CN115392949A - Rail transit early-peak time-sharing pricing method based on passenger departure time selection - Google Patents

Rail transit early-peak time-sharing pricing method based on passenger departure time selection Download PDF

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CN115392949A
CN115392949A CN202210920961.9A CN202210920961A CN115392949A CN 115392949 A CN115392949 A CN 115392949A CN 202210920961 A CN202210920961 A CN 202210920961A CN 115392949 A CN115392949 A CN 115392949A
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周慧娟
刘念念
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Abstract

The invention provides a rail transit early-peak time-sharing pricing method based on passenger departure time selection. According to the method, elastic trip passenger identification is carried out on the basis of AFC data, and passengers are divided into elastic trip passengers and rigid trip passengers through a clustering algorithm; secondly, according to variables influencing the selection of the departure time of subway users, constructing a utility function, and establishing a passenger departure time selection model based on MNL; and then, describing the response behavior of the passenger to fare adjustment by combining with a passenger departure time selection model, considering the maximization of the income of a rail transit operator and the minimization of the generalized travel cost of the passenger, introducing departure time selection utility and passenger time value, and constructing a time-of-use pricing double-layer planning fare model. The invention provides a time-sharing pricing implementation strategy according with the early peak travel characteristics, widens the research view of rail transit fare formulation, and provides a theoretical basis for scientifically formulating the fare.

Description

Rail transit early-peak time-sharing pricing method based on passenger departure time selection
Technical Field
The invention relates to the field of urban rail transit, in particular to a rail transit early-peak time-sharing pricing method based on passenger departure time selection.
Background
In the aspect of travel characteristic research, the prior art classifies travelers mainly based on traffic survey data, lacks objectivity, has the classification indexes of subjective attributes such as travel purpose, age, occupation and the like, and has the defects of unreasonable assumption and the like; secondly, the flexibility of the passenger in the choice of departure time has not been strictly mathematically defined.
In the aspect of departure time selection behavior research, the prior art mostly focuses on selection of a travel mode, and the research on the aspect of departure time selection behavior of rail transit passengers is not much. In addition, key influencing factors in the prior art are mostly based on survey data such as SP and RP, but the questionnaire is easy to have problems of error self-reporting or inconsistency between real behaviors and questionnaire filling, and the objectivity is not strong.
In the aspect of fare strategy research, in the research of time-sharing pricing strategies of rail transit systems in the prior art in China, passenger types are not distinguished to make a targeted fare strategy; in addition, due to the diversity of urban development, fare policies need to be developed based on characteristics of urban travelers.
Disclosure of Invention
In order to solve the technical problems, the invention constructs a relatively scientific passenger classification index based on AFC (automatic fare collection) data, provides an identification method of an elastic trip passenger, and defines the trip 'elasticity' of the passenger; passenger types are used as key influence factors, introduced into a passenger departure time utility function, and a passenger departure time selection model based on MNL is constructed, so that the problem of poor objectivity of the model is solved, and the research on the passenger departure time selection behaviors of urban rail transit is enriched; the method comprises the steps of taking a passenger departure time selection behavior as a visual angle, combining passenger time values, constructing an urban rail transit early-peak time-sharing pricing double-layer planning model, and respectively formulating a differential fare strategy for elastic passengers and rigid passengers. The following technical scheme is adopted specifically:
a rail transit early-peak time-sharing pricing method based on passenger departure time selection comprises the following steps:
(1) Elastic trip passenger identification is carried out based on AFC data, data cleaning is carried out firstly, and then according to a first departure time fluctuation coefficient, a trip distance fluctuation coefficient and a Zhou Chuhang day fluctuation coefficient, the passengers are divided into elastic trip passengers and rigid trip passengers through a clustering algorithm;
(2) Establishing passenger departure time selection model based on MNL
According to variables influencing the selection of the departure time of a subway user, a utility function expression is constructed as follows:
Figure BDA0003777524270000021
each symbol is defined as follows:
V kn : passenger k selects a utility value for departure for the nth time period, where n =1,2,3, ·,18; beta is a TFS : a parameter to be calibrated corresponding to the standard deviation of the first departure time; beta is a TT : a parameter to be calibrated corresponding to the travel time; beta is a SDE : the parameter to be calibrated corresponding to the early-arrival time quantity; beta is a SDL : the parameters to be calibrated corresponding to late arrival time; beta is a FD : a parameter to be calibrated corresponding to the daily trip times; beta is a beta FW : parameters to be calibrated corresponding to the days of the week trip; beta is a beta FWS : the parameters to be calibrated correspond to the days of the week trip standard deviation; beta is a beta ω : parameters to be calibrated corresponding to the types of the traveling passengers; beta is a beta P : a parameter to be calibrated corresponding to the passenger ticket expense; TFS: the standard deviation of the first departure time of the one-month departure record; TT: a travel time average for a period of travel; and (3) SDE: the amount of time may be reached in advance; and (3) SDL: the amount of arrival time can be delayed; FD: daily average trip times recorded for a month trip; FW: zhou Chuhang days recorded one month out; FWS: the standard deviation of the weekly travel days recorded in one month of the travel; ω: the type of passenger; p: the cost of the passenger ticket; v. of kn : a disturbance term;
the probability that passenger k selects alternative n is expressed as:
Figure BDA0003777524270000022
in the formula (I), the compound is shown in the specification,
Figure BDA0003777524270000023
average trip utility for all choices;
(3) Establishing a double-layer planning time-sharing pricing model based on departure time selection
(3.1) constructing an upper layer model objective function and constraint conditions
Figure BDA0003777524270000024
In the formula, C l Representing an operation cost function related to passenger flow; f. of n Representing the train departure number in the nth selectable departure time interval o-d; c l ·f n Is the total operating cost of the track transportation line 1 in the n-time period slave interval o-d,
Figure BDA0003777524270000025
in order to be a function of the demand,
Figure BDA0003777524270000026
as a function of the price and
Figure BDA0003777524270000027
is an operation cost function;
(3.1.1) calculating the demand function
Figure BDA0003777524270000031
Figure BDA0003777524270000032
In the formula, P kn Corresponding to the probability that passenger k selects alternative n,
Figure BDA0003777524270000033
for the average trip utility of all the selection items, theta is a parameter reflecting the familiarity degree of passengers with the subway network, theta is more than 0, and a disturbance item v is formulated n The desired requirement of the probability space;
(3.1.2) calculating a price function
Figure BDA0003777524270000034
Figure BDA0003777524270000035
In the formula, PR od Representing the current ticket price; variable of fare
Figure BDA0003777524270000036
Is the rate of change of the fare;
(3.1.3) track traffic operation cost function
Figure BDA0003777524270000037
Figure BDA0003777524270000038
In the formula (I), the compound is shown in the specification,
Figure BDA0003777524270000039
representing the number of different types of passengers within the interval o-d over the nth selectable period; k is a radical of formula l The per-person operation cost of the rail transit line l is calculated;
in summary, the upper model objective function is represented as:
Figure BDA00037775242700000310
constraint condition 1: rigid trip passenger commute preferential fare constraint:
Figure BDA00037775242700000311
constraint 2: and (4) restricting upper and lower limits of the ticket price:
Figure BDA00037775242700000312
constraint condition 3: non-negative constraints:
Figure BDA00037775242700000313
(3.2) constructing a lower layer model objective function and constraint conditions
The lower layer objective function is expressed as:
Figure BDA0003777524270000041
wherein the travel time cost F TT Early arrival cost F AE Late to cost F AL The cost of congestion
Figure BDA0003777524270000042
And a ticket price
Figure BDA0003777524270000043
(3.2.1) travel time cost
The time value formula of the traveler selecting the trip in the nth time interval is expressed as follows:
Figure BDA0003777524270000044
calculating the time value of each type of passenger in different time periods, wherein the calculation formula is as follows:
Figure BDA0003777524270000045
in the formula (I), the compound is shown in the specification,
Figure BDA0003777524270000046
representing the proportion of the ith class passengers in the nth time period, and sharing the class I passengers; VOTT kn Representing the time value of the passenger in the nth time period; VOTT in Representing the time value of the ith class of passengers during the nth time period;
Figure BDA0003777524270000047
representing travel times within the nth time interval o-d for the class i passenger.
