CN113408926B - Urban rail transit passenger flow distribution method under short interruption condition - Google Patents
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Abstract
The invention provides a passenger flow distribution method for urban rail transit under the condition of short interruption. Under the condition of short interruption, the method analyzes the path decision behavior of the passengers by applying the accumulated prospect theory, sets endogenous reference points based on time reliability, calculates the accumulated prospect value of the travel path of the passengers, establishes a random balanced distribution model, gives out an equivalent variation inequality model thereof, and solves by utilizing a successive average algorithm. Aiming at the short interruption condition, the invention applies the accumulated prospect theory to analyze the path decision behaviors of the passengers under the condition of considering the travel time reliability of the passengers, establishes a random balanced distribution model, is more in line with the actual condition of the passengers, and provides a theoretical basis for passenger flow distribution under the short interruption condition.
Description
Technical Field
The invention belongs to the field of rail transit, and particularly relates to a passenger flow distribution method for urban rail transit under the condition of short interruption.
Background
The network operation facilitates the traveling of passengers, attracts more passengers, and further generates large passenger flow phenomena under certain conditions, such as commute large passenger flow of the peaks in the morning and evening, traveling large passenger flow of holidays and the like. The urban rail transit system under the networking operation condition has more complex road network structure, and the transfer mode of passengers in the rail transit system and the driving organization mode of trains are more and more diversified, so that the rail transit operation system is more complex, and the daily emergency frequency is increased. When the passenger flow of the rail transit is large, once a sudden operation accident occurs, regional operation problems can be caused, and a certain influence can be caused on adjacent areas, so that the operation efficiency and the operation safety of the rail transit system and passengers are influenced.
In a seamless transfer rail transit system, passenger transfer is more convenient, but the system cannot record the specific path selection condition of passengers, so that the difficulty is increased for operation management of rail transit. The urban rail transit ticket sorting, congestion prediction, key road section identification and other works, and when sudden operation accidents occur, the prediction, the control and the like of the passenger flow of each road section of the rail transit are all performed based on the distribution of the passenger flow on different road sections of a road network, so that a reasonable passenger flow distribution method is very important for the operation management of the rail transit. More and more students perfect the passenger flow distribution model, and the distribution result is more reasonable as much as possible due to factors such as model checking difficulty, limited related data quantity and the like, so that data support is provided for operators to grasp the operation condition of the rail transit system.
Under the background, the urban rail transit system with networked operation has more complex road network structure, more various path selections of passengers, more convenient travel and more great challenges for the safe operation of rail transit due to the occurrence of sudden operation events. The invention takes the short interruption event of the rail transit as a background, considers the limited rationality of passengers in the sudden operation state, is closer to the actual path selection state of the passengers, distributes the passenger flow in the short interruption operation period of the rail transit, and provides a theoretical basis for the operation organization work of the rail transit system.
The prior art research is mainly embodied in aspects of passenger flow distribution models, effective path search algorithms, passenger flow distribution algorithms, track traffic path impedance establishment and the like, but has a few defects in the research, especially in aspects of research on urban track traffic emergency occurrence, the prior art research utilizes accumulated prospect theory to establish models to consider incomplete rationality when passengers make decisions, and is mainly applied to urban road traffic or applied to combined travel of travelers, and when the emergency occurs to the track traffic, the travel decisions of the passengers in a track traffic system are less. In view of the above, the invention takes the condition that the urban rail transit system is interrupted briefly as a research background, considers the incompleteness of the path decision made by passengers in the state when the road network structure is changed after the interruption is analyzed, analyzes the path decision behavior of the rail transit passengers in the condition, and distributes the road network passenger flow in the interruption time period, so that the distribution result is more reasonable.
Disclosure of Invention
In order to solve the technical problems, the invention takes the condition that the urban rail transit network is interrupted in a short time in a peak period as a research background, researches the path selection behavior of passengers under the condition of uncertainty, mainly considers the incomplete rationality of the passenger path decision when an emergency occurs, analyzes the passenger behavior by utilizing the accumulated prospect theory, establishes a random balanced distribution model, and distributes the road network passenger flow under the condition of short time interruption. The invention adopts the following technical scheme:
A passenger flow distribution method for urban rail transit under the condition of short interruption comprises the following steps:
step 1: passenger travel impedance calculation
Abstracting a rail transit network into a directed graph G= (I, A), wherein I= {1,2,3 …, I } is a set of nodes and represents a station; a= { a 1 ,a 2 ,a 3 ,…,a n -a set of directed arcs, representing road segments; the set of all OD point pairs on the U-path network, one OD point pair on the U-path network, and U E U, R u ＝{r 1 ,r 2 ,…,r k -all active path sets between OD pairs u;
(1) Calculating the riding time
The time on the train during the travel of the passengers comprises the following steps: train running time and stop time
wherein ,tij -the length of time of operation of the road segment (i, j);
