With the successful application of automatic fare collection (AFC) system in urban rail transit (URT), the information of passengers’ travel time is recorded, which provides the possibility to analyze passengers’ path-selecting by AFC data. In this paper, the distribution characteristics of the components of travel time were analyzed, and an estimation method of path-selecting proportion was proposed. This method made use of single path ODs’ travel time data from AFC system to estimate the distribution parameters of the components of travel time, mainly including entry walking time (ewt), exit walking time (exwt), and transfer walking time (twt). Then, for multipath ODs, the distribution of each path’s travel time could be calculated under the condition of its components’ distributions known. After that, each path’s path-selecting proportion can be estimated. Finally, simulation experiments were designed to verify the estimation method, and the results show that the error rate is less than 2%. Compared with the traditional models of flow assignment, the estimation method can reduce the cost of artificial survey significantly and provide a new way to calculate the path-selecting proportion for URT.
As the basis of network flow assignment calculation, the path-selecting proportion is directly related to the operation and management of urban rail transit (URT), including operation indicators calculating, train plan making, and fare clearing. Currently, there have been many research results on flow assignment for URT under the condition of network operation, most of which are multipath models based on path utility.
Nguyen et al. [
Poon et al. [
Xu et al. [
Si et al. [
The basic idea of such models above can be summarized as follows: determine the impedance of each path, which can be time costs or mileage; design the utility function based on the path impedance; calculate the flow assignment proportion of each path; distribute each OD’s total passenger flow of one day to paths between the origin stations and the destination stations (OD).
Such models can basically guarantee the accuracy of flow assignment. However, the parameters of these models, including the entry and exit walking time at stations and transfer time, are calibrated by manual survey, which is really a time-consuming and costly work. In addition, when the network structure or operation organization changes, the parameters need to be recalibrated in order to keep accurate. Therefore, it is necessary to study a new method of network flow assignment.
In recent years, the AFC system is widely used in URT, which can accurately record the passengers’ entry time at the origin stations and the exit time at the destination stations. With many years of application, the AFC system has accumulated vast amounts of passengers’ travel information. However, such information has rarely been used to study the behavior of travelling and path-selecting.
Chapleau et al. [
Lee and Hickman [
Kusakabe et al. [
Zhou and Xu [
Sun and Xu [
Based on the above background, this paper works on analyzing passengers’ travel time data recorded by AFC system with the theory of mathematical statistics and proposes a new estimation method of path-selecting proportion. This method provides a new idea of network flow assignment for URT.
Travel time of passengers in URT network mainly consists of the following six parts: entry walking time (the time of passengers walking from the AFC gate to the platform in the origin station, denoted by entry platform waiting time (the time of passengers waiting for the train on the platform in the origin station, denoted by on-train time (the time of passengers travelling on the train, denoted by transfer walking time (the time of passengers walking from the arrival platform to the departure platform in the transfer station, denoted by transfer platform waiting time (the time of passengers waiting for the train on the platform in transfer station, denoted by exit walking time (the time of passengers walking from the platform to the AFC gate in the destination station, denoted by
Components of travel time.
Lots of random factors can affect passengers’ travel time, so this paper makes the following assumptions: passengers arrive at the station randomly, dispersedly, and stably; all passengers can board the first train after arriving at the platform; the trains run according to the plan strictly with a certain speed level and no abnormal condition occurs.
For one station, suppose the walk distances for different passengers are the same, and then the distribution of walking time only depends on the walking speed. For walking speed, most research results [
The distribution can be verified by the following simulation experiment. The experimental environment is as follows: the interval of the trains at Station
The experimental procedure is as follows.
MATLAB is used to do the simulation experiment. Assuming
KS test.
Same as
Generally speaking, when the interval of transfer line is big, the faster passengers walk and the longer passengers may wait; when the interval of transfer line is small, the faster passengers walk and the shorter passengers may wait. It can be seen that there is strong correlation between
The factors affecting distribution of
Factors affecting
Obviously,
Let
Suppose that the passengers arrive at the transfer station with the coordination time
In the above formula,
Based on the assumption, all the trains run according to the timetable strictly with a certain speed level. So, between two certain stations (Station
Whether the components of travel time are independent is very important to analyze distribution characteristics of the path’s travel time. According to the analysis in the previous section,
Based on the above analysis, all the components of travel time are independent.
In China, smart cards and AFC system are applied in most cities, which can record part of the passengers’ traveling information on the URT network. The basic structure of AFC data is shown in Table
Structure of AFC data.
Records |
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Entry time |
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Exit time | Ticket type |
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Record 1 | 000102 | 8:05:12 | 000425 | 8:45:43 | Single card |
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Thus, based on the AFC data structure, any passenger’s travel time can be calculated.