Figure BDA0003777524270000048
Travel time expenses generated when different categories of travelers select the nth time interval to travel are represented as follows:
Figure BDA0003777524270000049
(3.2.2) early and late cost
If the traveler arrives at the destination in advance, an early arrival cost F will be incurred AE Wherein, in the process,
Figure BDA00037775242700000410
represents the early arrival cost of the ith class of passengers within the nth interval o-d:
Figure BDA00037775242700000411
if the traveler delays arriving at the destination, a delay cost F is incurred AL Wherein, in the step (A),
Figure BDA00037775242700000412
late arrival cost in class i passenger nth interval o-d:
Figure BDA00037775242700000413
in the formula, theta e And theta l Respectively representing the time penalty factors of the traveler's early arrival and late arrival;
(3.2.3) cost of congestion in vehicle
Congestion charges are incurred when the passenger flow is greater than the number Z of passengers that can be accommodated when the congestion state is about to be reached, and the congestion sensitivity is expressed as:
Figure BDA0003777524270000051
where μ and γ are the congestion sensitive parameters to be calibrated; ω represents the full load rate within each selectable departure period; z represents the number of passengers which can be accommodated when the train is about to reach a crowded state;
Figure BDA0003777524270000052
is the amount of travel of the different classes of passengers within the interval o-d over the nth selectable time period; f. of n Representing the line capability in each time interval OD interval;
Figure BDA0003777524270000053
representing the rated passenger carrying quantity of the train; z l Representing the number of seats of the train, p representing the standing passenger density, S l The area of the train on a line l is the area of the seat, and the line l is a subway line;
Figure BDA0003777524270000054
representing the passenger riding time, the calculation is as follows:
Figure BDA0003777524270000055
in the formula, TR n Representing the train running time of the section;
Figure BDA0003777524270000056
representing the stop time of the train at the d +1 station;
the congestion cost is expressed as:
Figure BDA0003777524270000057
in the formula, λ represents a penalty coefficient of congestion degree;
in summary, the objective function of the lower layer plan is represented as:
Figure BDA0003777524270000058
constraint condition 1: the total passenger flow quantity is unchanged before and after time-lapse pricing in the research period:
Figure BDA0003777524270000059
constraint 2: the number of people in any interval is not more than the rated passenger capacity of the train at any time:
Figure BDA00037775242700000510
constraint 3: non-negative constraints:
Figure BDA00037775242700000511
preferably, the specific solving steps of the double-layer planning time-sharing pricing model are as follows:
step1: PSO algorithm initialization:
(1) Initializing various parameters c in the PSO algorithm 1 、c 2 ，r 1 、r 2 ，ω 1 、ω 2 Etc.;
(2) The model variable of the upper layer (discount rate delta of fare price in each time period) n ) The particles constituting the particle group are initialized at random with a group size n and a position X of each particle in the group α And velocity V α Setting the maximum number of iterations G max Let i =1,G max ＝100；
(3) The current position of each particle is denoted as p 0 The position of the optimal particle in the population is denoted as g 0 ；
Step2: solving the lower layer model
The position X of the upper model variable α Substituted into the lower model and fed by differenceOptimization of chemical method at present
Figure BDA0003777524270000061
Solving the optimal solution of the lower model under the condition
Figure BDA0003777524270000062
Namely the passenger flow in each time interval;
step3: judging whether convergence conditions are reached
Judging whether the maximum iteration number G is reached max If yes, output
Figure BDA0003777524270000063
And
Figure BDA0003777524270000064
if not, turning to Step4;
step4: calculating fitness function values
Will be provided with
Figure BDA0003777524270000065
Substituting into the upper layer model to calculate the fitness function value
Figure BDA0003777524270000066
Namely the profit B (delta, q) of the rail transit operator;
step5: updating historical optimal locations for individuals and populations
(1) If it is used
Figure BDA0003777524270000067
The corresponding fitness function value is superior to the optimal position p of the current individual 0 The fitness function value of, then p 0 Is updated to
Figure BDA0003777524270000068
Is marked as
Figure BDA0003777524270000069
The individual optimal solution of the corresponding lower layer is updated to
Figure BDA00037775242700000610
Is marked as
Figure BDA00037775242700000611
(2) If it is not
Figure BDA00037775242700000612
The corresponding fitness function value is superior to the optimal position g of the current group 0 The fitness function value of (1) is g 0 Is updated to
Figure BDA00037775242700000613
Is marked as
Figure BDA00037775242700000614
The corresponding lower-layer group optimal solution is updated into
Figure BDA00037775242700000615
Is marked as
Figure BDA00037775242700000616
(3) Let i = i +1 go to Step2.
The invention has the following beneficial effects:
(1) A passenger departure time selection model based on MNL is constructed: compared with the traditional questionnaire survey data acquisition problems that self-reporting is wrong or real behaviors are not consistent with questionnaire filling and the like easily occur, the method is completely based on AFC data expansion, reduces the difference with an actual scene, and is more objective and scientific; defining travel fluctuation coefficients from three dimensions of time, space and travel intensity as passenger classification indexes, and providing an elastic travel passenger identification method based on a K-means clustering algorithm; passenger types are used as key influence factors, a departure time selection utility function expression is introduced, a passenger departure time selection model based on MNL is constructed, and theoretical basis is provided for scientific fare formulation.
(2) An urban rail transit early-peak time-sharing pricing model based on departure time selection is constructed: the passenger departure time selection model is combined to describe the passenger response behavior to fare adjustment, a time-sharing pricing double-layer planning model is constructed based on the passenger departure time selection behavior, the difference of rigid trip and flexible trip passenger fare policy making is reflected, the effectiveness of fare regulation and control on relieving peak passenger flow congestion is verified, a time-sharing pricing implementation strategy according with the early peak trip characteristics is provided, and the research view of rail transit fare making is widened.
Drawings
Fig. 1 is a flow chart of elastic trip passenger discrimination.
Figure 2 model frame diagram.
FIG. 3 is a flow chart of a solution algorithm for a two-level planning model.
Fig. 4 is a diagram showing the accumulated passenger flow at each station of subway number 9 in a certain city in time intervals.
Fig. 5 is a comparison graph of time-interval ratios of two types of passengers.
Detailed Description
1. Elastic trip passenger identification based on AFC data
(1.1) data cleansing
The original AFC data contains partially dirty data, and in order to improve the data mining accuracy, it is necessary to perform data cleaning work first. Dirty data can be broadly classified into the following categories:
(1) The time of entering and leaving the station is unreasonable, namely the time of leaving the station is earlier than the time of entering the station;
(2) The station entering and exiting are unreasonable, namely the station exiting and the station entering are the same station;
(3) The card type is not reasonable, i.e., one-way ticket passengers are purchased. Only travelers who take subways for a long time have the elastic time, but the traveling rule of single ticket passengers cannot be explored, so the travelers do not belong to elastic time research objects;
(4) Travel times are too large or too small.
Considering that the number of samples is large, a direct deletion processing method is adopted for the types (1), (2) and (3); for type (4), a 6 σ test criterion is used to determine a reasonable travel time range, which is less affected by data loss. Let t min Represents the minimum travel time, t max The maximum travel time is shown, so that reasonable travel is realizedThe line time judgment rule is as follows:
r min ＝max{t y ，μ-6σ} (2-1)
t max ＝min{t m ，μ+6σ} (2-2)
t min ＜t eff ＜t max (2-3)
in the formula, t y Indicating the shortest running interval time, t, of the train m Represents the effective time t of the traffic card on a single trip eff Represents the eligible travel time, μ represents the mean of the normal distribution, and σ represents the standard deviation of the normal distribution.
(1.2) elastic trip passenger identification method
"elastic" travel characteristics: the commute passenger flow is often called "rigid" travel, which is reflected in the regularity, periodicity, stability and other aspects of travel, as opposed to "elastic" travel, i.e. travel activities including shopping, catering, leisure, entertainment and the like, aiming at elastic needs. Relevant studies have shown that: compared with rigid travel, elastic travel is more susceptible to traffic policies; rigid travelers prefer to change travel time over changing destinations or cancelling trips.
Since the trip characteristics of the elastic traveler are represented by unstable departure time, trip distance, trip intensity and the like, the invention develops research from three aspects of trip intensity, departure time regularity and trip OD regularity so as to analyze the trip characteristics of passengers from an individual refined view angle. On the basis of identifying rigid trip passenger flow AFC records, the trip information of the passenger in a long period is traced back by using a traffic card number, fluctuation coefficients of three dimensions of time, space and trip intensity are constructed to serve as judgment indexes, a target passenger is screened according to the indexes, then the passenger type is divided through a clustering algorithm, and the trip behavior is analyzed. Fig. 1 shows the overall flow of discriminating passengers for flexible trips.
(1.3) passenger Classification index construction
In probability statistics, the standard deviation or variance is used to measure the dispersion degree of sample data, and the data volatility increases with the increase of the standard deviation or variance. According to the method, the sample statistics and analysis are carried out by taking days as units, the characteristics of departure time, trip distance, zhou Chuhang days and the like of different working days in sample data are considered to have certain differences, meanwhile, the indexes are different in dimension, if the whole trip fluctuation of a passenger on the working days is measured by the total variance or standard deviation of the whole sample, the influence of the units cannot be eliminated, so that the standard deviation rate is adopted to define the trip fluctuation coefficient of the passenger, and the fluctuation degrees of multiple groups of data are compared.
According to the invention, the passenger travel volatility is considered from three dimensions of time, space and travel intensity respectively and is calculated by a formula (2-4) and a formula (2-5), and the larger the travel fluctuation coefficient is, the poorer the travel stability of a passenger group in a target time period is, and the greater the travel elasticity is.
Figure BDA0003777524270000081
Figure BDA0003777524270000091
In the formula, δ represents the fluctuation coefficient of each index, μ is the mean value of each index, and σ is the standard deviation of each index.
