities. Besides transfer speed characteristics, this paper analyzes the passenger walking behavior with respect to different pedestrian facilities in subway transfer stations. In “Transfer time prediction function” section, the time prediction model of the platform, the elevator and the horizon passage is established based on transfer flow volume and walking time on different facilities. In “Parameter estimation” section, model parameters are estimated according to the learning set. In “Transfer time model validation” section, the accuracy of transfer time model is validated by testing set including four transfer stations. Calculation results indicate that the transfer time prediction model can not only reduce waiting time for passengers, but also improve the subway operation efficiency.
Transfer time prediction function
For the facility i, L _{ i } means the length, v _{ i } means the speed.
Transfer walking on the platform
Transfer walking in the horizon passage
In the horizon passage, where is straight, long and nonstair, the main factor of walking speed is passenger volume. Pedestrians can walk freely when the transfer passenger volume is properly low (CanónicoGonzález et al. 2013). However, in case the passengers get crowded, walking speed will decline gradually at peak time.
Walking on the stairs is also regulated with passenger volume while the speed is related to the climbing direction. According to the former research (Chen et al. 2011), the rate of upstairs walking time to horizon passage was 1.30 and the downstairs rate was 1.20. It should be noted that people would be more inclined to use the escalator instead of stairs.
Transfer behavior on the escalator
Waiting time
As can be seen from the above formula, the waiting time is influenced by the subway timetable and the time passengers spend in walking. If transfer walking time is equal to transfer time, the waiting time is reduced to zero. In such case, when a passenger arrives at the receiving platform, the subway is just about to leave.
Parameter estimation
Data acquisition
In Beijing, Chaoyangmen station is an important transfer station between subway Line 2 and Line 6 with 12,000 passengers per day. The research time lasted from 6:00 a.m. to 9:59 a.m. and from 4:00 p.m. to 7:59 p.m. The survey data set was divided into two parts. In the first subset, transfer volume was counted to analyze the sectional number of the transfer pedestrian. In the second one, walking time of transfer passengers was recorded to analyze the regulation of walking speed.
The data groups in different passages
Passage no.  Group no.  N (p/min)  v _{1} (m/s)  p _{1} (p/m s)  T _{1} (s)  v _{2} (m/s)  p _{2} (p/m s)  T _{2} (s)  v _{3} (m/s)  p _{3} (p/m s)  T _{3} (s)  T _{ w } (s) 

1  1  11  1.73  0.02  4.91  1.25  0.05  85.60  0.50  0.15  50.04  140.55 
2  32  1.56  0.05  5.45  1.11  0.15  96.40  0.50  0.44  50.00  151.85  
3  45  1.46  0.07  5.82  1.05  0.21  101.90  0.50  0.63  50.10  157.83  
4  70  1.33  0.11  6.39  0.97  0.33  110.31  0.50  0.97  50.00  166.70  
5  121  1.27  0.19  6.69  0.88  0.58  121.59  0.41  1.68  69.26  197.54  
6  126  1.25  0.20  6.80  0.86  0.60  124.42  0.40  1.75  74.62  205.84  
2  1  38  1.41  0.08  5.67  1.15  0.16  126.96  0.50  0.58  48.00  180.63 
2  42  1.39  0.09  5.76  1.12  0.20  130.36  0.50  0.64  47.86  184.07  
3  46  1.41  0.10  5.67  1.07  0.22  136.45  0.50  0.70  48.06  190.14  
4  71  1.26  0.15  6.35  1.00  0.34  146.00  0.50  1.08  48.10  200.35  
5  99  1.22  0.21  6.56  0.98  0.47  148.98  0.46  1.50  55.46  211.00  
6  119  1.17  0.25  6.84  0.95  0.57  153.68  0.38  1.80  66.54  227.06  
3  1  7  1.75  0.01  4.57  1.31  0.03  103.05  0.50  0.11  47.92  155.54 
2  32  1.46  0.07  5.48  1.17  0.15  115.38  0.50  0.48  47.98  168.84  
3  44  1.42  0.09  5.63  1.15  0.21  117.39  0.50  0.67  48.06  171.09  
4  85  1.27  0.18  6.30  0.95  0.40  142.11  0.49  1.29  48.76  197.16  
5  129  1.17  0.27  6.84  0.93  0.61  145.16  0.36  1.95  72.50  224.50  
6  167  1.03  0.35  7.77  0.88  0.80  153.41  0.28  2.53  94.72  255.90 