t i -the stop duration of train station i, typically a fixed value;
(2) Calculating congestion coefficients
The expression of the congestion function with overlong perception time caused by the congestion of the carriage is as follows:
wherein ,xij -section (i, j) section passenger flow volume;
a—a general congestion overhead coefficient;
b—an overcrowded overhead coefficient;
z-number of seats in the train;
c, rated passenger capacity of the train;
the road section driving time considering the congestion degree is as follows:
when passengers select the track traffic to go out, the riding time length of the kth path considering the crowdedness between the OD pair u is as follows:
(3) Calculating transfer duration
The transfer time when a passenger performs transfer at a transfer station is expressed as:
wherein ,
-time station j is transferred from line m to n;
the transfer time of the passenger is amplified:
h is the train departure interval;
lambda-transfer penalty coefficient;
the path transfer time is the sum of multiple transfer times and is subjected to transfer penalty
wherein ,
-the transfer duration of the kth path between OD versus u;
(4) Calculating the perceived time of a passenger
The perceived time of the passenger is calculated as follows
wherein ,
-the number of transfers of the kth path between OD versus u;
omega-transfer number penalty coefficient;
(5) Calculating the time length of entering and exiting the station
The passenger arrival time includes the travel time and waiting time of the arrival
wherein ,ra -travel time into station a;
w a -waiting time for entering station a;
r b -travel time into station b;
To sum up, the travel time of the kth path between OD versus u is:
step 2: passenger flow distribution based on accumulated prospect theory
(1) Passenger flow distribution method
Taking the impedance of the path as a variable, the condition of the model can be expressed as:
in the formula：
-selecting a probability of OD for the kth path between u;
establishing an unconstrained model according to the conditions
wherein ,
in the formula：
-a desired perceived impedance of the traveler;
c u (x) -the actual impedance between OD versus u;
(2) Path selection strategy based on accumulated prospect theory
1) Calculating passenger travel time reliability
The travel time reliability of the kth path between OD versus u is defined as:
u∈U
wherein U-the set of all OD pairs in the road network;
2) Reference point selection based on temporal reliability
The OD has the following budget time expression for the kth path between u:
wherein ,
-OD versus reference point of the kth path between u;
ρ—a parameter of passenger considering travel time reliability, the larger its value the greater the path reliability, the higher the likelihood that the passenger will avoid the uncertainty risk;
The minimum budget time of each path between OD pairs is adopted as a reference point:
wherein ,θu -OD versus reference point of u;
3) Subjective value determination
The cost function of each alternative for passenger routing is as follows:
wherein α—the degree of risk avoidance at the time of return;
beta-risk preference at loss;
a-gain pursuit coefficient;
b-loss aversion coefficient;
wherein 0 < α, β < 1, a larger value indicating that the passenger is more sensitive to risk; a is more than 0 and less than b;
4) Cumulative foreground value
The decision function expression is as follows:
w(p)＝exp[-(-ln p) γ ],0＜γ＜1
when the passenger performs path selection, the continuous function expression of the accumulated foreground value is as follows:
wherein ,
-as a variant->
Is a distribution function of (a);
step 3, random equalization distribution model based on accumulated foreground value
Regarding travel time as a random variable, regarding the perceived deviation of passengers, the path utility of the passengers is divided into two parts, one part accumulates the foreground value
The other part is random error item->
in the formula：
-path accumulation foreground actual observations;
the probability of any OD to the kth path between u being selected is:
wherein θ is a parameter reflecting the familiarity of the passenger with the road network; according to the random user theory, when the network reaches a random user equilibrium state, the following conditions should be satisfied:
q u ≥0
The satisfaction function of the passenger path selection is defined as:
in the formula：vu Is that
Vector form of (2) is about->
Is a continuous function of (1), and has->
/>
Finding a set of feasible path traffic f * e.OMEGA.where.OMEGA.is a set of feasible path traffic sets f such that
The following inequality is satisfied:
step 4, model solving
(1) Solution algorithm
Taking the accumulated foreground value of the traveler as a basis of path selection, solving the model by adopting an MSA algorithm, wherein the steps are as follows:
step 0 initializing, initializing parameters, searching a feasible path set between any two points in a road network by using a graph traversal algorithm based on a network topology structure to obtain an effective path set R of any OD pair u u ；
Step 1, calculating initial path impedance, when the traffic volume of the road network is 0, calculating the initial path impedance of each path in the road network, calculating the accumulated prospect value of the paths, and carrying out once Logit-form random network loading on the fixed passenger flow demand between OD pairs in the network to obtain the initial path flow
And initial road traffic +.>
n＝1；
Step 2, updating the path foreground value, updating the path impedance according to the section flow, and updating the path foreground value again
Step 3 determines the update direction based on the path foreground value
For traffic demand q u Loading on road network to obtain auxiliary path flow +. >
Further get the update direction of the path flow>
wherein />
Step 4, updating the path and road section flow:
obtaining the road section flow from the path correlation matrix>
Step 5 convergence test: when (when)
The algorithm ends, otherwise n=n+1, returning to Step 1.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of classification of network traffic at a certain time period.
Detailed description of the preferred embodiments
1. Analysis of travel influence of short interruption on rail transit passengers
The urban rail transit system consists of a plurality of subsystems, including equipment systems such as vehicles, tracks, signals, stations and the like, a power supply system and the like, and when any part of the system breaks down to cause sudden operation events of rail transit, the operation system is affected to different degrees, such as late trains, line breaks and the like, so that the operation efficiency, the passenger trip efficiency and the safety of the rail transit are affected.