(1) First departure time fluctuation coefficient
The first departure time fluctuation coefficient explores the trip elasticity of passengers from a time dimension. The passenger presents certain trip characteristics in the aspect of the first departure time, and the first departure time of the passenger is mostly the early peak period if the rigidity trip, and the departure time is more fixed. In equation (2-5), j =1 and μ 1 is the average departure time, representing the first departure time x of all subway passengers in the sample i Average value of (a) ("sigma 1 Standard deviation of first departure time, δ 1 The first departure time fluctuation coefficient.
(2) Travel distance (travel time) fluctuation coefficient
The travel distance fluctuation coefficient explores the travel elasticity of the passengers from the space dimension. The trip distance can embody the passenger type to a certain extent, and generally speaking, rigidity trip passenger space stability is stronger. In the formula, j =2,μ 2 the average travel distance and the travel time can be regarded as a linear relation, the travel distance and the travel cost can also be regarded as a linear relation due to the fact that the subway fare is priced according to mileage, and the average travel distance can be approximately represented by the travel time, namely the travel distance x of all subway passengers in a sample i Average value of (a) ("sigma 2 To standard deviation of travel distance, delta 2 The travel distance fluctuation coefficient.
(3) Zhou Chuhang day-of-day fluctuation coefficient
The Zhou Chuhang day fluctuation coefficient explores the passenger travel elasticity from the travel strength. Zhou Jun trip intensity reflects passenger type by representing the frequency of riding rail transit trips within one week of the passenger, and the greater the trip intensity is, the stronger the rail transit loyalty is, and the less the trip elasticity is. In the formula, j =3, μ 3 Zhou Jun days of travel, representing the days x of travel of all subway passengers in the sample i Average value of (a) ("σ 3 Days of week travel standard deviation, delta 3 The coefficient of fluctuation of the days of the week trip is shown. And 2-2, summary information of the trip elasticity judgment indexes of the passengers is given.
TABLE 2-2 passenger trip elasticity discrimination indicators summarization
Figure BDA0003777524270000092
Figure BDA0003777524270000101
(1.4) target passenger screening
(1) Personal transportation card trip passenger identification
Card type screening requires detailed analysis based on actually acquired data and application scenarios. In the passenger trip elasticity research, the passenger taking a temporary card cannot observe the long-term trip rule of the passenger, the original data used by the invention contains the part of the passenger, and the passenger with the temporary card cannot be directly removed from a ticket bank. The invention provides an identification method of transport card trip passengers, which distinguishes temporary card trip passengers and transport card trip passengers according to three indexes of trip time fluctuation coefficient, trip distance fluctuation coefficient and Zhou Chuhang days fluctuation coefficient,
according to the characteristics of passengers who carry personal transportation cards to go out, at least 1 trip record is bound to exist in the trip records in a period of time; if the three indexes of the travel time fluctuation coefficient, the travel distance fluctuation coefficient and the Zhou Chuhang day fluctuation coefficient of a certain passenger are all smaller than zero, the passenger is shown to have only 1 travel record within 16 working days of research statistics. Considering that the sample size is great, can regard this type of passenger to be temporary card trip passenger, and remaining passenger is transportation card trip passenger, sets up the identification rule as follows:
Figure BDA0003777524270000102
in the formula, λ represents whether the passenger is traveling with the personal transportation card, λ =1 when the passenger is traveling with the personal transportation card, and λ =0 when the passenger is traveling with the temporary transportation card.
(2) Early peak passenger screening
Compared with the late peak of a working day, the phenomenon of traffic congestion during the early peak is more obvious, and the traffic congestion is difficult to regulate and control, so that the method is worthy of research. Due to the difference of urban rail transit network distribution, early-peak time periods are different in different lines, and early-peak passengers are screened according to passenger flow conditions of all lines.
2. MNL-based passenger departure time selection model
The method utilizes AFC data of rail transit to establish a quantitative model capable of explaining and predicting passenger departure time period selection behaviors. Because AFC data cannot represent social and economic characteristics of travelers, the selection behavior of the departure time period is initially explored by a discrete selection multi-item Logit model, the multiple-item Logit model assumes that all individuals are homogeneous and obeys IIA characteristics, and the passenger departure time selection behavior is suitable for the multiple-item Logit model.
In the application of the traffic field, if the continuous time is discretized into time periods, each time period is a passenger travel time selection limb, the passenger is a studied behavior decision unit, and the selection preference of the passenger is influenced by relevant variables such as time, space and travel intensity. When a passenger goes on a trip, the individual usually considers the influence factors of each trip scheme before going on a trip, and selects a time for going on a trip which the individual considers to have the maximum effect. According to the method, a plurality of Logit models are applied to the starting time selection modeling, the mutual influence mechanism of the variables and the starting time selection behavior is analyzed, the influence degree of passenger elasticity and rigidity requirements on the starting time selection is explored, and a certain theoretical support is provided for the railway traffic fare strategy compilation.
2.1 MNL-based departure period selection model construction
2.1.1 passenger departure time selection impact factor analysis
The subway automatic fare collection data stores a large amount of continuous travel information for each card holder, and can track behavior changes of passengers in a period of time. And the intelligent card transaction data is mined from the AFC system, so that a new opportunity is brought to the modeling of travel behaviors and requirements.
The factors influencing the selection of the passenger departure time interval are many, and can be generally summarized into two types of socioeconomic attributes and travel-related attributes, the socioeconomic attributes usually reflect the heterogeneity of travelers, are indirect influencing factors of the selection of the passenger travel time, and mainly comprise: gender, age, income level, travel purpose, social status, etc. The travel related attributes are main influence factors of the behavior decision of travelers, including travel time, traffic cost, crowdedness and the like.
The first step of the departure time selection behavior process is generally to generate travel demands, including travel origin-destination points, travel purposes and the like; in the second step, the passenger can select the optimal travel time according to the personal cognitive condition. After the departure time is determined, the passengers accumulate the influence factors such as the traffic cost, the travel time and the crowding degree in the vehicle spent in the trip as experience, and feed back and update the original cognitive structure of the passengers, so as to determine the selection of the next departure time period. Through the circulation of the process, the departure time selection preference of the passengers finally reaches a stable state, namely the personal optimal departure time is found.
According to the method, the selection behavior of the departure time of the passenger is quantitatively analyzed based on AFC total data, the passenger types are divided through a clustering algorithm, the trip purpose of the traveler is approximately represented, and a discrete selection model is introduced as a key factor, and main influence factors can be divided into three dimensions of time attribute, trip intensity and socioeconomic attribute, as shown in a table 3-1.
TABLE 3-1 Main influencing factors for passenger departure time selection behavior
Figure BDA0003777524270000111
Figure BDA0003777524270000121
(1) Time attribute
The time attribute is the most direct influence factor of passenger departure time selection behavior, and specifically comprises the following steps:
(1) travel time
The travel time is used for depicting the activity time range of the traveler, and the selection of the departure time of the passengers can be influenced to a certain extent by the length of the travel time. Because the travel time and the travel distance are approximately in a linear relationship, the travel time can be used as a substitute index of the travel distance.
(2) Amount of early arrival time
The amount of early arrival time can change the cost of passenger travel, thereby affecting the selection of the departure time of the passenger. The median of the departure time over a period of time may be approximately considered the expected departure time, and the expected amount of time of arrival for a passenger may then be approximately represented by the median of the first arrival time in the travel record for that passenger over a period of time. The difference between its expected and actual amount of time of arrival is approximately the amount of time the passenger can arrive earlier, i.e., the amount of time earlier. The expression is as follows:
AE = max [ (expected amount of time to reach — actual amount of time to reach), 0] (3-7)
(3) Late to time amount
The late arrival time amount is similar to the early arrival time amount, and the travel cost of the passengers is influenced by the late arrival time amount, so that the departure time of the passengers is changed. The difference between the actual amount of time of arrival of the passenger and the expected amount of time of arrival is approximately the amount of time that the passenger may delay the arrival, i.e., late. The expression is as follows:
AL = max [ (actual amount of arrival time-desired amount of arrival time), 0] (3-8)
(4) Standard deviation of
The standard deviation is used for describing the stability of the departure time of the passenger, and influences the selection of the departure time of the passenger to a certain extent. The adopted indexes comprise the standard deviation of the first departure time and the standard deviation of the number of days of the week trip. The first departure time is represented by the median of the first departure time of passengers in the continuous period; zhou Chuhang days are expressed as the standard deviation of the average number of days per week a passenger travels over a continuous period.
(2) Intensity of travel
The travel intensity is used for describing the utilization degree of the passenger on the rail transit, the higher the degree is, the higher the loyalty degree of the passenger on the rail transit is, the stronger the dependency is, and the method specifically comprises the following steps: (1) the average daily trip times are expressed by the average daily trip times of a certain passenger in a continuous period and are used for describing the utilization degree of the passenger on the rail transit in one day; (2) zhou Chuhang days, expressed as the average number of days a passenger travels per week over successive periods, is used to describe the utilization of rail traffic by the passenger over the week. Generally, the time selection of passengers with more travel times or travel days is more unfixed, and the departure time is more prone to change.
