| Citation: | ZHANG Song-liang, LI De-wei, YIN Yong-hao. Trip reservation and train operation plan optimization method of urban rail transit under demand responsive mechanism[J]. Journal of Traffic and Transportation Engineering, 2022, 22(4): 285-294. doi: 10.19818/j.cnki.1671-1637.2022.04.022
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As a large volume public service facility, it is necessary to improve the daily operation and organization of urban rail transit after the COVID-19. Some cities have adopted measures such as real name boarding and information registration to trace passenger travel. Although these measures can play a role in epidemic prevention and control, they still cannot meet the requirements of precise passenger flow control. How to organize passenger flow in this scenario has important theoretical and practical significance for future urban rail transit to respond to public health emergencies.
At present, there is relatively little involvement in the precise control of urban rail transit passenger flow both domestically and internationally. Data driven technology can quantitatively analyze the impact of emergencies on rail transit passenger flow[1-2]Miao Qin[3]Explored the operational organization plan under the condition of sudden large passenger flow in the subway; Zhang Qi and others[4]Discussed the spread of passenger congestion effects in rail transit; Jiang et al[5]With the goal of minimizing passenger risk within the station, reduce the frequency of passenger congestion through passenger flow control; Yuan et al[6]Focus on the service quality during peak hours of the subway, and determine the duration and intensity of passenger flow control at different stations based on the discretization of passenger movement processes; Yang et al[7]We studied the coordinated control of passenger flow in different directions at the network level by utilizing the spatiotemporal relationship between rail transit stations and lines. In addition, the station can also be targeted based on passenger travel behavior[8]And lines[9]Predicting passenger flow distribution to provide decision-making basis for orderly organization. The above research has made useful explorations on risk prevention and operational organization in special scenarios of urban rail transit, but passengers are still in a passive role and cannot fully adapt to the needs of epidemic prevention and control.
In recent years, exploring the organizational mode of urban rail transit transportation in response to passenger flow demand has been a hot topic that many scholars have been focusing on[10-12]Robenek et al[13]When designing the train timetable, passenger satisfaction was taken into account; Canca et al[14]Studied the balance of interests between passengers and operating companies; Barrena et al[15]Studied the timetable of rail transit trains that adapt to dynamic demands; Bucak et al[16]In response to the phenomenon of over saturation of passenger demand in rail transit, the train timetable has been optimized with a passenger oriented approach. This type of problem often uses branch and bound method[17]Or genetic algorithm[18]Particle Swarm Optimization Algorithm[19]Waiting for heuristic algorithms to optimize passenger waiting time. The passenger flow driven transportation organization model can improve the level of rail transit services, but it lacks coupling between transportation resources and passenger flow demand.
With the development of emerging technologies, there is a solution to the problem of information asymmetry between supply and demand. The use of mobile platforms to achieve passenger travel reservations has the characteristics of "fixed person, fixed point, and timed", which can meet the needs of precise policy implementation in the event of public health emergencies. Online ride hailing service[20-21]Customized public transportation[22]It belongs to the transportation products under this "reservation response" mechanism, characterized by information exchange between travelers and transportation service providers. Wang Jingpeng and others[23]By analyzing passenger choice behavior and driver supply behavior, point out the game relationship between supply and demand in ride hailing platforms; Shu et al[24]Design a route planning method tailored to the characteristics of customized public transportation to meet the diverse travel needs of passengers. For rail transit, it can be combined with passenger booking behavior and flexible demand[25]Given the focus on system robustness[26]Through the theory of user equilibrium[27]And probability prediction methods[28]To achieve optimal matching between passenger transportation products and multi granularity demands. Generally, when the demand for passenger transportation does not match the supply structure, the operating department often finds it difficult to adjust the supply strategy in a timely manner, thus unable to adapt to changes in actual demand. Travel reservations can effectively solve this problem and enable operators to effectively grasp the daily passenger flow scale. Since the outbreak of the epidemic, Beijing Metro has successively launched pilot programs for reservation entry at Tiantongyuan Station and Shahe Station. In the following year, this service involved a total of 1.17 million passengers, saving a total of 40000 hours of waiting time for passengers. The survey results of Beijing Metro on passenger travel also show that 88% of passengers are willing to make the strategy of booking travel a normalized means, and hope to open more booking entry channels and stations. From this, it can be seen that travel reservation has become a new mode of passenger flow organization in urban rail transit. How to use reservation information to guide the preparation of train operation plans and respond to the travel demands submitted by reservations will become a new problem faced by urban rail transit in the future.