Platform (Passage 1: effected width = 10.5 m and length of measurement section = 3.3 m; Passage 2: effected width = 8.0 m and length of measurement section = 3.5 m; Passage 3: effected width = 8.0 m and length of measurement section = 3.5 m);

Escalator (Passage 1: effected width = 1.2 m and length of measurement section = 12.0 m; Passage 2: effected width = 1.1 m and length of measurement section = 12.0 m; Passage 3: effected width = 1.1 m and length of measurement section = 12.0 m; the speed of escalators: 0.5 m/s);

Horizon passage (Passage 1: effected width = 3.5 m and length of measurement section = 107 m; Passage 2: effected width = 4.0 m and length of measurement section = 146.0 m; Passage 3: effected width = 4.0 m and length of measurement section = 135.0 m).
Results of Mann–Whitney and Kolmogorov–Smirnov tests
Mann–Whitney tests  v _{ i } 

Mann–Whitney U  0.000 
Wilcoxon W  4656.000 
Z  −12.153 
Significance (both tails)  0.000 
Kolmogorov–Smirnov tests  
Extreme difference  
Absolute value  1.000 
Positive  1.000 
Negative  0.000 
Kolmogorov–Smirnov Z  6.928 
Significance (both tails)  0.000 
H _{0}: v _{1}, v _{2} and v _{3} come from the same population.
α = 0.05.
In Table 2, results indicate that the both tails from Mann–Whitney U test and Kolmogorov–Smirnov Z are p _{1} = 0.000 < α and p _{2} = 0.000 < α. Thus, H _{0} is rejected. It means v _{1}, v _{2} and v _{3} show significant differences. Therefore, to analyze the walking speed and transfer time with respect to various pedestrian facilities has necessity.
Walking time model on the platform
Passengers tend to get impatient easily, since they get off from the crowded subway. As transfer volume increases, the sectional number of transfer pedestrians is getting higher. It leads to the decline of the walking speed. As shown in the Table 2, the speed obtained from the platform concentrates on 1.2–1.5 m/s, which is higher than usual. When the sectional number increases to 0.35 (p/m s), the average speed declines to 1.03 m/s. The formula (4) below is built by the fitting method in MATLAB 2013.
Walking time model in horizon passage
The data of the speed obtained from horizon passage concentrates on 0.9–1.2 m/s. Passengers in horizon passage have less space than that on the platform. Thus the speed in horizon passage is slower. Therefore, the sectional number in horizon passage is the main factor affects the walking time. Formula (4) is built by the fitting method in MATLAB 2013.
Walking time model on the escalator
Transfer time model validation
The calculation results in different stations
Group no.  N (p/min)  L _{1} (m)  B _{1} (m)  v _{1} (m/s)  p _{1} (p/m s)  L _{2} (m)  B _{2} (m)  v _{2} (m/s)  p _{2} (p/m s) 