(3) Social and economic attributes
The socio-economic attributes are important factors influencing the selection of departure time of travelers, and specifically comprise the following factors: (1) the method comprises the steps of classifying travelers into rigid travelers, partial elastic travelers and elastic travelers through clustering analysis, wherein different types of travelers have different departure times; (2) passenger ticket cost and price regulation are common transportation management methods, and can have certain influence on the departure time of passengers.
(2.2) model selection based on MNL departure time
According to variables influencing the selection of the departure time of a subway user, a utility function expression is constructed as follows:
Figure BDA0003777524270000131
the symbols are defined as follows:
U kn : passenger k selects a utility value for departure for the nth time period, where n =1,2,3, ·,18;
β TFS : parameter to be calibrated corresponding to first departure time standard deviation
β TT : parameter to be calibrated corresponding to travel time
β SDE : parameter to be calibrated corresponding to early-arrival time quantity
β SDL : the parameter to be calibrated corresponding to late arrival time
β FD : to-be-calibrated parameter corresponding to daily trip times
β FW : to-be-calibrated parameter corresponding to days of week trip
β FWS : to-be-calibrated parameter corresponding to weekly trip day standard deviation
β ω : to-be-calibrated parameter corresponding to type of travelling passenger
β P : parameter to be calibrated corresponding to passenger ticket fee
TFS: standard deviation of first departure time of one-month-out record
TT: average travel time for a trip
And (3) SDE: can be reached in advance
And (3) SDL: can delay the amount of arrival time
FD: daily average trip times recorded for one month trip
FW: zhou Chuhang days recorded in one month out
FWS: standard deviation of days of week trip recorded for one month trip
ω: type of passenger
P: fare for passenger tickets
v kn : disturbance term
The probability that passenger k selects alternative n is expressed as:
Figure BDA0003777524270000141
let the parameter θ =1 in the MNL model, assuming that a passenger has two departure time options, namely, time interval 1 and time interval 2.
(1) If the utility values for time period 1 and time period 2 are 20 and 26, respectively, the selection probabilities for the two time schemes are, according to the MNL model:
Figure BDA0003777524270000142
(2) if the utility values for time period 1 and time period 2 are-30 and-36, respectively, the selection probabilities for the two time schemes according to the MNL model are:
Figure BDA0003777524270000143
in the scenarios (1) and (2), the two time scheme selection probabilities are calculated according to the MNL model, and the selection probabilities under the two scenarios are obtained through calculation because the difference values of the two scheme utility value fixed items are opposite to each other. Therefore, the original method is improved into 'utility relative difference determination selection probability', and the model form is improved into the following formula:
Figure BDA0003777524270000151
in the formula (I), the compound is shown in the specification,
Figure BDA0003777524270000152
the average trip utility for all choices.
Calculating the travel time selection probability of the scenarios (1) and (2) again according to the improved multiple Logit model, and obtaining different results as follows:
scenario (1):
Figure BDA0003777524270000153
scenario (2):
Figure BDA0003777524270000154
3. double-layer planning time-sharing pricing model based on departure time selection
The double-layer planning model can give consideration to benefits of decision makers of an upper layer and a lower layer, decision makers of the upper layer make decisions preferentially and influence behaviors of the lower layer, decision makers of the lower layer restrict implementation of an upper layer target, balance of benefits of both sides is achieved finally, and the double-layer planning model is suitable for solving a time-sharing pricing strategy.
3.1 early peak time-sharing pricing two-layer planning model framework
The conventional time-sharing pricing model has relatively few researches on the ticket price of urban rail transit, and lacks deep research on the mechanism of interaction between the selection of departure time of passengers and the ticket price, so that a targeted pricing scheme for solving the problem of congestion of a specific road section is few. Due to the great diversity in urban development, fare policies need to be developed based on the characteristics of travelers in each city.
Urban rail transit services have a remarkable public welfare characteristic, and in general, social welfare is the sum of producer interests and user interests, namely the sum of track traffic operation department profits and passenger profits. On the basis of identifying passengers in the elastic trip, the invention starts with the behavior of selecting the departure time of the passengers and constructs an early peak rail transit time-sharing pricing double-layer planning model: the upper layer model takes the fare change rate as a decision variable, selects effectiveness by combining with the departure time of a passenger, describes the reaction behavior of the passenger on fare adjustment, and aims to increase the income of a subway operation department; the lower-layer model takes passenger flow as a decision variable, the time cost of passengers traveling is reflected by combining time value, in addition, traveling cost is generated by arriving at a destination in advance or in a delayed manner and congestion in a vehicle, particularly, a traveler may start in advance or in a delayed manner to avoid fare improvement during an early peak period, so that the traveler arrives at the destination in advance or in a delayed manner, and negative effect of arriving in advance or in a delayed manner is generated, so that early arrival penalty factors and late arrival penalty factors are introduced to reflect the early arrival cost and the late arrival cost; the passenger riding comfort is reduced due to congestion in the automobile, and the congestion cost in the automobile is generated, so that passengers are combined into two types of rigid traveling and flexible traveling in the chapter, the generalized expenses of the passengers are considered in the classification, including the traveling time cost, the early arrival cost, the late arrival cost and the congestion cost in the automobile, and the purpose is to minimize the generalized expenses of the passengers, so that the traveling cost of the passengers is reduced, the passenger income is increased, and the social welfare is maximized. The upper and lower layer models are mutually influenced and restricted, and finally the benefit balance of both parties is realized.
The constructed time-sharing pricing model is divided into a passenger departure time selection scheme by taking 10min as an interval in the time dimension, and is divided into an elastic trip passenger and a rigid trip passenger on the passenger attribute so as to reflect the transfer effect of the fare on the passengers with different trip characteristics. Fig. 2 is a frame diagram of an urban rail transit early-peak time-sharing pricing double-layer planning model constructed by the invention.
3.2 construction of early-peak time-sharing pricing double-layer planning fare model
3.2.1 symbols and Definitions
(1) Collection
N: the first departure time period number set that the passenger can select, N = {1,2., N-1, N + 1., | N | }
NP l : the set of peak traffic time periods for line l,
Figure BDA0003777524270000161
Figure BDA0003777524270000162
the set of non-peak traffic periods for line l,
Figure BDA0003777524270000163
l: subway line set
I: set of passenger types
(2) Function(s)
U kn : utility function for departure of passenger k at nth selectable departure time period
Figure BDA0003777524270000164
Price function of ith class passenger going out in nth optional departure time interval o-d
Figure BDA0003777524270000165
Demand function of ith class passenger for traveling in nth optional departure time interval o-d
C l : traffic related cost function
(3) Index and parameter
Q: total travel within the research time interval o-d
l: subway lines, L ∈ L
n: passenger selectable first departure time period number, N ∈ N
d: station number of rail transit line
D: total number of sites of line l
i: passenger type
Figure BDA0003777524270000171
The proportion of the nth time interval of the ith passenger
PR od : the passengers going out in the interval o-d need to payAverage fare of
f n : number of departures in nth selectable departure time period
k l : per-person operation cost of line l
VOTT kn : time value of traveler selecting travel in nth time interval
VOTT in : time value of class i passenger for selecting travel in nth time interval
Figure BDA0003777524270000172
Travel time of class i passenger within nth selectable departure time interval o-d
Figure BDA0003777524270000173
Early-to-early amount of time for class i passengers within nth selectable departure interval o-d
Figure BDA0003777524270000174
Late arrival time amount of class i passengers within nth selectable departure time interval o-d
θ e : cost per unit time value of traveler's early arrival
θ l : cost per unit time value of a traveler arriving late
F TT : passenger travel time fee
F AE : early cost of traveler
F AL : late cost to traveler
ω: full load rate in each selectable departure period
Z: the number of passengers can be accommodated when the train is about to reach the crowded state
Figure BDA0003777524270000175
Riding time of passenger
Z l : number of seats of train
ρ: density of standing passengers
S l : floor area of train on line l
Figure BDA0003777524270000181
Passenger congestion fee
Figure BDA0003777524270000182
Rated number of passengers on line l
Figure BDA0003777524270000183
Number of passengers carried by the overtaking train on line l
PR min : lower limit of subway fare
PR max : upper limit of fare of subway
(3) Decision variables
Figure BDA0003777524270000184
Number of class i passengers within nth selectable departure time interval o-d
Figure BDA0003777524270000185
Fare rate of change for class i passengers during nth alternative departure time interval o-d
3.2.2 Upper layer model objective function and constraint conditions
The objective function of the upper layer planning model is to maximize the benefit of the rail transit operating company, which is profit, i.e., revenue minus cost.
The invention defines a demand function based on a discrete selection Logit method from the viewpoint of passenger departure time selection
Figure BDA0003777524270000186
And price function
Figure BDA0003777524270000187
Coming watchAnd (3) characterizing the passenger ticket income of the rail transit operation company, as shown in a formula 4-1:
Figure BDA0003777524270000188
in the formula, C l Representing an operation cost function related to passenger flow; f. of n Representing the train departure number in the nth selectable departure time interval o-d; c l ·f n Is the total operating cost of the track traffic line l within the slave interval o-d during the period n. Wherein the demand function
Figure BDA0003777524270000189
Price function
Figure BDA00037775242700001810
And an operating cost function
Figure BDA00037775242700001811
Are respectively defined as follows:
(1) Demand function
Demand function based on discrete selection Logit method
Figure BDA00037775242700001812
The method represents the travel demands of different types of passengers in the nth time interval o-d, is a key characteristic for representing the passenger ticket income of the rail transit operation company, obeys Gumbel distribution, can simulate and quantify the passenger departure time selection behavior, and is used for predicting the possible transfer of passenger flow after the change of the ticket price. The expression of the demand function is as follows.