According to the analysis in Section
Distribution characteristics and parameters of the components of travel time.
Components of travel time | Probability density function | Parameters to be estimated | Mean | Variance |
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— | — | TT |
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As formula ( |
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From Table
Take the OD with single path and no transfer (the origin station and the destination station are on the same line) as the research object, and the travel time is only comprised of
Based on
Because the components of travel time are independent, the following equations are established:
Equation (
Therefore, for any station on the line
To describe and solve PES problem, define
Take the five stations of line
Relationship graph of parameter sets.
Part of URT network
Undirected graph of parameter sets of line
In order to estimate the parameters accurately, the sample size should be as large as possible. Therefore, the PES problem can be summarized to seek the maximum spanning tree in Figure
The most common algorithm used to calculate the optimal spanning tree is Kruskal algorithm [
Set
Choose the edge
If there is any loop in the graph
If
For example, suppose the passenger flows of ODs in Figure
Results of maximum spanning tree.
Weighted graph of parameter sets of line
Maximum spanning tree
According to the maximum spanning tree, the node
Sequence of parameters estimation.
Based on the above analysis, the estimation method of
Build the relationship graph of parameter sets, of which the value of each edge is the passenger flow between its two vertices collected by AFC system.
Use Kruskal algorithm to calculate the maximum spanning tree of the relationship graph.
Find the node with the maximum number of edges and use the artificial survey to collect its samples of walking time (
According to the maximum spanning tree, estimate the parameters (
In URT system, transfer path means the path from the platform of one line to the platform of another line at the transfer station. Therefore, for a two-line transfer station, there are four transfer paths in total. Based on the analysis of most URT networks in China, for any transfer path of one transfer station, certain OD with single path and one transfer can be always found to contain the transfer path, of which the travel time only includes
Suppose that a certain OD (
Under the conditions of
Let
Based on (
Combining (
The OD “
Detailed information of paths: “
Paths | Stations | Transfer stations |
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Path 1 |
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Path 2 |
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Part of URT network.
Based on the method proposed in this paper, the process for estimating the proportion of two paths is as follows.
Build the relationship graph of parameter sets and use Kruskal algorithm to calculate the maximum spanning tree of the graph. Based on the maximum spanning tree, the parameter estimation sequence of stations is obtained.
Take line
To verify the parameter estimation method, a simulation of station
MATLAB is used to do the simulation experiment. The entry walking time data are collected to be the
From Table
Results of parameter estimation.
Parameters |
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Actual value | Estimation value | Error rate | Actual value | Estimation value | Error rate | |
Mean | 145 | 144.91 | −0.06% | 165 | 165.21 | 0.13% |
Standard deviation | 20 | 19.93 | −0.35% | 20 | 19.81 | −0.95% |
With the walking time parameters of all the stations on the URT network known, calculate
Suppose the values of parameters estimated in Step 1 and Step 2 are partly shown in Table
Design the simulation experiment as follows: generate randomly 10,000 passengers from
Do the simulation three times with different path-selecting proportions between Path 1 and Path 2 (0.7 : 0.3, 0.5 : 0.5, 0.3 : 0.7). Also, the entry and exit time data of simulation are collected to be AFC data.
Then, each path’s path-selecting proportion can be estimated by formula (
The results in Table
Values of parameters.
Parameters | Mean |
Standard deviation |
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ewt of |
125 |
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exwt of |
145 |
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twt of |
205 |
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twt of |
170 |
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twt of |
192 |
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Estimation results of path-selecting proportion.
Path-selecting proportion | Error rate of path 1 | ||||
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Actual value | Estimation value | ||||
Path 1 | Path 2 | Path 1 | Path 2 | ||
Simulation 1 | 0.7 | 0.3 | 0.6884 | 0.3116 | −1.66% |
Simulation 2 | 0.5 | 0.5 | 0.5050 | 0.4950 | 0.10% |
Simulation 3 | 0.3 | 0.7 | 0.2954 | 0.7046 | −1.53% |
In the network operation phase of URT, path-selecting proportion is the key to network flow assignment and fare clearing. This paper analyzed the distribution characteristics of the components of travel time and then proposed an estimation method of path-selecting proportion, making use of the travel time data from the AFC system. Also, simulation experiments were created to verify the estimation method, and the results show that the error rate is less than 2% and the method is reliable.
Compared with the traditional models based on path utility, the estimation method of path-selecting proportion has the following advantages:
In fact, the estimation method in this paper is being used to analyze and validate the URT network flow assignment results in Shanghai.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by China Postdoctoral Science Foundation (Project no. 2014M551454). The authors also wish to acknowledge Shanghai Shentong Metro Group Co., Ltd., for providing basic data during the research.