Selection and optimization model of standby train deployment stations on urban rail transit for large passenger flow

YE Mao, QIAN Zhong-wen, LI Jun-cheng, CAO Cong-yong. Selection and optimization model of standby train deployment stations on urban rail transit for large passenger flow[J]. Journal of Traffic and Transportation Engineering, 2021, 21(5): 227-237. doi: 10.19818/j.cnki.1671-1637.2021.05.019

Citation:

YE Mao, QIAN Zhong-wen, LI Jun-cheng, CAO Cong-yong. Selection and optimization model of standby train deployment stations on urban rail transit for large passenger flow[J]. Journal of Traffic and Transportation Engineering, 2021, 21(5): 227-237. doi: 10.19818/j.cnki.1671-1637.2021.05.019

Citation:

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Selection and optimization model of standby train deployment stations on urban rail transit for large passenger flow

doi: 10.19818/j.cnki.1671-1637.2021.05.019

YE Mao^{1, 2
,},
QIAN Zhong-wen^{1, 2},
LI Jun-cheng³,
CAO Cong-yong^{1, 2}

1.
School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
MIIT Key Lab of Traffic Information Fusion and System Control, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
3.
Guangzhou Metro Group Co., Ltd., Guangzhou 510380, Guangdong, China

Funds:

National Key Research and Development Program of China 2017YFB1201202

Transportation Science and Technology Project of Jiangsu Province 2020Y17

More Information

Author Bio:
YE Mao(1982-), male, associate professor, PhD, yemao0924@163.com
Received Date: 2021-06-18
Available Online: 2021-11-13
Publish Date: 2021-10-01

Abstract

Abstract

In order to quickly relieve the large passenger flow of stations on urban rail transit lines and reduce the total waiting time of passengers, the problem of standby train deployment was studied. Based on the consideration of train tracking relationship, train dwelling time, and other constraints, a multi-objective optimization model was established to determine the timing of standby train deployment, select the best station, and dynamically adjust the schedule. The conditions for the deployment of standby trains were defined and a quantitative determination method for the timing of the standby train operation was proposed. A 0-1 variable was used to characterize whether the station was equipped for standby trains, and it was used as the model input. Then, a mixed integer nonlinear programming (MINP) model of standby train deployment was established to minimize the waiting time of passengers at the station with large passenger flow, and the deviation time (delay time) of the timetable was constructed. The model compared the efficiency of different standby train deployment schemes to get the best standby train deployment station and the subsequent operation plan. An improved particle swarm optimization algorithm with a penalty function was designed to deal with the 0-1 variable and continuous variables simultaneously. Research results show that the method can make plans for all stations satisfying the conditions of standby train deployment, and further select the best standby train stations from the alternative stations. The maximum total passenger waiting time reduces by 1 318 209 s, and the optimization efficiency reduces about 21.9%. Moreover, the improved particle swarm optimization algorithm has good applicability to the MINP model. Compared to the existing urban rail line train operation adjustment and schedule optimization methods, the proposed method provides a more quantitative judgment on the timing of the standby train deployment in response to large passenger flow situations. It provides the evacuation capacity and efficiency of stations with large passenger flow stations and optimizes the operation plans of the standby and subsequent trains. The problem of large passenger flows at stations during peak hours can be relieve effectively. 4 tabs, 9 figs, 30 refs.
- urban rail transit,
- standby train,
- multi-objective optimization model,
- particle swarm optimization algorithm,
- large passenger flow,
- timetable

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Disclaimer: The English version of this article is automatically generated by Baidu Translation and only for reference. We therefore are not responsible for its reasonableness, correctness and completeness, and will not bear any commercial and legal responsibilities for the relevant consequences arising from the English translation.