Figure BDA00037775242700001813
Wherein, P kn The calculation formula from which the expected demand is derived is given by equations 3-7:
Figure BDA0003777524270000191
in the formula, P kn Corresponding to the probability that passenger k selects alternative n,
Figure BDA0003777524270000192
theta is a parameter reflecting the familiarity of passengers with the subway network, and theta is more than 0. Formulation of a disturbance term v n The desired requirement of probability space.
(2) Price function
The subway price function is the fare change rate
Figure BDA0003777524270000193
The current price of the passenger ticket
Figure BDA0003777524270000194
The expression is:
Figure BDA0003777524270000195
in the formula, PR od The fare required to be paid by the travelers in the interval o-d is represented; variable of fare
Figure BDA0003777524270000196
Is a rate of change of fare depending on passenger departure time selection and passenger type, is a parameter that is desired to be optimized.
(3) Track traffic operation cost function
The urban rail transit operation cost is the sum of all operation and production related expenses paid by enterprises and can be divided into fixed cost and variable cost, wherein the fixed cost is not changed greatly along with the change of passenger capacity in a short period and can be regarded as fixed expenses under certain conditions, such as depreciation and maintenance expenses of fixed facilities and equipment, management expenses and the like; the variable cost refers to the cost which directly changes linearly with the change of the passenger capacity, such as the train operation energy consumption, the vehicle operation and repair cost, the operation and security inspection cost and the like.
In urban rail transit system, the higher the full load rate of train, the higher the operation cost. When the number of vehicles in use is constant, the full load rate of the train increases with the increase of passenger capacity, which causes the increase of variable cost and the increase of fixed cost, therefore, the rail transit operation cost can be expressed as a function related to the passenger capacity
Figure BDA0003777524270000197
Figure BDA0003777524270000198
In the formula (I), the compound is shown in the specification,
Figure BDA0003777524270000199
representing the number of different types of passengers within the interval o-d over the nth selectable period; k is a radical of formula l The per-person operation cost of the rail transit line l is saved.
In summary, the upper model objective function can be expressed as:
Figure BDA0003777524270000201
constraint 1: rigid trip passenger commute preferential fare constraint:
Figure BDA0003777524270000202
constraint 2: and (4) restricting upper and lower limits of the ticket price:
Figure BDA0003777524270000203
constraint 3: non-negative constraints:
Figure BDA0003777524270000204
3.2.3 lower layer model objective function and constraint conditions
The objective function of the underlying planning model is to minimize the generalized travel cost of the passenger. General travel expenses of passengers including travel time expenses F TT Early to cost F AE Late arrival cost F AL The cost of congestion
Figure BDA0003777524270000205
And the fare
Figure BDA0003777524270000206
In four parts, the lower layer objective function is expressed as formula (4-7):
Figure BDA0003777524270000207
(1) Travel time cost
Travel time costs can be measured by time value. Passengers of the same type tend to select the same and most efficient mode of travel. The passenger departure time selection model in the previous chapter fully considers the loss of the traveler from the time dimension, and according to the formula (3-5) and the general time value calculation formula, the time value formula of the traveler selecting the trip in the nth time interval is expressed as:
Figure BDA0003777524270000208
the time value of each type of passenger in different time periods can be obtained by combining the composition proportion of different types of passengers in each time period in one day [70] The calculation formula is as follows:
Figure BDA0003777524270000209
in the formula (I), the compound is shown in the specification,
Figure BDA00037775242700002010
indicating the nth periodThe proportion of the class I passengers is that the class I passengers are shared; VOTT kn Representing the time value of the passenger in the nth time period; VOTT in Representing the time value of the ith class of passengers during the nth time period;
Figure BDA0003777524270000211
representing travel times within the nth time interval o-d for the class i passenger.
Figure BDA0003777524270000212
Travel time expenses generated when different categories of travelers select the nth time interval to travel are represented as follows:
Figure BDA0003777524270000213
(2) Early and late cost
The early arrival time amount AE and the late arrival time amount AL of a traveler are measured, and both the early arrival time amount AE and the late arrival time amount AL of a traveler generate a certain waiting time and thus a time cost.
The median of the departure time over a period of time may be approximately considered the expected departure time, and the expected amount of time of arrival for a passenger may then be approximately represented by the median of the first arrival time in the travel record for that passenger over a period of time. The difference between its expected and actual amount of time of arrival is approximately the amount of time that the passenger arrived early or late.
If the traveler arrives at the destination in advance, an early arrival cost F will be incurred AE Wherein, in the step (A),
Figure BDA0003777524270000214
represents the early cost of the ith class of passengers within the nth interval o-d:
Figure BDA0003777524270000215
if going outDelaying arrival at the destination will result in a late cost F AL Wherein, in the process,
Figure BDA0003777524270000216
late arrival cost in class i passenger nth interval o-d:
Figure BDA0003777524270000217
in the formula, theta e And theta l Respectively represents the time penalty factors of the early arrival and the late arrival of the traveler, and has been proved by the research l ＞θ e Always true [67] 。
(3) Cost of congestion in vehicle
The degree of congestion in the train compartment is generally expressed by the section full load rate, and the invention calculates the congestion cost through the train full load rate [68] When the passenger flow is larger than the number Z of passengers to be accommodated when the congestion state is about to be reached, the congestion cost is generated, and the congestion sensitivity can be expressed as formula 4-17:
Figure BDA0003777524270000221
in the formula, mu and gamma are congestion sensitive parameters to be calibrated, and mu =0.15 and gamma =4 are taken; ω represents the full rate within each selectable departure period; z represents the number of passengers which can be accommodated when the train is about to reach the congestion state;
Figure BDA0003777524270000222
is the amount of travel of the different classes of passengers within the interval o-d over the nth selectable time period; f. of n The method comprises the steps that the line capacity in OD intervals of each time period is represented, the departure number in n time periods is used for measuring, and when departure intervals are fixed, the section transport capacity of the line is a fixed value;
Figure BDA0003777524270000223
representing the rated passenger carrying quantity of the train; z l Representing the number of seats of the train, p representing the standing passenger density, S l The area of the train on the line l is the standing area of the train, and the line l is the subway line.
Figure BDA0003777524270000224
Representing the passenger riding time, the calculation is as follows:
Figure BDA0003777524270000225
in the formula, TR n Representing the train running time of the section;
Figure BDA0003777524270000226
representing the stop time of the train at the d +1 stop.
When the density rho of the seat exceeds 4 persons/m 2 In the process, passengers in the vehicle inevitably contact with other people, the walking is limited, the passengers are uncomfortable for a long time and are in a crowded state, so the rho =4 is adopted in the invention.
The congestion cost is expressed as:
Figure BDA0003777524270000227
in the formula, λ represents a penalty coefficient of congestion degree, and the study was made in accordance with Chen Peiwen [63] In the invention, λ =0.12 is taken.
In summary, the objective function of the lower layer plan can be expressed as:
Figure BDA0003777524270000228
constraint 1: the total passenger flow quantity before and after time-sharing pricing in the research period is unchanged:
Figure BDA0003777524270000229
constraint 2: the number of people in any interval is not more than the rated passenger capacity of the train at any time:
Figure BDA00037775242700002210
constraint 3: non-negative constraints:
Figure BDA0003777524270000231
3.2.4 fare model construction based on departure time selection
In summary, the urban rail transit early peak fare model selected based on the departure time is:
Figure BDA0003777524270000232
Figure BDA0003777524270000233
wherein, the decision variable of the upper layer model is the fare change rate in the interval o-d in the nth time interval of different classes of passengers
Figure BDA0003777524270000234
The decision variable of the lower layer model is the passenger flow in the interval o-d of the nth time interval of different classes of passengers
Figure BDA0003777524270000235
The upper layer model controls the fare, the lower layer model controls the passenger flow, the change of the optimal solution of the upper layer can influence the lower layer, the change of the lower layer also influences the upper layer, the upper layer and the lower layer are mutually restricted, the benefit balance of both parties is finally realized, in addition, the departure time selection utility is used as a parameter of the upper layer model, and the connection between the departure time selection model and the fare model is established.