Through statistical analysis of sudden operation events in recent years, the definition of short break events is mainly divided into the following categories:
the first type is mainly events with serious life and property loss caused by the factor of unreliability, such as natural disasters, terrorist events and the like, the occurrence probability is small, and when such sudden events occur, the space for passengers to autonomously make travel decisions is small. The second type of sudden event caused by major activities has predictability, and the operation management department can take corresponding measures in advance. Finally, the conditions of train running delay, interruption and the like caused by equipment faults and other unexpected operation events are counted, and the proportion of the unexpected events caused by vehicle equipment faults and unsafe behaviors of passengers is larger.
1. Path selection impact factor analysis
(1) Travel time factor
In rail transit systems, travel time is a primary factor considered by passengers, and a small percentage of passengers watch the number of transfers in the route and the comfort level of the passengers. The travel time is the time of passengers in the rail transit system and is the whole process time from the start station card swiping and entering to the card swiping and exiting.
(2) Service factors
1) Degree of congestion
When the passenger takes more than 20 minutes, most passengers consider the degree of congestion of the passenger. In a rail transit system operated in a net, the travel time of most passengers exceeds 20 minutes, and thus, the degree of congestion affects the travel of most passengers, which reflects the comfort of riding. When passengers ride in a crowded environment, the time for getting on and off passengers can be increased, and the travel safety of the passengers is influenced.
2) Convenience of transfer
Transfer refers to the act of riding a vehicle from one route to another at one station in order to reach a destination during the travel of rail transit passengers. In the passenger route selection process, the time spent for transfer and the number of transfers in the route are mainly considered. The transfer time is related to factors such as platform structures, train departure intervals and the like, when passengers transfer, the psychological perception time of the passengers can be correspondingly increased, the paths between the same OD pairs can be increased, and the probability of path selection can be reduced due to the increase of transfer times.
(3) Other factors
1) Passenger self factor
The difference of the factors of the passengers, such as gender, age, occupation and the like, causes the difference of the focus of the passengers on the traveling process, the older passengers pay more attention to the traveling comfort, the commuter passengers pay more attention to the traveling time, and the commuter passengers are an important component part of the passenger flow in the peak period, so that the riding comfort requirement is relatively low. Sex-wise, women may be relatively more comfortable riding than men.
2) Familiarity of passengers with road network
The familiarity of the passengers with the road network is related to the daily travel of the passengers, the passengers familiar with the road network can have more comprehensive knowledge of the travel, and the riding routes can be selected according to the demands of the passengers. While passengers unfamiliar with the road network need to learn about the road network by other means, a ride route with the shortest theoretical travel time is usually selected.
3) Travel expense
Travel fees are expressed as fares in rail transit. With government support, the travel expense is relatively low, and the influence on the selection of passengers is small, so that the influence of ticket prices on the travel of the passengers is not considered.
4) Personal preferences of passengers
The selection preference of the passenger for the route and the station is difficult to quantitatively analyze, and has a plurality of influencing factors, such as station layout, service facilities, service personnel and the like, which are not regularly circulated, and the influence of the preference of the passenger is usually ignored when the passenger performs the path selection.
2. Path selection analysis in short interruption situations
In an uncertain environment, the behavior of a person making a decision may be prone to risk or may be prone to security, unlike in the case of a deterministic environment. There are many factors that affect the decision making of people in an uncertain environment, but decision theorists consider that the factors are mainly determined by two factors: firstly, the value of different behavior results; and secondly, the probability of each outcome. Thus, in an uncertainty environment, we focus on two issues: firstly, the value judgment of different behavior results and secondly, the evaluation of the possibility of the different behavior results. These two problems are related to the cognitive and psychological factors of people in a decision making environment.
When the emergency occurs in the rail transit system, the decision environment of the passengers changes, and compared with the path decision of the passengers under the normal operation condition, the decision environment has stronger uncertainty. Meanwhile, under the condition that an emergency occurs, a passenger may generate certain psychological pressure, which is different from a complete rationality decision-making behavior in a normal road network environment, and a general theory assumes that the passenger is in a complete rationality state when carrying out path selection, so that the invention considers that the passenger makes a decision under the condition of limited rationality in the path selection behavior of the emergency passenger.
For analysis of decision-making behaviors of passengers in emergencies, the selection of the passengers is adjusted based on the original selection, the passengers possibly tend to leave the related area of the emergencies, the influence caused by the emergencies is reduced as much as possible, and the travel process is more hoped to be completed quickly and reliably.
3. Rail transit access network and determination of an active set of paths
The urban rail transit road network mainly comprises two parts of stations and lines, and the construction of the stations needs to comprehensively consider factors in all aspects, such as: geographic position, passenger demand, etc., the station is mainly the facility for passengers to take bus and wait, and collect and distribute passengers; the lines are facilities connected with each station and form a framework of a traffic network; the stations and lines form an urban traffic network.
(1) Definition of effective path
In urban rail transit systems, there are typically multiple paths between OD pairs for passengers to choose, but not every one of these viable paths will be chosen by a passenger. The passenger always selects the route with the maximum travel effect when going out, and the passenger does not select the route with repeated road sections, repeated stations, excessive transfer times and long time consumption in the actual travel process. Therefore, for the path searched between OD pairs, it is necessary to further judge whether it is within the range of selection of the passenger, and the path that may be selected by the passenger is called an effective path.