0. 引言

Large passenger flow refers to the concentrated flow of passengers arriving at a certain time period that exceeds the capacity of normal passenger facilities or passenger organization measures at the station. How to effectively organize the operation of urban rail stations under high passenger flow conditions, so that the advantages of "fast, convenient, comfortable, and safe" urban rail can be fully reflected, has always been an important research topic. Lu et al^[1]A large passenger flow recognition method based on card swiping data from automatic ticketing equipment has been proposed; Yong et al^[2-3]Analyzed the fluctuation characteristics and spatiotemporal distribution of subway passenger flow, providing a new perspective for controlling subway passenger flow fluctuations; Zheng et al^[4]By combining the advantages of complex network models in capturing collective passenger behavior and online learning algorithms in describing rapid changes in real-time data, a machine learning based method for predicting abnormally large passenger flows has been developed, providing a foundation for passenger transport organizations; Li et al^[5]The system studied the joint optimization design of dynamic scheduling and passenger flow control of subway lines, and established a coupled state space model of train departure time and passenger load at each station. In the latest research, Wu Min^[6]Starting from the three aspects of information perception, risk prediction, and disposal decision-making in the data-driven mode of passenger flow disposal in subway stations, this paper explores the technical implementation approach of passenger flow disposal mode driven by multi-source data fusion in subway stations; Li et al^[7]By modeling and simulating the process of passengers getting on and off trains or subway platforms in specific scenarios, it was found that parameters representing humble behavior have a significant impact on the basic map and density distribution of pedestrians. By setting humble parameters reasonably, congestion can be alleviated and the total time for getting on and off trains can be reduced; Gu et al^[8]A real-time and accurate method for detecting passenger flow anomalies has been proposed under constantly changing passenger flow conditions; Liu Tao and others^[9]The concept of continuous cycle of large passenger flow at transfer stations and the strategy for handling large passenger flow at transfer stations were proposed, with a focus on analyzing the important role in handling large passenger flow at transfer stations; Li Jiajie and others^[10]On the basis of analyzing the process of passengers entering and transferring, a collaborative optimization model of out of station flow restriction and train timetable was constructed; Fang family and others^[11]Based on mobile signaling data in Shanghai, this study analyzed the spatiotemporal distribution patterns and changes in tourist behavior caused by the 2014 Shanghai Gucun Cherry Blossom Festival, and attempted to provide early warning for the large passenger flow; Xu et al^[12]A new multi station coordinated passenger flow control model has been proposed, which can simultaneously adjust the number of passengers entering and transferring at multiple stations or lines; Liu Jumei^[13]On the basis of traditional point line surface passenger flow control, a network passenger transport organization and control strategy based on station passenger flow density coefficient and passenger flow control efficiency has been established, and an urban rail network passenger flow control application platform has been built.

The above research can be classified into two aspects: strengthening station passenger flow organization and control, and adjusting line transportation capacity. In practical operational scenarios, temporarily adding station and line hardware facilities is obviously impractical. Therefore, the focus of this study is to explore the best backup vehicle deployment plan to quickly evacuate emergency situations in congested stations. When the concentrated arrival of passengers at a station during a certain period exceeds the capacity of normal passenger transportation facilities or organizational measures, it means that the original train operation plan cannot be relieved and may even exacerbate the congestion situation at the station. At this point, the necessity of deploying backup vehicles is obvious, but the question of when and where to deploy them deserves further quantitative exploration. Most studies are conducted from the perspective of dealing with sudden failures, in order to prevent the entire operation diagram from deviating too much and reducing the timeliness of rail transit. However, there is currently a lack of research on the deployment of backup vehicles aimed at improving transportation capacity in a timely manner to quickly alleviate station passenger flow.

1. 备用车开行前提条件

1.1 Determination of prerequisites for the operation of standby vehicles

On the basis of the calculation method for the maximum cross-sectional load factor per hour, define the maximum cross-sectional load factor per hourc_maxdo

$c_{\max }=\frac{s_{\max }}{F}$

(1)

Figure 1. Maximum section full load ratios in up and down direction of an urban rail line

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$Z_{l}=I_{l}-R_{l}$

(2)

$I_{l}=\sum\limits_{i=1}^{m}\left[\frac{v\left(F_{1, i, k}-D_{1, i, k}\right)}{F_{1, i, k}-F_{1, i-1, k}}+\frac{v\left(F_{2, i, k}-D_{2, i, k}\right)}{F_{2, i, k}-F_{2, i-1, k}}\right]$

(3)

In the formula:Z_lFor the thlWarning coefficient for large passenger flow within a unit of time;R_lFor the thlThe passenger flow entering the station within a unit time can be obtained by the Automatic Fare Collection (AFC) system of the subway;I_lUnder the current driving planlThe number of passengers that can be transported away within a unit of time;D_{1, i, k}andD_{2, i, k}They are the up and down directions in the timetable, respectivelyiA car is in placekThe arrival time of the station;F_{1, i, k}andF_{2, i, k}They are the up and down directions in the timetable, respectivelyiA car is in placekThe departure time of the station;vThe product of walking speed and number of driving doors;mThe number of train departures during peak hours.