4. Double-layer planning model solving algorithm design
And (4) iteratively solving the proposed time-sharing pricing model by combining the particle swarm and a differential evolution algorithm. The algorithm flow chart is shown in fig. 3, and the specific solving steps are as follows:
step1: PSO algorithm initialization:
(1) Initializing various parameters c in the PSO algorithm 1 、c 2 ，r 1 、r 2 ，ω 1 、ω 2 Etc.;
(2) The model variable of the upper layer (discount rate delta of fare price in each time period) n ) The particles constituting the particle group, the size n of the group and the position X of each particle in the group are initialized at random α And velocity V α Setting the maximum number of iterations G max Let i =1,G max ＝100；
(3) The current position of each particle is denoted as p 0 The position of the optimal particle in the population is denoted as g 0 ；
Step2: solving the lower layer model
Position X of upper layer model variable α Substituting into the lower layer model, and using differential evolution method to optimize at present
Figure BDA0003777524270000241
Solving the optimal solution of the lower model under the condition
Figure BDA0003777524270000242
Namely the passenger flow in each time interval;
step3: judging whether convergence conditions are reached
Judging whether the maximum iteration number G is reached max If yes, output
Figure BDA0003777524270000243
And
Figure BDA0003777524270000244
if not, turning to Step4;
step4: calculating fitness function values
Will be provided with
Figure BDA0003777524270000245
Substituting into the upper model to calculate fitness function value
Figure BDA0003777524270000246
Namely the profit B (delta, q) of the rail transit operator;
step5: updating historical optimal locations for individuals and populations
(1) If it is not
Figure BDA0003777524270000247
The corresponding fitness function value is superior to the optimal position p of the current individual 0 The fitness function value of, then p 0 Is updated to
Figure BDA0003777524270000248
Is marked as
Figure BDA0003777524270000249
The individual optimal solution of the corresponding lower layer is updated to
Figure BDA00037775242700002410
Is marked as
Figure BDA00037775242700002411
(2) If it is not
Figure BDA00037775242700002412
The corresponding fitness function value is superior to the optimal position g of the current group 0 The fitness function value of (1) is g 0 Is updated to
Figure BDA00037775242700002413
Is marked as
Figure BDA00037775242700002414
The corresponding lower-layer group optimal solution is updated into
Figure BDA00037775242700002415
Is marked as
Figure BDA00037775242700002416
(3) Let i = i +1 go to Step2.
5. Example analysis
5.1 example background
(1) Travel demand
In 2019, the total daily traffic of urban work in a central city area of a city is 3957 ten thousand people (including walking), the number of the daily traffic is increased by 0.8 percent on a same scale, wherein the number of the rail traffic reaches 652 ten thousand people, the daily traffic accounts for 16.5 percent of the total daily traffic of the work, and the daily traffic is the first in public traffic. The rail transit (without suburban railways) finishes the passenger traffic for 39.62 hundred million persons, the passenger traffic is increased by 2.96 percent compared with the last year, the average daily passenger traffic is 1085.6 ten thousand persons, the highest daily passenger traffic reaches 1377.5 ten thousand persons, and the rail transit has the necessity of traffic demand management.
(2) Early peak trip condition
The central urban commuting trip 3 accounts for 47.1 percent of the total trip amount and is a rigid trip passenger; the proportion of the living class to the total travel amount is 52.9%, the passenger is elastic travel, the proportion is large, and a certain ticket price regulation space is provided. The early peak period 7 is that.
(3) Rail transit ticket system price
In urban rail transit (except airport lines), taxing time-limited ticket making prices are adopted from 2014, and mileage pricing follows progressive decrement in kilometer units: 3 yuan in 6 km (inclusive); 6-12 km (inclusive) 4 yuan; 12-22 km (inclusive) 5 yuan; 22-32 km (inclusive) 6 yuan; more than 32 km, each plus 1 element can be 20 km. Using an all-purpose card or electronic payment to give a step discount preferential after the monthly expenditure is accumulated to a certain amount: after the total expenditure of each card is 100 yuan in each natural month, giving 8 discount benefits for each time of taking the rail transit fare; giving 5-fold discount after 150 yuan; the fare advantage is not given after the full 400 yuan.
And from 12 and 28 days in 2014, setting the valid period of the metro ticket. The time from the card swiping to the station leaving cannot exceed 4 hours, otherwise, the overtime fare must be paid according to the one-way lowest ticket price, and if the 10-fold fine is found in the case of card changing midway, the amount of the fine can reach 90 yuan at most.
In 2019, 20 months and 1 year, the on-line application of the electronic promissory note for the urban rail transit comprises a first-day note, a second-day note, a third-day note, a fifth-day note and a seventh-day note, and is suitable for all lines except airport lines. Each 20 yuan of daily ticket of the specific fare and each 90 yuan of weekly ticket can be swiped with two-dimensional codes for taking a bus according to the unlimited times of the tickets within the service life of the tickets by passengers.
The function of an electronic one-way ticket is released at the end of 6 months in 2020, and a passenger can enter and exit the station by scanning codes through a small program embedded in a payment bank. The fare of the rail transit in 2007 to date is shown in the table 5-1.
According to the traffic comprehensive treatment action plan in the city in 2021, the city can develop the research of 'peak fare and commuting preference' of the subway, the fare of the subway is increased in the morning and evening, the main purpose is to guide passengers with non-rigid demands such as travel and life trip from the early peak to the flat peak, and for rigid trip demands such as commuting passengers, the city can apply for enjoying 'commuting preference' without increasing the travel cost of residents.
TABLE 5-1 Ticket prices of Rail transit Ticket to date in 2007 in a certain City
Figure BDA0003777524270000251
Figure BDA0003777524270000261
5.2 passenger traffic condition analysis of 9 lines of the city subway
According to data published by the city traffic development research institute in 2019, a subway 9 number line has a limited flow station 3 seat; 7, 30-8; the amount of passenger flow in the up direction (Guoguang-national library) at the early peak time period is significantly greater than in the down direction (national library-Guoguang); the quantity of the early peak station to enter and exit the west station in the city reaches 1.56 ten thousand times, is positioned at the 16 th site of the whole road network and accounts for 14.57 percent of the quantity of the station to enter and exit the city station all day; the Guogongzhuang early peak transfer amount reaches 4.74 ten thousand persons, is positioned at the 3 rd position of the whole road network transfer station and accounts for 30.15 percent of the whole day; the passenger transport intensity is high on working days, and is only next to the No. 1 line, the No. 2 line and the No. 5 line; the minimum departure interval is shortened to be within 2 minutes (the whole network only has 6 lines), and specific technical indexes are shown in a table 5-2.
In summary, the 9 th line of the city subway at the early peak has the characteristic of large passenger flow, meanwhile, the number of stations is small, calculation and research are convenient, the number of the stations in each subway in the city subway has certain representativeness, the station numbers are shown in the table 5-2, the specific passenger flow of the uplink and the downlink of each station is shown in the table 5-3, and it can be obviously seen that the passenger flow of the 9 th line in the uplink direction (guogong village-national library) at the early peak is far greater than that in the downlink direction (national library-guogong village). Therefore, the invention performs example analysis by taking the passenger passing through the No. 9 line of the subway in the city as a target, and the research time period is 6-00.
TABLE 5-2 station numbering table for city subway No. 9 line
Figure BDA0003777524270000262
Figure BDA0003777524270000271
5.3 timesharing fare calculation
5.3.1 fare model base data and parameter values
The total passenger flow of the city subway 9 number line in each time period is 64.965 ten thousands of people, the passenger flow of different stations in different time periods is obviously different, fig. 4 is a passenger flow accumulation broken line graph of each station in a research time period, the horizontal axis is a selectable departure time ID, and the vertical axis is the total passenger flow and represents the passenger flow accumulation amount in each time period. It can be found that there is a significant increase in traffic starting from n =8 (7-10-7) with traffic concentrated in the sitz seven banker (933), the six-mile bridge (931), the six-mile bridge east (929), the municipality station (927), the military museum (925), this section defines 7 l ∈{12,13,14,15。
According to the technical parameters of the national standard B1 type train: six marshalling train determiners 1460, superman 1860 and seats 46; 19000mm of car body length, 2800mm of car body width (standard car), then a section of standard carriage area is 53.2 square meters. According to a train departure schedule published by a subway in the city, the train departure workshop interval of a subway No. 9 line on a working day 5.
According to the empirical estimation of the low-arrival and early-arrival unit time value coefficients by Small, theta should be l ＝1.2,θ e ＝0.8 [73] . From 12/28 days in 2014, except for airport lines, the initial fare of the urban rail transit is adjusted to be 3 yuan, the highest fare is 8 yuan (no consideration is given to the fine amount caused by overtime and the like), and the parameter values of the fare optimization model are given in tables 5-4. The data source of the example verification is AFC passenger flow data of 14 days and Mondays in 1 month and 14 months in 2019 of the city subway, wherein the total outgoing amount of an OD interval belonging to a subway number 9 line is about 161.98 ten thousands of people, and the OD outgoing amounts in 11 th and 18 th optional periods are shown in tables 5-6 and tables 5-7. Not shown for the rest of the time period limited to the space.
Table 5-2 list of technical indexes of number 9 line of subway in certain city in 2019
Figure BDA0003777524270000272
TABLE 5-3 nth time period departure quantity (f) n ) Value taking
Figure BDA0003777524270000281
Table 5-4 fare model parameter values
Figure BDA0003777524270000282
According to the clustering result of 2.3.3, the passengers are partially elastic trip passengers when i =1, and the proportion of the passengers under different departure time selections is used
Figure BDA0003777524270000283
Represents; rigid travel passengers when i =2, and rigid travel passengers when i =3For the elastic trip passenger, considering the practical application scenario, it is necessary to integrate the partially elastic trip passenger (i = 1) and the elastic trip passenger (i = 3) into the elastic trip passenger, which is used for the duty ratio
Figure BDA0003777524270000284
The specific sizes are shown in tables 5-5. The comparison graph of the time interval ratio of the class 2 passengers is shown in fig. 5, and it can be found that: in period 6-12 (6.
