The suburban line connects the suburbs and the city centre; it is of huge advantage to attempt the express-slow mode. The passengers’ average travel time is the key factor to reflect the level of rail transport services, especially under the express-slow mode. So it is important to study the passengers’ average travel time under express-slow, which can get benefit on the optimization of operation scheme. First analyze the main factor that affects passengers’ travel time and then mine the dynamic interactive relationship among the factors. Second, a new passengers’ travel time evolution algorithm is proposed after studying the stop schedule and the proportion of express/slow train, and then membrane computing theory algorithm is introduced to solve the model. Finally, Shanghai Metro Line 22 is set as an example to apply the optimization model to calculate the total passengers’ travel time; the result shows that the total average travel time under the express-slow mode can save 1 minute and 38 seconds; the social influence and value of it are very huge. The proposed calculation model is of great help for the decision of stop schedule and provides theoretical and methodological support to determine the proportion of express/slow trains, improves the service level, and enriches and complements the rail transit operation scheme optimization theory system.
Starting from the beginning of the 21st century, the urban rail transit in China entered a rapid period of development, the urban development grows faster, the urban traffic congestion of metropolises has become more and more serious, and people’s living costs continue to increase, so the advantage of suburban is very obvious, and the suburban passenger flow surges forward; therefore, it is of great market demand to attempt express-slow mode between city and suburbs. The suburban line is longer than the ordinary one, and the passenger flow has more obvious spatial and temporal distribution. Lin and Sheu [
The basic problems such as studying the formulation rail transit line planning and establishing the operation scheme of multigoal programming model according to the general situation of dedicated passenger line and high-speed rail line planning from passengers’ travel time and cost benefits were studied. It involves some new concepts, such as the calculation model of passenger transfer fatigue recovery time, the consumption choice model of passenger lines, the calculation of the number of trains, and so forth. Through the analysis and calculation above, programming model, integrating the railway operation scheme optimization problem, was determined, and at last, a high feasibility optimization method of operation scheme was proposed.
This paper intends to study the dynamic quantitative relation between the passengers’ total travel time and train stop scheme and express/slow trains ratio in the express-slow mode and then aim to establish the optimization model of passengers’ travel time.
The passengers on suburban lines can be divided into two categories: the slow passengers, who at least get down at one common station, and express passengers, in which the OD is usually large passenger stations. The slow train passengers can get more satisfied service with single station stop scheme, while it will affect the travel time of express passengers [
According to the actual situation, the passengers of the same direction continued to reach the station one after another in section
Assuming that the amount of passengers arriving at the station is
So let the departure time for train
We can assume that the amount of passengers getting on the train
So the mathematical expectation of waiting time can be shown in formula (
Through the analysis above, the train departure interval is very important, according to which the reasonable waiting time can be obtained, so the mathematical expectation value can be expressed as
And the waiting time by slow trains can be expressed as in formula (
The stop scheme of Shanghai Metro Line 16.
Passengers’ travel time is an important indicator of the services level of urban rail transport, so how to save the total passengers’ travel time is an important goal to study the optimization of stop scheme. The passenger’ travel time can be divided into waiting time, train running time, and stop time at station; if the transfer is included at the same line [
① When only the slow trains are used, the passengers’ total travel time can be expressed as formula (
② While under the express/slow mode, using
③ For the total time passengers spend on rail transit trains, the additional time of start and stop are included in formula (
④ So the total time of passengers can be expressed as formula (
Through the study in Section
The total time of passengers mainly consists of all passengers’ time on the train and the time waiting at the station, while travel time of express and slow trains differs much; it is too hard to calculate any one separately; besides, it is not easy to compare and solve [
Firstly, the time consumption matrix is studied under the express-slow mode.
Suppose there are five stations numbered from
The running time matrix in certain conditions.
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To obtain accurate
The spacing of suburban lines between stations is usually larger than the ordinary ones; the train speed can reach the maximum value in each interval, so each running time of section can be calculated from (
The total passengers’ travel time can be expressed by formula (
Formula (
The length of Shanghai Metro Line 22 is 56.4 kilometers from Shanghai South Railway Station to Jinshanwei Station, passing by Xuhui District, Minhang District, Songjiang District, and Jinshan District [
The route map of Shanghai Metro Line 22.
During the course of modelling, it is assumed that each station is of skip ability, and each station has the potential as an express stop station. The steps of the algorithm are as follows.
Obtain the related information of Shanghai Metro Line 22, as shown in Table
The related information of Shanghai Metro Line 22.
Section | Length (km) | Running time ( | Stopping time ( |
---|---|---|---|
South Shanghai~Chunshen | 8.90 | 239.0667 | 65 |
Chunshen~Xinqiao | 5.70 | 191.869 | 45 |
Xinqiao~Chedun | 6.70 | 206.618 | 40 |
Chedun~Yexie | 8.50 | 233.167 | 45 |
Yexie~Tingling | 5.10 | 183.019 | 50 |
Tingling | 8.10 | 227.267 | 50 |
Jinshanyuanqu~Jinshanwei | 11.20 | 272.989 | 55 |
Calculate the running time interval matrix, based on the operation data of each station. The acceleration and deceleration of the trains are about 0.41 m/s2 in normal condition, the maximum speed is 27.8 m/s, and it requires 67.8 s to the maximum speed. The section running time of South Shanghai Railway Station to Chunshen is
After calculating the time matrix in Step
The OD matrix of Metro Line 22.
