1. A method for distributing urban rail transit passenger flow under the condition of short-time interruption is characterized by comprising the following steps:

step 1: passenger travel impedance calculation

Abstracting a rail transit network into a directed graph G (I, A), wherein I is a set of nodes which represent stations, and 1,2,3 …, I is shown in the drawing; a ═ a₁,a₂,a₃,…,a_nThe set of directed arcs represents a road section; a set of all OD point pairs on the U road network, one OD point pair on the U road network, and U belongs to U and R^u＝{r₁,r₂,…,r_kRepresents the set of all valid paths between OD pairs u;

(1) calculating riding time

The time of the passengers on the train in the traveling process comprises the following steps: train running time and station stop time

Wherein, t_ij-the length of time of travel of the section (i, j);

t_ithe stop time of the train station i is usually a fixed value;

(2) calculating congestion coefficients

The congestion function with overlong perception time caused by the congestion of the carriage has the following expression:

wherein x is_ij-section (i, j) section traffic;

a-overhead coefficient of general congestion;

b-overcrowded overhead factor;

z is the number of seats of the train;

c-the rated passenger capacity of the train;

the road section driving time considering the congestion degree is as follows:

when the passenger selects the rail transit trip, the riding time length of the kth route considering the congestion degree between the OD and the u is as follows:

the ride time of the kth path between the OD and the u is long;

(3) calculating transfer duration

The transfer time when a passenger makes a transfer at a transfer station is expressed as:

wherein the content of the first and second substances,-the time that station j transfers from line m to n;

-station j transfers the travel time from line m to n;

-station j transfers the latency from line m to n;

the transfer time of the passenger is amplified:

wherein, H is train departure interval;

λ -transfer penalty coefficient;

the path transfer time is the sum of multiple transfer times, and transfer punishment is carried out

Wherein the content of the first and second substances,-the transfer duration of the kth path between OD and u;

(4) calculating the perception time of the passenger

The perception time of the passenger is calculated as follows

Wherein the content of the first and second substances,-the number of transfers of the k path between OD and u;

omega-transfer times penalty coefficient;

(5) calculating the time length of entering and leaving station

The passenger arrival time comprises the travel time and waiting time of arrival

Wherein r is^a-travel time to station a;

w^a-waiting time at ingress point a;

r^b-travel time to station b;

-the length of time for the k path between the OD pair u to enter and exit;

-the length of the arrival time of the kth path between OD pair u;

-the length of outbound time of the kth route between OD pair u;

in summary, the travel time of the k-th path between OD and 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 the probability of the kth path between OD pair u;

establishing an unconstrained model according to the above conditions

Wherein the content of the first and second substances,

in the formula:-the expected perceived impedance of the traveler;

c^u(x) The actual impedance between OD and u;

-the perceived impedance of the kth path;

(2) path selection strategy based on accumulated foreground theory

1) Calculating the reliability of the travel time of the passenger

The travel time reliability of the kth path between the OD and u is defined as:

u∈U

wherein, U is the set of all OD pairs in the road network;

-the reliable trip impedance of the path at confidence β;

-the trip impedance of the kth path between OD and u;

2) reference point selection based on time reliability

The budget time expression of OD to the kth path among u is as follows:

wherein the content of the first and second substances,-OD to the reference point of the kth path between u;

rho is a parameter of the passenger considering the reliability of travel time, and the larger the value of the parameter is, the greater the reliability of the path is, the higher the possibility that the passenger avoids the uncertain risk is;

the minimum budget time of each path between OD pairs is taken as a reference point:

wherein, theta^u-a reference point of OD to u;

3) subjective value determination

The cost function for the passenger routing alternatives is as follows:

wherein, alpha is the risk avoidance degree in income;

β -degree of risk bias at loss;

a-profit pursuit coefficient;

b-loss of aversion coefficient;

wherein 0 < alpha, beta < 1, with larger values indicating more risk sensitivity of the passenger; a is more than 0 and less than b;

4) accumulated foreground value

The decision function expression is as follows:

w(p)＝exp[-(-lnp)^γ],0＜γ＜1

when the passenger selects the path, the continuous function expression of the accumulated foreground value is as follows:

wherein the content of the first and second substances,being a variableA distribution function of (a);

step 3, random equilibrium distribution model based on accumulated foreground value

The travel time is taken as a random variable, the perception deviation of the passenger is divided into two parts, and the foreground value is accumulated in one partAnother part is a random error term

In the formula:-the path accumulates the foreground actual observations;