TABLE 5-5 time-interval ratio of two classes of passenger categories
Figure BDA0003777524270000285
Figure BDA0003777524270000286
Figure BDA0003777524270000291
According to the proportion of each passenger, the traveling quantity of the two types of passengers in different OD zones can be respectively calculated
Figure BDA0003777524270000292
Travel time
Figure BDA0003777524270000293
Amount of early arrival time
Figure BDA0003777524270000294
And late time to time
Figure BDA0003777524270000295
For reasons of space, only the OD yield values of 7.
It can be found that the trend of the above-mentioned indexes of the two passenger classes is consistent: the change situation of the travel time shows that the later the departure time is, the smaller the travel time is; the shorter the OD distance, the less travel time, indicating that distant passengers will typically choose to depart at an earlier time period and near passengers will typically choose to depart at a later time period. The early arrival time amount and the late arrival time amount both show the change trend that the later the departure time is, the larger the early arrival time amount or the late arrival time amount is; the variation trend of the parameters accords with general practice.
Table 5-6 two classes of passengers 11 th alternative time period (7
Figure BDA0003777524270000296
Value (a) elastic trip passenger
Figure BDA0003777524270000297
Figure BDA0003777524270000301
(b) Rigid trip passenger
Figure BDA0003777524270000302
Table 5-7 two classes of passengers 18 th alternative time period (8
Figure BDA0003777524270000303
Value (a) elastic trip passenger
Figure BDA0003777524270000304
Figure BDA0003777524270000311
(b) Rigid trip passenger
Figure BDA0003777524270000312
5.3.2 time value and departure time selection probability calculation
According to AFC travel record data of each passenger in a research section, the relative utility of each passenger is calculated by combining the departure time selection utility function obtained by calculation of the invention, the departure time selection probability of each passenger is calculated, and finally, the departure time selection probabilities P of different types of passengers can be obtained by averaging according to passenger types kni The results are shown in tables 5 to 8.
According to the calibration result of each influencing factor parameter and the formula (4-9), the time values of the two types of passengers can be easily calculated
Figure BDA0003777524270000321
As shown in tables 5-9.
TABLE 5-8 passenger departure time selection probabilities (P) kni ) Value taking
Figure BDA0003777524270000322
TABLE 5-9 time values of two classes of passengers at each time interval
Figure BDA0003777524270000323
Value taking
Figure BDA0003777524270000324
Figure BDA0003777524270000331
5.3.3 analysis of results
The invention uses the particle swarm algorithm to solve the upper layer model of the fare double-layer programming by python environment programming and in order to obtain the convergence result, sets the particle population as 100,maximum number of iterations of 100, learning factor c 1 ＝2，c 2 =2, inertial weight ω max ＝0.8，ω min =0.3, particle velocity v max ＝0.05，-v max = -0.05 solve; solving a fare double-layer planning lower-layer model by using a differential evolution algorithm, setting the particle population as 100 and the maximum iteration number as 120; and (3) the upper layer model and the lower layer model are mutually influenced, and iteration is carried out circularly, wherein the maximum iteration number is set to be 900. The invention only compares and analyzes the fare change rate and the passenger flow transfer result of the 11 th optional period (7-7.
(1) Fare result analysis
According to the model and the algorithm constructed by the invention, the discount rates of the fare of the rigid trip passenger and the elastic trip passenger in each time period can be obtained, and the time-sharing pricing result can be analyzed to find that:
in the time dimension, due to commuting preference, the fare of a rigid trip passenger is kept unchanged in a peak time period of 7-8; similarly, the flexible travel passengers have different degree of fare increase in the peak period 7-8.
In the spatial dimension, in the period 7; in the time period of 8-9, the fare change rate of the rigid passenger is five folds except that the sections of the Toyota scientific and technological garden (943) -Liu Li Qiao east (931) and the Toyota scientific and technological garden (943) -Keyi road (941) are six folds; the elastic passenger fare change rate is only eight-fold in part of the interval and seven-fold in the rest, as shown in tables 5-12. Overall, the fare variation trend is that the peak time interval rises, and non-peak time interval descends, and the fare discount intensity of rigidity trip passenger is higher than elasticity trip passenger.
Considering the application of a 'peak fare + commuting preference' strategy, rigid trip passengers such as commutes or commutes can issue commuting tickets or real-name-system one-card between two fixed stations, and passengers holding the cards enjoy fare preference in corresponding time periods; the passengers who go out flexibly, i.e. the passengers who do not handle the commuting ticket or the real-name all-purpose card, do not enjoy the commuting privilege.
Table 5-10 two classes of passengers 11 th optional period (7
Figure BDA0003777524270000341
Table 5-11 two classes of passengers 11 th selectable time period (7
(a) Elastic trip passenger
Figure BDA0003777524270000342
Figure BDA0003777524270000351
(b) Rigid trip passenger
Figure BDA0003777524270000352
Table 5-12 two classes of passengers 18 th alternative time period (8
(a) Elastic trip passenger
Figure BDA0003777524270000353
Figure BDA0003777524270000361
(b) Rigid trip passenger
Figure BDA0003777524270000362
(2) Passenger flow volume analysis
According to the model and the algorithm constructed by the invention, the distribution of the passenger flow in different types of OD intervals can be obtained as shown in tables 5-14. Defining the passenger flow acceleration rate before and after the implementation of the fare policy as the passenger flow transfer rate, and if the percentage is positive, indicating that the passenger flow is increased; if the percentage is negative, then the traffic is reduced.
From the time dimension, the passenger flow is reduced in the peak period, the passenger flow of the elastic passengers is reduced most rapidly in the 11 th optional period (7.
From the spatial dimension, the passenger in the 11 th optional period (7; the passenger flow transfer of rigid travel is overall and average, and the passenger flow transfer speed is the fastest and 9.75% in Fengtai Nanlu (939) -national library (921); the overall trend of passenger flow of two types in 18 th optional time period (8); the passenger flow transfer speed of rigid trip passengers is fastest in a Liu-Li-bridge (933) -Fengtai science and technology park (943), and the passenger flow transfer rate reaches 18.94 percent, which is detailed in tables 5-13 and 5-14.
The passenger flow before and after the time-sharing pricing of the passengers in the flexible trip and the rigid trip is obviously transferred, the passenger flow distribution is balanced, the defects of supersaturation of the passenger flow in the peak time period, less passenger flow in the low-peak time period and waste of transport energy are overcome to a certain extent by adjusting the fare, the passenger flow in the peak time period is regulated and controlled, and the subway in the market is shown to implement a differentiated pricing strategy according to the departure time. Can effectively play the role of guiding the passenger flow by the fare.
Table 5-13 passenger classes 11 optional period (7
(a) Elastic trip passenger
Figure BDA0003777524270000371
Figure BDA0003777524270000381
(b) Rigid trip passenger
Figure BDA0003777524270000382
Table 5-14 passenger class 18 optional period (8
(a) Elastic trip passenger
Figure BDA0003777524270000383
Figure BDA0003777524270000391
Table 5-15 passenger class 18 th optional period (8
(a) Elastic trip passenger
Figure BDA0003777524270000392
(b) Rigid trip passenger
Figure BDA0003777524270000393
Figure BDA0003777524270000401
5.4 time-sharing pricing policy implementation
The invention takes the passenger passing through the city subway 9 number line as a research object, based on the passenger flow distribution condition of rigid trip and flexible trip passengers in each time period, respectively making the 11 th selectable time period (7:
(1) The rigid trip passenger belongs to a group with fixed trip time and trip distance and is not easy to be regulated and controlled by fare compared with the elastic passenger. Based on the "peak fare + commuter offer" study plan, the fare remains unchanged during the period 7; in the 18 th optional period (8).
(2) The flexible trip passengers belong to trip groups which are easy to be regulated and controlled by fare, the pricing strategy of the flexible trip passengers is influenced by rigid trip passengers, and the flexible trip passengers are adjusted upwards to different degrees within a time period of 7-50-8; in the 18 th optional period (8.