(2) Passenger travel impedance calculation
When a rail transit passenger selects a path, the rail transit passenger is comprehensively influenced by a plurality of factors, and the abstract expression of the factors is the path impedance of the passenger. Path impedance is a criterion for passenger path selection and plays an important role in passenger flow distribution. By analyzing the influence factors of the passenger's path selection and the passenger's path selection behavior under the condition of short interruption of the peak period, the passenger traveling in the period pays more attention to the travel time, and meanwhile, due to the short interruption of the local track traffic, the passenger is more prone to rapidly leave the accident influence area, the passenger flow distribution state changes, and the passenger traveling is influenced. In summary, when the path trip impedance of the passenger is calculated, the path impedance function of the passenger is established mainly by considering the trip time, the crowding degree and the transfer factor of the passenger.
The invention abstracts a track traffic network into a directed graph G= (I, A), wherein I= {1,2,3 …, I } is a set of nodes, representing a station, A= { a 1 ,a 2 ,a 3 ,…,a n The directed arcs are set to represent road sections, set of all OD point pairs on the U-path network, one OD point pair on the U-path network, and U is U, R u ＝{r 1 ,r 2 ,…,r k The OD represents the set of all active paths between the us and explores the kth path between the us.
According to the travel process of passengers, dividing the time into three parts: ride time, transfer duration, in-out duration.
1) Duration of riding
The time on the train during the travel of the passengers comprises the following steps: train running time and stop time.
wherein ,tij -the length of time of operation of the road segment (i, j);
t i the stop duration of the train station i is usually a fixed value.
2) Congestion factor
The perceived riding time of the passengers is related to the crowding degree of the trains, the crowded riding environment not only reduces the comfort level, increases the boarding and alighting time of the passengers and perceived traveling time, but also increases the traveling risk of the passengers. When short interruption occurs in peak period, road network passenger flowThe distribution state changes, and the impedance varies when the passenger performs the route selection. Reference Wu Xiangyun et al [14] The proposed congestion function with excessively long perceived time caused by the congestion of the carriage has the following expression:
wherein ,xij -section (i, j) section passenger flow volume;
a—a general congestion overhead coefficient;
b—an overcrowded overhead coefficient;
z-number of seats in the train;
c, rated passenger capacity of the train.
Therefore, the link travel time considering the degree of congestion is:
when passengers select the track traffic to go out, the riding time length of the kth path considering the crowdedness between the OD pair u is as follows:
3) Transfer duration
The transfer time includes the travel time from one line to another, and the waiting time after transfer. Due to the different structures of the stations, the transfer distances are different, and the running time is different. Therefore, the transfer travel time needs to be obtained through actual investigation. In the peak period, the passenger flow is large, passengers arrive in the train arrival interval and approximately follow uniform distribution, and the waiting time is 1/2 of the departure interval.
Thus, the transfer time when a passenger performs a transfer at a transfer station can be expressed as:
wherein ,
-time station j is transferred from line m to n;
Through analyzing the traveling behaviors and the psychology of the passengers, the transfer can increase the perceived traveling time of the passengers, so that the transfer time of the passengers is amplified, namely:
h is the train departure interval;
lambda-transfer penalty coefficient.
Multiple transfers may be required in the passenger travel path, so the path transfer time is the sum of the multiple transfer times and the transfer penalty is performed.
wherein ,
-transfer duration of the kth path between OD versus u.
4) Number of transfer times
Along with the network operation of rail transit, the transfer times of passengers in the traveling process can be more than one time, and the increase of the transfer times can also increase the perception time of the passengers.
wherein ,
-the number of transfers of the kth path between OD versus u;
omega-transfer number penalty coefficient;
5) Duration of in-out
The passenger arrival time comprises the arrival travel time and the waiting time, and the waiting time is half of the departure interval, and is similar to transfer, the layout and the structure of each station are different, the travel time is different, and the waiting time is half of the departure interval.
wherein ,ra -travel time into station a;
w a -waiting time for entering station a;
r b -travel into station bLine time;
To sum up, the travel time of the kth path between OD versus u is:
in the invention, the running time of the train in the section is mainly obtained according to the ratio of the distance between stations to the average running speed of the train; the stop time of the train is obtained through investigation; the transfer time is obtained by investigating each transfer site.
Passenger flow distribution method based on accumulated prospect theory
Conventional passenger flow distribution methods are generally based on ideal conditions, i.e. assuming that passengers can grasp the information of the entire road network, which is not the case in practice. Under the condition that an emergency occurs, the path decision state of the passenger is different from that of the passenger under the normal condition, the incomplete rationality of the passenger in the process of making the path decision is considered, the path decision behavior of the passenger is analyzed by applying the accumulated prospect theory, and a random user balance model is established.
1. Passenger flow distribution method
Passenger flow distribution is the process of distributing the travel demands of passengers among the OD pairs in the urban rail transit system to the road network. And converting the travel time of the passengers into generalized travel expense, searching an effective path according to the network structure of the rail transit system, and reasonably distributing the demand quantity among the OD pairs in the network according to a distribution model. The chapter mainly introduces a random user balanced distribution method.