-a path utility random error term;

the probability that the kth path between any OD pair u is selected is:

wherein theta is a parameter reflecting the familiarity of passengers with the road network; according to the random user theory, when the network reaches the random user equilibrium state, the following conditions should be satisfied:

q^u≥0

the satisfaction function for passenger routing is defined as:

in the formula: v. of^uIs composed ofIs in the form of a vector ofAnd a continuous function of

Finding feasible path flow set f^*E Ω, Ω is the set of feasible path flow sets f, such thatThe following inequalities are satisfied:

step 4, model solving

(1) Solving algorithm

Taking the accumulated foreground value of the traveler as the basis of path selection, and solving the model by adopting an MSA algorithm, wherein the steps are as follows:

initializing Step 0, initializing parameters, searching a feasible path set between any two points in a road network based on a graph traversal algorithm of a network topology to obtain an effective path set R of any OD to 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 an accumulated foreground value of the path, and carrying out one-time Lobitmode random network loading on the fixed passenger flow demand between OD pairs in the network to obtain the initial flow volume of the pathAnd initial road section flow

Step 2, updating the foreground value of the path, updating the impedance of the path according to the cross-section flow, and updating the foreground value of the path

Step 3, determining an updating direction and based on a path foreground valueFor traffic demand q^uLoading in the road network to obtain the auxiliary path flowFurther obtain the path flow updating directionWherein

Step 4, updating the path and the road section flow:obtaining road section flow from path incidence matrix

Step 5 convergence test: when in useAnd (4) ending the algorithm, otherwise, returning to Step 1.

Background

The net-forming operation facilitates the traveling of passengers, attracts more passengers, and further generates a large passenger flow phenomenon under certain conditions, such as large commuting passenger flow at the peak in the morning and at the night, large traveling passenger flow at holidays and the like. In the urban rail transit system under the network-forming operation condition, the road network structure is more complex, the transfer mode of passengers in the rail system and the running organization mode of trains are more and more diversified, so that the rail transit operation system is more complex, and the frequency of daily emergencies is increased. When the passenger flow of the rail transit is large, once an accident occurs, regional operation problems can be caused, and certain influence can be caused on adjacent regions, so that the operation efficiency and the operation safety of a rail transit system and passengers are influenced.

In a rail transit system for seamless transfer, passenger transfer is more convenient, but the system cannot record the specific path selection condition of passengers, so that the difficulty is increased for the operation management of rail transit. The works of ticket service clearing, congestion prediction, key road section identification and the like of urban rail transit, and when an emergency operation accident occurs, the prediction, the passenger flow control and the like of each road section of the rail transit are carried out 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 scholars perfect the passenger flow distribution model, and due to factors such as model checking difficulty and limited related data volume, the distribution result is more reasonable as much as possible, and data support is provided for an operator to grasp the operation condition of the rail transit system.

Under the background, the urban rail transit system operated in a network mode is more complex in road network structure, more diverse in passenger path selection and more convenient to travel, and the occurrence of an emergency operation event brings greater challenges to rail transit safety operation. The invention takes the short-time interruption event of the rail transit as the background, considers the limited rationality of passengers in the sudden operation state, is more close to the actual path selection state of the passengers, distributes passenger flow in the short-time interruption operation period of the rail transit, and provides a theoretical basis for the operation organization work of a rail transit system.

The prior art researches are mainly embodied in aspects of passenger flow distribution models, effective path search algorithms, passenger flow distribution algorithms, rail transit path impedance establishment and the like, but the researches have some defects, particularly aiming at the aspect of researches on emergencies of urban rail transit, the existing researches utilize an accumulation prospect theory to establish models to consider the incomplete rationality of passenger decision making, and are mainly applied to urban road traffic or combined travel of travelers, and aiming at the aspect of less travel decision making of passengers in a rail transit system when the emergencies of the rail transit occur. In view of the above, the method and the system take the short-time interruption condition of the urban rail transit system as a research background, consider the incomplete rationality of the path decision of the passenger in the condition when analyzing the change of the road network structure after the interruption, analyze the path decision behavior of the rail transit passenger in the condition, and distribute 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 situation that the urban rail transit network is interrupted for a short time in the peak period as a research background, researches the path selection behavior of passengers under the uncertain situation, mainly considers that the passenger path decision is not complete and rational when an emergency occurs, analyzes the passenger behavior by utilizing the accumulated foreground theory, establishes a random equilibrium distribution model and distributes the road network passenger flow under the short-time interruption condition. The invention specifically adopts the following technical scheme:

a method for distributing urban rail transit passenger flow under the condition of short-time 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 is a set of nodes which represent stations, and 1,2,3 …, I is shown in the drawing; a ═ a₁,a₂,a₃,…,a_nThe set of directed arcs represents a road section; a set of all OD point pairs on the U road network, one OD point pair on the U road network, and U belongs to U and R^u＝{r₁,r₂,…,r_kRepresents the set of all valid paths between OD pairs u;