Claims (2)

1. A rail transit early-peak time-sharing pricing method based on passenger departure time selection is characterized by comprising the following steps:
(1) Elastic trip passenger identification is carried out based on AFC data, data cleaning is carried out firstly, and then according to a first departure time fluctuation coefficient, a trip distance fluctuation coefficient and a Zhou Chuhang day fluctuation coefficient, the passengers are divided into elastic trip passengers and rigid trip passengers through a clustering algorithm;
(2) Establishing passenger departure time selection model based on MNL
According to variables influencing the selection of the departure time of a subway user, a utility function expression is constructed as follows:
Figure FDA0003777524260000011
each symbol is defined as follows:
V kn : passenger k selects a utility value for departure for the nth time period, where n =1,2,3, ·,18; beta is a TFS : a parameter to be calibrated corresponding to the standard deviation of the first departure time; beta is a beta TT : a parameter to be calibrated corresponding to the travel time; beta is a beta SDE : a parameter to be calibrated corresponding to the early arrival time amount; beta is a SDL : the parameter to be calibrated corresponding to late arrival time; beta is a beta FD : a parameter to be calibrated corresponding to the daily trip times; beta is a FW : parameters to be calibrated corresponding to the days of the week trip; beta is a beta FWS : the parameters to be calibrated correspond to the days of the week trip standard deviation; beta is a ω : parameters to be calibrated corresponding to the types of the passengers going out; beta is a beta P : a parameter to be calibrated corresponding to the passenger ticket expense; TFS: the standard deviation of the first departure time of the one-month departure record; TT: a travel time average for a period of travel; and (3) SDE: the amount of time may be reached in advance; and (3) SDL: the amount of time of arrival may be delayed; FD: daily average trip times recorded for a month trip; FW: zhou Chuhang days recorded one month out; FWS: the standard deviation of the days of the week trip recorded for one month trip; ω: the type of passenger; p: a fare for the passenger ticket; v. of kn : a disturbance term;
the probability that passenger k selects alternative n is expressed as:
Figure FDA0003777524260000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003777524260000013
average trip utility for all choices;
(3) Establishing a double-layer planning time-sharing pricing model based on departure time selection
(3.1) constructing an upper layer model objective function and constraint conditions
Figure FDA0003777524260000021
In the formula, C l Representing an operation cost function related to passenger flow; f. of n Representing the train departure number in the nth selectable departure time interval o-d; c l ·f n Is the total operating cost of the track transportation line 1 during the n time period from within the interval o-d,
Figure FDA0003777524260000022
in order to be a function of the demand,
Figure FDA0003777524260000023
as a function of the price and
Figure FDA0003777524260000024
is an operation cost function;
(3.1.1) calculating the demand function
Figure FDA0003777524260000025
Figure FDA0003777524260000026
In the formula, P kn Corresponding to the probability that passenger k selects alternative n,
Figure FDA0003777524260000027
for the average trip utility of all the selection items, theta is a parameter reflecting the familiarity degree of passengers with the subway network, theta is more than 0, and a disturbance item v is formulated n The expected demand of the probability space of (a);
(3.1.2) calculating a price function
Figure FDA0003777524260000028
Figure FDA0003777524260000029
In the formula, PR od Representing the current ticket price; variable of fare
Figure FDA00037775242600000210
Is the rate of change of the fare;
(3.1.3) Rail transit operation cost function
Figure FDA00037775242600000211
Figure FDA00037775242600000212
In the formula (I), the compound is shown in the specification,
Figure FDA00037775242600000213
representing the number of different types of passengers within the interval o-d over the nth selectable period; k is a radical of l The per-person operation cost of the rail transit line l;
in summary, the upper model objective function is represented as:
Figure FDA00037775242600000214
constraint 1: the commuting preferential ticket price constraint of the passengers on rigid trips:
Figure FDA00037775242600000215
constraint 2: and (4) limiting the upper limit and the lower limit of the ticket price:
Figure FDA0003777524260000031
constraint 3: non-negative constraints:
Figure FDA0003777524260000032
(3.2) constructing a lower layer model objective function and constraint conditions
The lower layer objective function is expressed as:
Figure FDA0003777524260000033
wherein the travel time cost F TT Early arrival cost F AE Late to cost F AL The cost of congestion
Figure FDA0003777524260000034
And a ticket price
Figure FDA0003777524260000035
(3.2.1) travel time cost
The time value formula of the traveler selecting the trip in the nth time interval is expressed as follows:
Figure FDA0003777524260000036
calculating the time value of each type of passenger in different time periods, wherein the calculation formula is as follows:
Figure FDA0003777524260000037
in the formula (I), the compound is shown in the specification,
Figure FDA0003777524260000038
the proportion of the ith passenger in the nth time interval is represented, and I passengers are shared; VOTT kn Representing the time value of the passenger in the nth time period; VOTT in Representing the time value of the ith class of passengers during the nth time period;
Figure FDA0003777524260000039
representing travel times within the nth time interval o-d for the class i passenger.
Figure FDA00037775242600000310
Travel time expenses generated when different categories of travelers select the nth time interval to travel are represented as follows:
Figure FDA00037775242600000311
(3.2.2) early and late cost
If the traveler arrives at the destination in advance, an early arrival cost F will be incurred AE Wherein, in the step (A),
Figure FDA00037775242600000312
represents the early cost of the ith class of passengers within the nth interval o-d:
Figure FDA00037775242600000313
if the traveler delays arriving at the destination, a delay cost F is incurred AL Wherein, in the process,
Figure FDA00037775242600000314
late arrival cost in class i passenger nth interval o-d:
Figure FDA0003777524260000041
in the formula, theta e And theta l Respectively representing the time penalty factors of the early arrival and the late arrival of the traveler;
(3.2.3) cost of congestion in vehicle
Congestion charges are incurred when the passenger flow is greater than the number Z of passengers that can be accommodated when the congestion state is about to be reached, and the congestion sensitivity is expressed as:
Figure FDA0003777524260000042
in the formula, mu and gamma are congestion sensitive parameters to be calibrated; ω represents the full load rate within each selectable departure period; z represents the number of passengers which can be accommodated when the train is about to reach the congestion state;
Figure FDA0003777524260000043
is the amount of travel of the different classes of passengers within the interval o-d over the nth selectable time period; f. of n Representing the line capability in each time interval OD interval;
Figure FDA0003777524260000044
representing the rated passenger carrying quantity of the train; z is a linear or branched member l Denotes the number of seats of the train, p denotes the standing passenger density, S l The area of the train on a line l is the area of the seat, and the line l is a subway line;
Figure FDA0003777524260000045
representing the passenger riding time, the calculation is as follows:
Figure FDA0003777524260000046
in the formula, TR n Representing the train running time of the section;
Figure FDA0003777524260000047
representing the stop time of the train at the d +1 station;
the congestion cost is expressed as:
Figure FDA0003777524260000048
in the formula, λ represents a penalty coefficient of the congestion degree;
in summary, the objective function of the lower layer plan is represented as:
Figure FDA0003777524260000049
constraint condition 1: the total passenger flow quantity is unchanged before and after time-lapse pricing in the research period:
Figure FDA00037775242600000410
constraint 2: the number of people in any interval is not more than the rated passenger capacity of the train at any time:
Figure FDA0003777524260000051
constraint 3: non-negative constraints:
Figure FDA0003777524260000052
2. the method for the time-sharing pricing of the early peak of the rail transit based on the departure time of the passenger as claimed in claim 1,
the specific solving steps of the double-layer planning time-sharing pricing model are as follows:
step: PSO algorithm initialization:
(1) Initializing various parameters c in PSO algorithm 1 、c 2 ，r 1 、r 2 ，ω 1 、ω 2 Etc.;
(2) The model variable of the upper layer (discount rate delta of fare price in each time period) n ) The particles constituting the particle group are initialized at random with a group size n and a position X of each particle in the group α And velocity V α Setting the maximum number of iterations G max Let i =1,G max ＝100；
(3) The current position of each particle is denoted as p 0 The position of the optimal particle in the population is denoted as g 0 ；
Step2: solving the lower layer model
Position X of upper layer model variable α Substituting into the lower layer model, and using differential evolution method to optimize at present
Figure FDA0003777524260000053
Solving the optimal solution of the lower model under the condition
Figure FDA0003777524260000054
Namely the passenger flow in each time interval;
step3: judging whether a convergence condition is reached
Judging whether the maximum iteration number G is reached max If yes, output
Figure FDA0003777524260000055
And
Figure FDA0003777524260000056
if not, turning to Step4;
step4: calculating fitness function values
Will be provided with
Figure FDA0003777524260000057
Substituting into the upper model to calculate fitness function value
Figure FDA0003777524260000058
Namely the profit B (delta, q) of the rail transit operator;
step5: updating individual and group historical optimal locations
(1) If it is not
Figure FDA0003777524260000059
The corresponding fitness function value is superior to the current individual optimal position p 0 The fitness function value of (2), then p 0 Is updated to
Figure FDA00037775242600000510
Is marked as
Figure FDA00037775242600000511
The individual optimal solution of the corresponding lower layer is updated to
Figure FDA00037775242600000512
Is marked as
Figure FDA00037775242600000513
(2) If it is not
Figure FDA00037775242600000514
The corresponding fitness function value is superior to the optimal position g of the current group 0 The fitness function value of (1) is g 0 Is updated to
Figure FDA00037775242600000515
Is marked as
Figure FDA00037775242600000516
The corresponding lower-layer group optimal solution is updated into
Figure FDA00037775242600000517
Is marked as
Figure FDA00037775242600000518
(3) Let i = i +1, go to Step2.
CN202210920961.9A 2022-08-02 2022-08-02 Rail transit early-peak time-sharing pricing method based on passenger departure time selection Pending CN115392949A (en)

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