The user balance model considers that the traveler can grasp the information of the whole road network, and can know the condition of the road network in real time to obtain the impedance of the path in the road network, which is difficult to realize in practical situations. The random user balance model is based on cognition of travelers on path impedance, the optimal path is selected for traveling, the impedance of the path is taken as a variable, and the condition of the model can be expressed as follows:
in the formula：
-selecting the probability of OD versus the kth path between u.
The above conditions may be equivalent to the following unconstrained model.
wherein ,
in the formula：
-a desired perceived impedance of the traveler;
c u (x) -the actual impedance between OD versus u;
Because passengers cannot fully master road network information, the invention regards the travel impedance of rail transit passengers in the network as a random variable, and therefore, the invention selects a random user balancing method to distribute passenger flows.
2. Rail transit passenger travel time feature analysis
(1) Passenger travel time fluctuation feature
According to the invention, the travel time of the passengers in the rail transit is statistically analyzed through the AFC card swiping data, and the fact that the travel start and stop points are the same and the travel time periods are similar can be found, so that the travel time of the rail transit of the passengers is different, the travel time of different passengers at the same station fluctuates within a certain range, and the fluctuation of the travel time of the passengers is related to the factors of the passengers and the road network states.
Taking Beijing subway as an example, analyzing the travel time of the passengers in the rail transit and the fluctuation condition of the travel time of the passengers according to the AFC card swiping data of the passengers. The AFC card swiping data records related information of passengers in the traveling process, mainly comprises the entering and exiting stations and time, and cannot record the path selection process of the passengers.
According to the invention, when a track traffic network of a working day of 2 months 2019 is normally operated, passenger AFC card swiping data between 17:00-19:00 of late peak time is selected, and the travel time of the passenger is statistically analyzed. The invention analyzes the rail transit travel time of the passengers at the above origin and destination by screening card swiping data of the late peak 17:00-19:00 and counting the origin and destination of the passengers, and screening out that the origin and destination with higher travel frequency at the peak time is a west two flag-standing water bridge, a west two flag-Tiantong yuan, a morning sun-grass house and a sea lake Huang Zhuang-standing water bridge, as shown in table 1:
table 1 OD travel time statistics
As can be seen from table 1, there is a difference in travel time for different passengers between the same OD pair, and fluctuation occurs within a certain range. The two-part bridge and the two-part bridge are two OD point pairs on the same line, so that the line to be transferred is not selected when passengers go out, the O and the D of the two-part bridge and the sea lake Huang Zhuang-bridge are positioned on different lines, and the passengers need to be transferred at least once when passengers go out. As can be seen from the table, in the traveling process of the passengers, the standard deviation of the traveling time of the OD point pair needing to be transferred is larger than that of the path without transfer, which indicates that the transfer behavior in the traveling process of the passengers increases the fluctuation of the traveling time. Thus, the data indicate that the number of transfers increases the volatility of the passenger travel time.
And according to fluctuation characteristics of travel time among different OD point pairs of passengers, carrying out assumption on travel time distribution, and carrying out fitting inspection. Therefore, the invention selects normal distribution to fit the travel time of the rail transit of the passenger, and the fitting result is shown in table 2.
TABLE 2 normal fitting Single sample K-S test
a. The test distribution is a normal distribution.
b. And calculating according to the data.
The Kolmogorov-Smirnov test was performed on the assumption that the rail transit travel time of the passenger meets the normal distribution using the SPSS, and the results are shown in table 2. From the test results of the table, the significance of both sides is greater than 0.05 when the K-S test is performed, and the results show that the fitting of the fluctuation characteristics of the travel time of the passenger rail transit by using the normal distribution is acceptable.
(2) Travel time distribution rule of rail transit
According to analysis of the fluctuation characteristics of the travel time of the passenger rail transit, the travel time of the passenger is assumed to be compliant with normal distribution, the SPSS is used for checking the assumption, and the checking result shows that the normal distribution can fit the fluctuation characteristics of the travel time of the passenger rail transit.
Under the condition of rail transit networking operation, a plurality of feasible paths are arranged between each OD pair, and when passengers select the same path between the OD pairs to go out, the travel time of the passengers is also different and fluctuates within a certain range. The fluctuation of the travel time of passengers on the same path between OD pairs is influenced by various factors, and the difference is represented by different passenger travel speeds when the passengers travel in the inbound passage, the transfer passage and the outbound passage, and uncertainty of the passenger inbound waiting time and the transfer waiting time, and is also influenced by some unpredictable factors, such as an increase in the riding time caused by congestion, train faults and the like.
For the same path between the OD point pairs, since the rail transit train is driven according to the train operation diagram plan, the riding time is relatively fixed, and therefore, the riding time mean value of the passengers is self, and the variance is 0, namely:
therefore, the mean and variance for the ride time for the kth path between OD versus u is:
for the transfer time of the passengers at the transfer station, the transfer time consists of transfer travel time of the passengers at the transfer station and waiting time after transfer, the transfer travel time is determined by transfer distance and walking speed of the passengers, and the waiting time after transfer is related to departure interval H of a line where the passengers are located. In the peak period, the passenger flow is larger, transfer passengers are approximately subjected to uniform distribution of [0, H ] in the arrival interval of the train, and the transfer running time of the passengers is taken as different fixed values according to the different station structures. Thus, the mean and variance are:
thus, the mean and variance for the transfer time for the kth path between OD versus u is:
in general, the arrival of the passengers at the arrival station is random, but the arrival passenger flow is large and the distribution characteristics are smooth in the peak time, the arrival of the arrival passengers is approximately uniform in [0, H ], and the arrival and arrival travel time is taken as a constant value. Thus, the mean and variance of the in-out time is:
To sum up, the time mean and variance of the kth path between OD versus u is:
thus, the travel time of the kth path passenger between OD versus u obeys the following normal distribution,
wherein ,
-OD impedance to the kth path between u.