Establishing a demand response mechanism in the field of rail transit through appointment mode can to some extent break down the information barriers between supply and demand, balance the volatility of passenger flow demand and the planning of transportation organization. Therefore, the train operation plan should have a certain degree of "flexibility" to adapt to passenger flow demand. Compared to traditional transportation organization models, demand response mechanisms have put forward more flexible and efficient requirements for train scheduling and vehicle utilization turnover. With the booming development of virtual grouping and unmanned train driving technology, automation and informatization will become the development direction of future urban rail transit systems. The train will break through multiple restrictions such as fixed routes and uncoupling positions, and there is no need to consider the allocation of drivers and passengers. At that time, the difficulty for transportation companies to respond to passenger travel needs will be reduced, and train operations can be flexibly adjusted according to passenger travel needs to better serve passengers. The demand response mechanism proposed in this article relaxes the above constraints and accurately allocates transportation resources by collecting the travel needs of reserved passengers, providing decision-making basis for flexible organization of train operations.
Travel reservation and demand response together constitute the "reservation response" mechanism. in compliance withFigure 1As shown, passengers submit their travel needs through the platform; The rail transit operation department coordinates the transportation capacity, maximizes the satisfaction of passengers' travel intentions, prepares train operation plans, and informs passengers through the reservation platform before the start of operation. After obtaining passenger travel information, the urban rail transit operation department needs to optimize the operation plan based on passenger demand and provide feedback on the response results to passengers. Consider this process as one cycle, which includes three time periods: appointment period, planning period, and train operation period. This mechanism tightly establishes a coupling relationship between supply and demand, achieving precise matching between passenger flow and transportation capacity.
Establish a nonlinear mixed integer programming model with the goal of minimizing passenger travel costs and train operating costs. Due to the need to pay attention to social distancing during the epidemic, it is necessary to ensure the smooth operation of rail transit while strictly controlling train load rates and station congestion levels.
During the appointment process, there areNPassengers participate in the reservation, forming a groupΠ={n|1, 2, …, N}, passengernThe demand is expressed asxn={on, dn, tn, an}Considering that different passengers have varying levels of time sensitivity, calibrate the urgent demand parametersUDistinguishing between different types of passengers: Whenan＜UAt that time, passengersnBelonging to time sensitive passengers, otherwise belonging to time abundant passengers. The former has a higher time cost, while the latter is relatively lower.
in compliance withFigure 2As shown, for the operating rail transit lines, a total ofSA station, forming a collectionΩ={s|1, 2, …, S}Operating on the routeKTrain, forming a collectionΓ={k|1, 2, …, K}During the operational period, specify the time granularityθDivide it intoTA time period, forming a setΦ={t|1, 2, …, T}Known passenger needsxn={on, dn, tn, an}For the convenience of modeling, usern, o, d, tIndicating as a passengernExpected in timetfollowoStation departure to godWhen standing,rn, o, d, t=1. Otherwisern, o, d, t0
Assumption 2: The train stopping time and interval running time are known and fixed.
Assumption 3: The last train departs from the first station at a fixed time, ensuring that all passengers entering the station during the study period can board[31].
Urban rail transit needs to consider shortening passengers' stay time in public places, that is, the generalized travel cost; At the same time, try to control operating costs as much as possible. objective functionzConsider expanding passenger travel costs in a broad sensezpAnd the cost of train operationzvMinimize and assign weight coefficients separatelyσ1andσ2That is
| minz=σ1zp+σ2zv | (1) |
For all passenger flows during the study period within the route, considering that passengers need to make advance reservations for travel and that there is a deviation between the suggested time feedback from the response mechanism and the expected travel time of passengers, the generalized travel cost for passengerszpIncluding the cost of booking time for each passengerfnAnd the cost of delay timehnThat is
| zp=∑n∈Π(fn+hn) | (2) |
| gn=∑k∈Γpn,k∑t∈Φ∑o∈Ω∑d∈Ωrn,o,d,tqk,o−∑o∈Ω∑d∈Ω∑t∈Φtrn,o,d,t | (3) |
| hn={ξ1gngn<an 且 an<Uξ1λgngn⩾ | (4) |
gn、anandUanswerhnThe impact can be achieved throughFigure 3Description, including time sensitive type (corresponding toa1）And the time abundant type (corresponding toa2）Two types of passengers. If there is a delay in the durationgnDelay time cost within acceptable range for passengershnfollowgnThe growth rate is slower thangnExceeding the level of passenger acceptance.