1  6  2.80  11.50  1.73  0.01  88.50  4.50  1.29  0.02 
2  9  3.20  9.00  1.26  0.02  123.00  3.50  1.26  0.04 
3  15  2.60  10.50  1.40  0.02  142.50  4.50  1.21  0.06 
4  29  3.50  8.50  1.53  0.06  105.50  4.50  1.14  0.11 
5  33  3.30  8.00  1.45  0.07  152.50  4.50  1.12  0.12 
6  34  4.20  6.50  1.48  0.09  115.50  4.50  1.10  0.13 
7  43  4.00  6.00  1.34  0.12  133.00  3.50  1.07  0.20 
8  64  3.50  6.00  1.24  0.18  97.00  4.50  1.03  0.24 
9  82  3.50  6.00  1.76  0.23  97.00  4.50  0.94  0.30 
10  96  4.20  6.50  1.23  0.25  115.50  4.50  0.96  0.36 
11  105  2.60  10.50  1.43  0.17  142.50  4.50  0.94  0.39 
12  110  4.00  6.00  1.19  0.31  133.00  3.50  0.89  0.52 
13  122  3.20  9.00  1.41  0.23  123.00  3.50  0.91  0.58 
14  143  3.30  8.00  1.24  0.30  152.50  4.50  0.83  0.53 
15  151  2.80  11.50  1.39  0.22  88.50  4.50  0.81  0.56 
16  158  3.50  8.50  1.29  0.31  105.50  4.50  0.80  0.59 
Group no.  L _{3} (m)  B _{3} (m)  v _{3} (m/s)  p _{3} (p/m s)  T (s)  T _{ tr } (s)  Error rate (%) 

1  24.00  1.20  0.50  0.08  190.76  191  0.13 
2  28.00  1.10  0.50  0.14  334.73  343  2.41 
3  25.00  1.20  0.50  0.21  307.56  307  0.18 
4  25.00  1.10  0.60  0.44  228.10  231  1.26 
5  25.00  1.20  0.60  0.46  316.25  333  5.03 
6  25.00  1.10  0.50  0.52  249.65  241  3.59 
7  28.00  1.10  0.60  0.65  348.78  339  2.88 
8  24.00  1.20  0.50  0.89  214.93  224  4.05 
9  24.00  1.20  0.49  1.14  223.37  236  5.35 
10  25.00  1.10  0.46  1.45  270.50  255  6.08 
11  25.00  1.20  0.41  1.46  351.75  359  2.02 
12  28.00  1.10  0.38  1.67  397.62  408  2.54 
13  28.00  1.10  0.38  1.85  386.48  388  0.39 
14  25.00  1.20  0.31  1.99  402.03  442  9.04 
15  24.00  1.20  0.28  2.10  270.76  256  5.77 
16  25.00  1.10  0.27  2.39  317.34  335  5.27 
Conclusions
This paper proposed a transfer time prediction model which was appropriate for different transfer stations. On the basis of the learning set, the model parameters of transfer speed and transfer volume were established with respect to the sectional number of transfer passengers. Through the testing set including 64 samples on four different transfer stations, the results demonstrated that the average error rate and the standard deviation were 3.50 % and 0.024. Results indicated that this transfer time model had the merits of accuracy, feasibility and reliability. By means of the model, transfer time could be predicted accurately. Furthermore, the proposal model was helpful for the operation department to coordinate subway trains between lines.
With more application of the model in the future, the regulation of transfer time should be further studied to analyze the distributions of waiting time and the transfer passage choice of passengers.
Declarations
Authors’ contributions
All authors took part in the experiment of time prediction model. YZ designed the research and wrote the manuscript. LY completed the survey project and wrote the manuscript. YG deduced the formula and verified the accuracy of the established model. YC supported the data processing and reviewed the manuscript. All authors read and approved the final manuscript.
Acknowledgements
We thank Dr. Jianhui Lai for the support for GIS analysis. We thank Dr. Yao Lu for the help in the survey organization. We thank Nuo Zhang and Chen Li for the participating in the survey. Financial support for this research was obtained through the National Natural Science Foundation of China (NNSFC) project: The research of connectivity and accessibility matrix optimization model for the urban transport network (No. 51208014); and Beijing Municipal Education Commission, the General Program of Science and Technology: Journey time estimator under traffic uncertainties (No. KM201310005026).
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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