(3) Path selection strategy based on accumulated prospect theory
Under the condition of short interruption, the network structure of the rail transit changes, the travel of passengers is influenced, and the instability in the travel process is enhanced, so that the accumulated prospect theory can be used for analyzing the path decision behavior under the condition of short interruption, and the path adjustment decision process of the passengers is divided into an editing stage and an evaluating stage. In the editing stage, converting the path impedance of the passenger into subjective value according to the selected reference point, and converting the probability root of the selected path into subjective probability; and in the evaluation stage, the accumulated prospect value of each travel scheme is obtained.
1) Passenger travel time reliability
Reliability refers to the likelihood that the system will achieve the intended goal at a particular time and condition. The method and the device are mainly used for researching the reliability of the rail transit travel time of passengers aiming at a certain specific travel path between the OD pairs.
Therefore, the travel time reliability of the kth path between OD versus u is defined as:
u∈U
Wherein U-the set of all OD pairs in the road network;
2) Reference point selection based on temporal reliability
In the "edit" stage of the path adjustment decision process, the subjective value and subjective probability of the passenger need to be determined. When the subjective value of the passengers is determined, firstly, a reference point is selected, wherein the reference point is an important concept in the accumulated prospect theory, and the passengers compare the travel time of each travel scheme with the reference point to obtain the relative value of each scheme. At present, the selection of the reference point does not have unified regulated standard, and related scholars also research the reference point, and the reference point is mainly divided into two main categories: exogenous reference points and endogenous reference points. The exogenous reference point usually takes the mean value, the median value, the minimum value and the like of a feasible scheme, and the value taking method is relatively simple and widely applied. The endogenous reference points are dynamic reference points, namely the reference points are changed along with the change of decision conditions, and the same decision conditions are different for different decision makers, so that the reference points are more in line with the actual conditions, and therefore, the invention selects the endogenous reference points as reference standards.
The invention has the research background that the condition of short interruption event occurs in the rail transit in the peak period, most of passengers traveling in the peak period are commute passenger flows, the traveling destination and regularity are strong, the traveling time is the most main influencing factor of the selected path, and the traveling time-space range is relatively fixed, so that the commute passengers have a certain planning on the traveling path and traveling time before traveling.
Therefore, when calculating the cost function of each alternative path, when any OD pair u is selected for the passengers, the average value and variance of the travel impedance of the kth path between the OD pair u selected by the passengers are calculated by combining the distribution of the travel impedance and travel time of the passenger rail transit, and the distribution function of the path is obtained. According to the characteristics of commute passenger flow and the reliability of the travel time of passengers, the invention selects the probability budget time of passengers for ensuring the expected punctual arrival as a reference point.
The OD has the following budget time expression for the kth path between u:
wherein ,
-OD versus reference point of the kth path between u;
ρ—the passenger considers a parameter of travel time reliability, the greater its value the greater the path reliability, indicating the higher the likelihood that the passenger will avoid the risk of uncertainty.
For more than one feasible path between any OD pair, according to the selection mode of the endogenous reference points, the invention uses the selection mode of the reference points, and adopts the minimum budget time of each path between the OD pairs as the reference point, namely:
wherein ,θu -OD vs. u reference point.
3) Subjective value determination
After determining the reference point for passenger path selection, i.e., taking the minimum budget time for all feasible paths between OD pairs as the reference point, the subjective value of each alternative path for the passenger can be further calculated. The cost function of each alternative for passenger routing is as follows:
wherein α—the degree of risk avoidance at the time of return;
beta-risk preference at loss;
a-gain pursuit coefficient;
b-loss aversion coefficient.
Wherein 0 < α, β < 1, a larger value indicating that the passenger is more sensitive to risk; 0 < a < b.
4) Cumulative foreground value
The decision function adopted by the invention is expressed as follows:
w(p)＝exp[-(-ln p) γ ],0＜γ＜1
applying cumulative prospects theory to rail traffic, passenger flow is generally considered as a continuous flow. According to the travel time rule of the rail transit passengers, passenger travel time distribution is given for each path of the OD pair. When the passenger performs path selection, the continuous function expression of the accumulated foreground value is as follows:
wherein ,
-as a variant->
Is a function of the distribution of (a).
The travel time of the rail transit path of the passenger fluctuates within a certain range, when an emergency occurs in the rail transit system, the uncertainty of the passenger on the cognition of the road network condition is increased, and the passenger selects the path with the largest cumulative prospect value to travel after editing and evaluating different feasible paths among the OD pairs according to the cumulative prospect theory.