As the operating time of the train increases, the operating cost of the train also increases, and the two are approximately proportional. Therefore, the operating time of the train unit formation is used to represent the operating cost of the trainzvThat is
| z_{\mathrm{v}}=\sum\limits_{k \in \varGamma}\left(T_{\mathrm{p}}+T_{\mathrm{o}} m_k\right) | (5) |
In the formula:TpPrepare time for the train;ToFor the train running time, correspond to the process of train preparation and turnaround and mainline operation respectively;mkFor the trainkTo adapt to the time imbalance of passenger flow demand, the line adopts an organizational mode of multi formation operation of trains.
The constraints involved in the model are mainly used to describe the train, passengers, and variable range. In addition to the defined parameters and variables, they also include the following variables and parameters:nandnThey are different passengers respectively;kandk'are different trains respectively;tandt'are different times respectively;dandd'' are the terminal stations corresponding to different passengers' travel;ckFor the trainkThe passenger capacity of the corresponding train;bk, sandqk, sThey are trains respectivelykArrival and departuresStanding time, between 1~TDuring any given time period;wsFor the train insThe stopping time of the station;usFor the train insStation ands+The running time between stations;IminandImaxThe lower and upper limits of the departure interval.
| \sum\limits_{t=0}^{q_{k, s}} \sum\limits_{d=s+1}^S \sum\limits_{n \in \varPi} r_{n, s, d, t} p_{n, k} \leqslant \sum\limits_{k \in \varGamma} c_k-\sum\limits_{t=0}^{q_{k, s-1}} \sum\limits_{o=1}^{s-1} \sum\limits_{d=s+1}^S \sum\limits_{n \in \varPi} r_{n, o, d, t} p_{n, k} \quad k \in \varGamma, s=2, 3, \cdots, S-1 | (6) |
| q_{k, s}=b_{k, s}+w_s \quad k \in \varGamma, s=1, 2, \cdots, S-1 | (7) |
| b_{k, s+1}=q_{k, s}+u_s \quad k \in \varGamma, s=1, 2, \cdots, S-1 | (8) |
| q_{k+1, s}-q_{k, s} \geqslant I_{\min } \quad k=1, 2, \cdots, K-1, s=1, 2, \cdots, S-1 | (9) |
| q_{k+1, s}-q_{k, s} \leqslant I_{\max } \quad k=1, 2, \cdots, K-1, s=1, 2, \cdots, S-1 | (10) |
| \sum\limits_{k \in \varGamma} p_{n, k}=1 \quad n \in \varPi | (11) |
| \left(\sum\limits_{k \in \Gamma} k p_{n, k}-\sum\limits_{k^{\prime} \in \varGamma} k^{\prime} p_{n^{\prime}, k^{\prime}}\right)\left(\sum\limits_{o \in \varOmega} \sum\limits_{d \in \varOmega} \sum\limits_{t \in \varPhi} t r_{n, o, d, t}-\sum\limits_{o \in \varOmega} \sum\limits_{d^{\prime} \in \varOmega} \sum\limits_{i^{\prime} \in \varPhi} t^{\prime} r_{n^{\prime}, o, d^{\prime}, t^{\prime}}\right) \geqslant 0 \quad n, n^{\prime} \in \varPi, o \in \varOmega | (12) |
The collaborative optimization model for demand response and operation planning of urban rail transit proposed in this article is a nonlinear mixed integer programming problem. Considering that the decision variables of the model involve departure time, passenger flow allocation scheme, and train formation, and that the complexity of the problem is related to passenger flow scale, number of stations, and operation time, it is difficult to solve with accurate algorithms. To improve solving efficiency, design an adaptive large-scale neighborhood search algorithm based on priority passenger flow allocation.
Step 1: Generate initial solution. Randomly generate initial train operation plans and passenger flow allocation schemes, calculate passenger travel costs, train operation costs, and objective function values, and use them as the optimal solution.