1.2 问题描述

Figure 2. Large passenger flow stations in urban rail line

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2. Station selection model for spare vehicle deployment

2.1 大客流车站乘客等待时间模型

The primary focus of this article is to address the issue of passenger evacuation at high passenger flow stations. Therefore, considering the retention time of passengers at the target station is the key to the problem. Therefore, variables are definedP_{i, k}、S_{i, k}.P_{i, k}In order toiThe car arrives at the stationkThe number of passengers already waiting at that time is positively correlated with time and can be determined by the arrival rate of passengers at the platformλ(t）Obtain;S_{i, k}For the thiA car leaves the stationkThe number of stranded passengers can be determined by the arrival rate of platform passengersλ(t）Obtain the train stopping time. By multiplying these two variables with the interval time between trains arriving at the platform and adding them together, the total waiting time for passengers at the high passenger flow station can be obtained.Figure 3The shaded area shows the number of stranded passengers at the high passenger flow station

$P_{i, k}=\int_{F_{1, i, k}}^{F_{1, i-1, k}} \lambda(t) \mathrm{d} t$

(4)

Figure 3. Stranded passenger number at station with large passenger flow

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$\begin{aligned} T_{1}=& \sum\limits_{i=1}^{m} \sum\limits_{k=1}^{s-1} \sum\limits_{p \in N}\left[\frac{P_{i, k}\left(D_{1, i, p}-F_{1, i-1, p}\right)}{2}+\right.\\ &\left.S_{i-1, k}\left(D_{1, i, p}-F_{1, i-1, p}\right)\right] \end{aligned}$

(5)

2.2 备用车投放后线路延误时间模型

$T_{2}=\sum\limits_{i=1}^{m} \sum\limits_{k=1}^{s}\left[\left|D_{1, i, k}-d_{1, i, k}\right|+\left|F_{1, i, k}-f_{1, i, k}\right|\right]$

(6)

Figure 4. Subsequent delay after adding a standby train

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2.3 备用车投放车站选择优化模型

2.3.1 目标函数

$\max T=\sum\limits_{d \in N} B_{d}\left(\alpha T_{1}+\beta T_{2}\right)$

(7)

2.3.2 约束条件

This model belongs to a mixed integer nonlinear programming model, which involves adjusting the timing of adding backup vehicles and subsequent train departure times. Therefore, its constraints are all derived from the tracking relationship and stopping time between backup vehicles and regular trains. The constraint conditions are as follows.

$F_{1, I, k}-D_{1, I, k}=b_{k}$

(8)

Except for the maximum stopping time of 70 seconds at high passenger flow stations, the stopping time at other stations is the same as the actual stopping time, which is calculated by subtracting the arrival time from the departure time of the backup car at each station (where 70 seconds comes from the Guangzhou Metro timetable, and the maximum stopping time set for ordinary trains at stations with the highest passenger flow is 70 seconds).

$F_{1, i, k}-D_{1, i, k}=t_{k}$

(9)

$w_{k}=D_{1, i, k+1}-F_{1, i, k}=D_{1, I, k+1}-F_{1, I, k}$

(10)

$\left\{\begin{array}{l} D_{1, i+1, k}-D_{1, i, k} \geqslant h_{\mathrm{t}} \\ D_{1, I, k}-D_{1, i_{0}, k} \geqslant h_{\mathrm{t}} \\ D_{1, i_{0}+1, k}-D_{1, I, k} \geqslant h_{\mathrm{t}} \end{array}\right.$

(11)

$D_{1, i_{0}+1, k}-D_{1, i_{0}, k} \leqslant 1.5 h_{\mathrm{s}}$

(12)

In the formula:h_sThe maximum travel interval for the train.