(4) Random equalization distribution model based on accumulated foreground values
1) Model building
The accumulated prospect theory considers the limited rationality of the passengers in the emergency state, the utility value of the travel path of the passengers is calculated through a cost function and a decision weight function, and the cognitive deviation problem of the passengers is not considered. Even if passengers select the same path, the reference points are the same, normal distribution functions obeyed by the paths are the same, and the accumulated prospect values of the paths between the OD pairs are not the same as the actual conditions of passengers when the passengers go out are different, and the distribution rules of the travel time cannot be completely mastered due to the fluctuation conditions of the passenger flow.
Therefore, the invention establishes a model by utilizing the random utility theory, takes the travel time as a random variable, divides the path utility of the passenger into two parts for the perception deviation of the passenger, and accumulates the foreground value in one part 
Another part is a random error term
Namely:
in the formula：
-path accumulation foreground actual observations;
assuming that the random error term is a gummel variable which is independent and distributed at the same time, according to the random utility theory, the probability that any OD pair is selected for the kth path between u is as follows:
wherein θ is a parameter reflecting the familiarity of the passenger with the road network. According to the random user theory, when the network reaches a random user equilibrium state, the following conditions should be satisfied:
q u ≥0
since the path cumulative foreground value function has asymmetry, the present invention uses the variation inequality to discuss the nature of the random user equalization model pattern solution.
The satisfaction function of the passenger path selection is first defined as:
in the formula：vu Is that
Vector form of (2) is about->
Is a continuous function of (1), and has->
When the OD demand of the passenger is known, then the model is equivalent to finding a set f of feasible path flows * e.OMEGA.where.OMEGA.is a set of feasible path traffic sets f such that
The following inequality is satisfied:
(5) Solution algorithm
1) Solution algorithm
And searching an effective path by using a graph traversal algorithm, calculating an accumulated prospect value of the path, and loading the passenger flow demand between the OD pairs into the road network. Taking the accumulated foreground value of the traveler as a basis of path selection, solving the model by adopting an MSA algorithm, wherein the steps are as follows:
Step 0 is initialized. Initializing parameters based on network topologyThe traversal algorithm of the graph searches a feasible path set between any two points in the road network to obtain an effective path set R of any OD pair u u ；
Step 1 calculates the initial path impedance. When the traffic volume of the road network is 0, the initial path impedance of each path in the road network is calculated according to formulas (3-5) to (3-20), and the accumulated prospect value of the path is calculated according to formulas (3-23) to (3-28). Adopting (3-43) to carry out random network loading in a logic form on the fixed passenger flow demand between the OD pairs in the network once so as to obtain the initial flow of the path
And initial road traffic +.>
n＝1；
Step 2 updates the path foreground value. According to the section flow, the path impedance is updated by the formulas (3-5) to (3-20), and the path foreground value is updated by the formulas (3-23) to (3-28)
Step 3 determines the update direction. Based on path foreground values
For traffic demand q u Loading on road network to obtain auxiliary path flow +.>
Further get the update direction of the path flow>
wherein />
Step 4, updating the path and road section flow:
obtaining the road section flow from the path correlation matrix>
Step 5 convergence test: when (when)
The algorithm ends, otherwise n=n+1, returning to Step 1./>
2) Passenger flow matrix extraction method
The research background of the invention is the short interruption condition of the peak period, and is mainly used for distributing the passenger flow in the short interruption time of the peak period, so that the online passenger flow in the period needs to be extracted, then converted into an OD passenger flow matrix and distributed on an effective path, so as to research the passenger flow distribution condition in the interruption period of the peak period. The definition of network traffic refers to the sum of all passengers traveling using urban rail transit over a period of time.
The method adopts a virtual starting and ending point method to extract the online passenger flow in a certain period, thereby obtaining the section passenger flow with higher accuracy. According to the arrival and arrival time of passengers, 4 parts of the online passenger flow in a certain period are formed, as shown in fig. 2, the class A passengers are passengers with card swiping time in the range of 18:00-18:30; class B passengers are passengers who are inbound at 18:00-18:30, outbound after 18:30; class C passengers are passengers who are inbound before 18:00, outbound at 18:00-18:30; class D passengers are passengers who are 18:00 forward stops, 18:30 backward stops.
In order to obtain accurate online passenger flow in a certain period, different types of passengers need to be distinguished, and the online passenger flow is obtained by adopting a virtual starting and ending point method. The actual OD of the class A passengers is the effective OD; b class passengers, wherein the first half part of travel is in a time range, O is an effective starting point, a destination station D needs to be changed into a virtual station, and the most probable station of the passenger at 18:30 is presumed to be taken as a point D' according to the arrival time of the passenger, the selected path and the time of the path; the second half part of the travel of the class C passengers is in a time range, D is an effective destination station, and the starting point O needs to be changed into a virtual node O'; and D, the starting and ending points of the class D passengers are all virtual nodes in the time range in the middle part of travel. Through the above process, the online passenger flow volume in a certain period is obtained.