Step 3: Allocate passenger flow and calculate the corresponding passenger travel cost and objective function value for the new solution.
Step 2: Check if each train exceeds its capacity limit in each operating section. If it exceeds the capacity limit, proceed to Step 3; Otherwise, proceed to step 5.
Using the model and algorithm designed in this article, simulate the operation of the demand response mechanism in the downward direction of the Beijing Subway Batong Line, and evaluate the effectiveness of the model and algorithm based on the simulation results.
The entire line starts serving from 5:20 and ends at 23:20, with a running time of 1080 minutes. The train stops at each station along the way for 1 minute, and the running time for each section from Tuqiao to Guoyuan is 1 minute. The running time for each section from Guoyuan to Sihui is 2 minutes. In order to better adapt to passenger demand, trains running on the line adopt a multi formation mode: 4-car and 6-car formations coexist, that ismk=4 or 6, corresponding to the passenger capacity of the trainck=960 or 1460 people,k∈ΓTrain preparation timeTp=10 minutes, train running timeTo=32 minutes. By analyzing vehicle design parameters and seating data, combined with epidemic prevention requirements and the per capita standing area of subway carriages, it is determined that the train's full load rate shall not exceed 40% of its passenger capacity.
| 参数 | 取值 | 参数 | 取值 | |
| U/min | 5 | θ/min | 1 | |
| Imin/min | 3 | T | 1 080 | |
| Imax/min | 10 | λ | 2 | |
| σ1 | 1 | ξ1 | 1.2 | |
| σ2 | 20 | ξ2 | 0.6 |
DownLoad:
CSV
| 运营场景 | 服务人数 | 开行列车数 | 使用车数 | 乘客平均等待时间/min |
| 原有运行图-无预约(场景1) | 41 496 | 216 | 1 296 | 5.53 |
| 优化运行图-无预约(场景2) | 41 496 | 186 | 910 | 5.61 |
| 优化运行图-有预约(场景3) | 41 496 | 186 | 910 | 3.58 |
DownLoad:
CSV
The optimized train operation diagram corresponding to scenario 3 is as followsFigure 5As shown. During the morning rush hour, the departure interval of trains is very small, and all trains used are 6-car formations, providing a large transportation capacity for the entire line; During non peak hours, by increasing the departure interval and switching some trains to 4-car formations, we can ensure passenger service quality while reducing train operating costs. The entire optimization process takes about 110 minutes and can be completed during non operating hours of urban rail transit at night. Feedback on the travel needs of scheduled passengers can be provided before the start of work on the operating day to facilitate their daily travel arrangements.
For passengers, the "reservation response" mechanism replaces the passive waiting process at the station with online demand collection, and coordinates the distribution of passenger flow within the station to better serve passengers. Especially during peak hours (6:30-9:30), the average waiting time of passengers at different times in the three scenarios is as follows:Figure 6As shown. The demand response mechanism ensures a stable distribution of average waiting time for passengers at different times. This is because clearly informing passengers of the expected arrival time at the station will coordinate individual passenger travel at a macro level, prevent short-term congestion caused by random passenger flow, and ensure smooth and orderly arrival of passengers at the station. This is beneficial for the current requirements of epidemic prevention and control in rail transit transportation organization.
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ZHANG Song-liang, LI De-wei, YIN Yong-hao. Trip reservation and train operation plan optimization method of urban rail transit under demand responsive mechanism[J]. Journal of Traffic and Transportation Engineering, 2022, 22(4): 285-294. doi: 10.19818/j.cnki.1671-1637.2022.04.022
| 参数 | 取值 | 参数 | 取值 | |
| U/min | 5 | θ/min | 1 | |
| Imin/min | 3 | T | 1 080 | |
| Imax/min | 10 | λ | 2 | |
| σ1 | 1 | ξ1 | 1.2 | |
| σ2 | 20 | ξ2 | 0.6 |
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| 运营场景 | 服务人数 | 开行列车数 | 使用车数 | 乘客平均等待时间/min |
| 原有运行图-无预约(场景1) | 41 496 | 216 | 1 296 | 5.53 |
| 优化运行图-无预约(场景2) | 41 496 | 186 | 910 | 5.61 |
| 优化运行图-有预约(场景3) | 41 496 | 186 | 910 | 3.58 |
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