3. Algorithm design for solving problems

3.1 求解方案设计

Figure 5. Flow of solving algorithm

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3.2 Algorithm Step Design

The timetable optimization part of the model adopts particle swarm optimization algorithm, also known as Particle Swarm Optimization (PSO) algorithm. In PSO algorithm, the potential solution of each optimization problem is a particle in the search space. All particles have a fitness determined by an optimization function, and each particle also has a velocity that determines their "flight" direction and distance. Then, the particles follow the current optimal particle to search in the solution space. The steps of particle swarm optimization algorithm are as follows.

Step 1: Random initializationmThe departure time of the subway is treated as a particle.

Step 2: Use train tracking and other methods as penalty function constraints on particles. If the penalty function requirements are not met, regenerate a group of particles and then calculate the penalty function.

Step 6: Compare the current individual optimal solution with the group optimal solution and update the group optimal solution.

4. 案例应用与结果分析

4.1 数据获取

Table 1. Running times of train at each section

区间	1~2	2~3	3~4	4~5	5~6	6~7	7~8	8~9	9~10	10~11	11~12	12~13
运行时间/s	119	76	106	71	101	92	114	89	64	75	86	121

| Show Table

DownLoad: CSV

Table 2. Stop times of train at each station

车站	1	2	3	4	5	6	7	8	9	10	11	12	13
停站时间/s	98	30	30	30	30	50	34	36	37	55	40	48	40

| Show Table

DownLoad: CSV

Figure 6. Station distributions in up direction and large passenger flow station

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Figure 7. Time distribution of passenger flow at Kecun Station

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4.2 结果分析

Using MATLAB R2018b programming to implement modeling and particle swarm optimization algorithm for selecting backup vehicle deployment stations. Firstly, solve the timetable scheme for adding backup vehicles at station 1, and then solve the timetable scheme for adding backup vehicles at station 5. Compare and analyze the best scheme between the two schemes through the objective function T. The internal parameter settings of the particle swarm algorithm are the same, with 35 particles, 100 iterations, and a convergence accuracy of 0.98. The optimization algorithm took 301 seconds in the experiment and began to converge after 43 iterations. After changing the deployment station and outputting the solution results, the operation diagram was organized as followsFigure 8As shown.

Figure 8. Train operation diagrams of additional plan

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Table 3. Arrival times at each station after deployment standby train

车站	方案1	方案2
1	18:33:43
2	18:37:20
3	18:39:06
4	18:41:22
5	18:43:03	18:31:57
6 (大客流车站)	18:45:14	18:34:08
7	18:47:36	18:36:30
8	18:50:04	18:38:58
9	18:52:09	18:41:03
10	18:53:50	18:42:44
11	18:56:00	18:44:54
12	18:58:06	18:47:00
13	19:00:55	18:49:49

| Show Table

DownLoad: CSV

Figure 9. Relieve effects comparison of two schemes

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Table 4. Scheme effect analysis of deployment standby trains

方案	原拥堵时间/s	备用车投放车站编号	开行备用车后拥堵时间/s	优化效率/%
1	5 991 932	1	4 673 723	21.9
2	5 991 932	5	5 099 190	14.9

| Show Table

DownLoad: CSV

Compared to existing research findings^[14]This article provides a more quantitative description of the timing of spare vehicle deployment in response to sudden large passenger flows, which can determine the specific timing of spare vehicle deployment and replace the qualitative usage principle of spare vehicles in previous research; Being able to dynamically adjust the operation of backup vehicles and subsequent trains to the timetable; In terms of application form, it also draws on the service measure of empty trains not stopping at stations and directly running to high passenger flow stations for passenger transportation.

5. 结语

(1) The timing of deploying spare trains in urban rail transit under high passenger flow conditions has been defined, and the prerequisite for deploying spare trains has been quantitatively described. That is, when the current timetable cannot evacuate the actual incoming passenger flow, spare trains will be deployed to enhance transportation capacity and alleviate passenger flow.

References(30)

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Selection and optimization model of standby train deployment stations on urban rail transit for large passenger flow

doi: 10.19818/j.cnki.1671-1637.2021.05.019