Station | South Shanghai | Chunshen | Xinqiao | Chedun | Yexie | Tingling | Jinshanyuanqu | Jinshanwei | Total |
---|---|---|---|---|---|---|---|---|---|
South Shanghai | 0 | 24 | 98 | 154 | 18 | 24 | 15 | 147 | 480 |
Chunshen | 67 | 0 | 31 | 57 | 8 | 11 | 34 | 14 | 222 |
Xinqiao | 59 | 31 | 0 | 54 | 2 | 0 | 3 | 27 | 176 |
Chedun | 117 | 53 | 11 | 0 | 8 | 20 | 27 | 38 | 274 |
Yexie | 47 | 8 | 9 | 34 | 0 | 2 | 5 | 1 | 106 |
Tingling | 68 | 12 | 21 | 17 | 0 | 0 | 3 | 0 | 121 |
Jinshanyuanqu | 34 | 17 | 14 | 38 | 6 | 19 | 0 | 14 | 142 |
Jinshanwei | 106 | 61 | 96 | 118 | 51 | 36 | 94 | 0 | 562 |
Calculate the average of
When calculating the interval time matrix, the stopping time in each station is also needed; during weekday peak time, the operation interval is 32 minutes [
The corresponding interval running time matrix can be drawn as shown in Table
The corresponding interval running time matrix ODT (s).
South Shanghai | Chunshen | Xinqiao | Chedun | Yexie | Tingling | Jinshanyuan | Jinshanwei | |
---|---|---|---|---|---|---|---|---|
South Shanghai | 0 | 7297.68 | 53012.12 | 121284.2 | 19183.14 | 31170 | 23640.3 | 279889.5 |
Chunshen | 0 | 0 | 7342.97 | 27558.93 | 6093.28 | 10941.48 | 43246.3 | 22399.16 |
Xinqiao | 0 | 0 | 0 | 13317.48 | 1049.58 | 0 | 3105.24 | 36802.89 |
Chedun | 0 | 0 | 0 | 0 | 2225.36 | 10223.4 | 21287.88 | 42424.34 |
Yexie | 0 | 0 | 0 | 0 | 0 | 466.04 | 2551.45 | 838.28 |
Tingling | 0 | 0 | 0 | 0 | 0 | 0 | 831.81 | 0 |
Jinshanyuanqu | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4591.86 |
Jinshanwei | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Sum all elements of ODT matrix and the OD, so the average travel time is 2335 s; when facing the same passenger flow, the average spending time is 2335 s in express/slow mode, that is 39 min 2 s, compared to the ordinary mode 40 min 28 s, per capita reduced time by 1 min 26 s.
For single passenger, 1 min 26 s is not of great importance, but more important to the peak period, the total passengers’ travel time is reduced, and the main advantage reflected can be described as follows.
① From the GDP calculation: according to the 2015 GDP data of Shanghai it has reached 24964.99 billion yuan [
When the time interval is 6 minutes and the daily total operating time is 5:50–22:00, the total time is 970 minutes, and there are 320 trips a day, the total economic benefits of conversion are as follows [
② If passengers cannot get their company on time, they may be subject to penalty units or absenteeism in the workplace, affecting the professional evaluation and promotion, and so forth.
③ For business people, if late, it will affect signature of major contract or lead to economic losses, and so on.
From the stop scheme calculation, it can save 2 min 59 s; if the stop plan can be further optimized, it will attract more passengers OD and cause more influence on the stop time, and the average travel time can be further reduced to 4 min 38 s. It is of great importance for going-work passengers during the peak time; in addition, the passengers’ total travel time can be reduced. Through the calculation and analysis, the train stopping at the express station will have more effect on the travel time of passengers. Because the passenger flow of the express station is large, when summing all the passengers’ travel time, calculate the average value; the travel time is less than the ordinary stop scheme [
The next 10–20 years is an important development period in which China’s economy will reach a higher stage, the 13th Five-Year Plan and the 14th Five-Year Plan will more focus on the construction of the city, and urbanization will further accelerate and promote the passengers. In this paper, a method of travel time optimization model is proposed, and the optimization object is defined as the minimum mean value of ODT. The smaller the average value of ODT is, the less time passengers spend on the trip, and it better benefits the passengers. Under the condition of imbalance flow, the express/slow mode can reduce passengers’ total travel time and improve the satisfaction of passengers, while during peak stage, it is not suitable to use express/slow mode. The demand for transport capacity and service level will be improved with the rapid increase of the passenger flow in the suburbs. The optimization result will be better if the passengers’ travel time, the proportion of trains, and the carrying capacity are considered. It is of great help to the operation practice of urban rail enterprise.
The authors declare that they have no competing interests.
This work was supported in part by the National Natural Science Foundation under Grants 71601110 and 61672002, the Key Technologies of Integrated Test and Authentication Platform for Urban Rail Transit under Grant 2015BAG19B02-28, and the Detection and Management of Risk and Control Technology of Disaster Prevention System for Urban Rail Transit under Grant 2016YFC0802505.