Claims (1)
1. The urban rail transit passenger flow distribution method under the condition of short interruption is characterized by comprising the following steps of:
step 1: passenger travel impedance calculation
Abstracting a rail transit network into a directed graph G= (I, A), wherein I= {1,2,3 …, I } is a set of nodes and represents a station; a= { a 1 ,a 2 ,a 3 ,…,a n -a set of directed arcs, representing road segments; the set of all OD point pairs on the U-path network, one OD point pair on the U-path network, and U E U, R u ＝{r 1 ,r 2 ,…,r k -all active path sets between OD pairs u;
(1) Calculating the riding time
The time on the train during the travel of the passengers comprises the following steps: train running time and stop time
wherein ,tij -the length of time of operation of the road segment (i, j);
t i -the stop duration of train station i, typically a fixed value;
(2) Calculating congestion coefficients
The expression of the congestion function with overlong perception time caused by the congestion of the carriage is as follows:
wherein ,xij -section (i, j) section passenger flow volume;
a—a general congestion overhead coefficient;
b—an overcrowded overhead coefficient;
z-number of seats in the train;
c, rated passenger capacity of the train;
the road section driving time considering the congestion degree is as follows:
when passengers select the track traffic to go out, the riding time length of the kth path considering the crowdedness between the OD pair u is as follows:
(3) Calculating transfer duration
The transfer time when a passenger performs transfer at a transfer station is expressed as:
wherein ,
-time station j is transferred from line m to n;
The transfer time of the passenger is amplified:
h is the train departure interval;
lambda-transfer penalty coefficient;
the path transfer time is the sum of multiple transfer times and is subjected to transfer penalty
wherein ,
-the transfer duration of the kth path between OD versus u;
(4) Calculating the perceived time of a passenger
The perceived time of the passenger is calculated as follows
wherein ,
-the number of transfers of the kth path between OD versus u;
omega-transfer number penalty coefficient;
(5) Calculating the time length of entering and exiting the station
The passenger arrival time includes the travel time and waiting time of the arrival
wherein ,ra -travel time into station a;
w a -waiting time for entering station a;
r b -travel time into station b;
To sum up, the travel time of the kth path between OD versus u is:
step 2: passenger flow distribution based on accumulated prospect theory
(1) Passenger flow distribution method
Taking the impedance of the path as a variable, the condition of the model can be expressed as:
in the formula：
-selecting a probability of OD for the kth path between u;
establishing an unconstrained model according to the conditions
wherein ,
in the formula：
-a desired perceived impedance of the traveler;
c u (x) -the actual impedance between OD versus u;
(2) Path selection strategy based on accumulated prospect theory
1) Calculating passenger travel time reliability
The travel time reliability of the kth path between OD versus u is defined as:
u∈U
wherein U-the set of all OD pairs in the road network;
2) Reference point selection based on temporal reliability
The OD has the following budget time expression for the kth path between u:
wherein ,
-OD versus reference point of the kth path between u;
ρ—a parameter of passenger considering travel time reliability, the larger its value the greater the path reliability, the higher the likelihood that the passenger will avoid the uncertainty risk;
The minimum budget time of each path between OD pairs is adopted as a reference point:
wherein ,θu -OD versus reference point of u;
3) Subjective value determination
The cost function of each alternative for passenger routing is as follows:
wherein α—the degree of risk avoidance at the time of return;
beta-risk preference at loss;
a-gain pursuit coefficient;
b-loss aversion coefficient;
wherein 0 < α, β < 1, a larger value indicating that the passenger is more sensitive to risk; a is more than 0 and less than b;
4) Cumulative foreground value
The decision function expression is as follows:
w(p)＝exp[-(-lnp) γ ],0＜γ＜1
when the passenger performs path selection, the continuous function expression of the accumulated foreground value is as follows:
wherein ,
-as a variant->
Is a distribution function of (a);
step 3, random equalization distribution model based on accumulated foreground value
Regarding travel time as a random variable forPerceived deviation of a passenger, dividing the path utility of the passenger into two parts, one part accumulating the foreground value
The other part is random error item->
in the formula：
-path accumulation foreground actual observations;
the probability of any OD to the kth path between u being selected is:
wherein θ is a parameter reflecting the familiarity of the passenger with the road network; according to the random user theory, when the network reaches a random user equilibrium state, the following conditions should be satisfied:
q u ≥0
The satisfaction function of the passenger path selection is defined as:
in the formula：vu Is that
Vector form of (2) is about->
Is a continuous function of (1), and has->
/>
Finding a set of feasible path traffic f * e.OMEGA.where.OMEGA.is a set of feasible path traffic sets f such that
The following inequality is satisfied:
step 4, model solving
(1) Solution algorithm
Taking the accumulated foreground value of the traveler as a basis of path selection, solving the model by adopting an MSA algorithm, wherein the steps are as follows:
step 0 initializing, initializing parameters, searching a feasible path set between any two points in a road network by using a graph traversal algorithm based on a network topology structure to obtain an effective path set R of any OD pair u u ；
Step 1, calculating initial path impedance, when the traffic volume of the road network is 0, calculating the initial path impedance of each path in the road network, calculating the accumulated prospect value of the paths, and carrying out once Logit-form random network loading on the fixed passenger flow demand between OD pairs in the network to obtain the initial path flow
And initial road traffic +.>
Step 2, updating the path foreground value, updating the path impedance according to the section flow, and updating the path foreground value again
Step 3 determines the update direction based on the path foreground value
For traffic demand q u Loading on road network to obtain auxiliary path flow +. >
Further get the update direction of the path flow>
wherein />
Step 4, updating the path and road section flow:
obtaining the road section flow from the path correlation matrix>
Step 5 convergence test: when (when)
The algorithm ends, otherwise n=n+1, returning to Step 1./>
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