(1) calculating riding time

The time of the passengers on the train in the traveling process comprises the following steps: train running time and station stop time

Wherein, t_ij-the length of time of travel of the section (i, j);

t_ithe stop time of the train station i is usually a fixed value;

(2) calculating congestion coefficients

The congestion function with overlong perception time caused by the congestion of the carriage has the following expression:

wherein x is_ij-section (i, j) section traffic;

a-overhead coefficient of general congestion;

b-overcrowded overhead factor;

z is the number of seats of the train;

c-the rated passenger capacity of the train;

the road section driving time considering the congestion degree is as follows:

when the passenger selects the rail transit trip, the riding time length of the kth route considering the congestion degree between the OD and the u is as follows:

the ride time of the kth path between the OD and the u is long;

(3) calculating transfer duration

The transfer time when a passenger makes a transfer at a transfer station is expressed as:

wherein the content of the first and second substances,-the time that station j transfers from line m to n;

-station j transfers the travel time from line m to n;

-station j transfers the latency from line m to n;

the transfer time of the passenger is amplified:

wherein, H is train departure interval;

λ -transfer penalty coefficient;

the path transfer time is the sum of multiple transfer times, and transfer punishment is carried out

Wherein the content of the first and second substances,-the transfer duration of the kth path between OD and u;

(4) calculating the perception time of the passenger

The perception time of the passenger is calculated as follows

Wherein the content of the first and second substances,-the number of transfers of the k path between OD and u;

omega-transfer times penalty coefficient;

(5) calculating the time length of entering and leaving station

The passenger arrival time comprises the travel time and waiting time of arrival

Wherein r is^a-travel time to station a;

w^a-waiting time at ingress point a;

r^b-travel time to station b;

-the length of time for the k path between the OD pair u to enter and exit;

-the length of the arrival time of the kth path between OD pair u;

-the length of outbound time of the kth route between OD pair u;

in summary, the travel time of the k-th path between OD and 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 the probability of the kth path between OD pair u;

establishing an unconstrained model according to the above conditions

Wherein the content of the first and second substances,

in the formula:-the expected perceived impedance of the traveler;

c^u(x) -OD to uActual impedance of the line;

-the perceived impedance of the kth path;

(2) path selection strategy based on accumulated foreground theory

1) Calculating the reliability of the travel time of the passenger

The travel time reliability of the kth path between the OD and u is defined as:

u∈U

wherein, U is the set of all OD pairs in the road network;

-the reliable trip impedance of the path at confidence β;

-the trip impedance of the kth path between OD and u;

2) reference point selection based on time reliability

The budget time expression of OD to the kth path among u is as follows:

wherein the content of the first and second substances,-OD to the reference point of the kth path between u;

rho is a parameter of the passenger considering the reliability of travel time, and the larger the value of the parameter is, the greater the reliability of the path is, the higher the possibility that the passenger avoids the uncertain risk is;

the minimum budget time of each path between OD pairs is taken as a reference point:

wherein, theta^u-a reference point of OD to u;

3) subjective value determination

The cost function for the passenger routing alternatives is as follows:

wherein, alpha is the risk avoidance degree in income;

β -degree of risk bias at loss;

a-profit pursuit coefficient;

b-loss of aversion coefficient;

wherein 0 < alpha, beta < 1, with larger values indicating more risk sensitivity of the passenger; a is more than 0 and less than b;

4) accumulated foreground value

The decision function expression is as follows:

w(p)＝exp[-(-ln p)^γ],0＜γ＜1

when the passenger selects the path, the continuous function expression of the accumulated foreground value is as follows:

wherein the content of the first and second substances,being a variableA distribution function of (a);

step 3, random equilibrium distribution model based on accumulated foreground value

The travel time is taken as a random variable, the perception deviation of the passenger is divided into two parts, and the foreground value is accumulated in one partAnother part is a random error term

In the formula:-the path accumulates the foreground actual observations;

-a path utility random error term;

the probability that the kth path between any OD pair u is selected is:

wherein theta is a parameter reflecting the familiarity of passengers with the road network; according to the random user theory, when the network reaches the random user equilibrium state, the following conditions should be satisfied:

q^u≥0

the satisfaction function for passenger routing is defined as:

in the formula: v. of^uIs composed ofIs in the form of a vector ofAnd a continuous function of

Finding feasible path flow set f^*E Ω, Ω is the set of feasible path flow sets f, such thatThe following inequalities are satisfied:

step 4, model solving

(1) Solving algorithm

Taking the accumulated foreground value of the traveler as the basis of path selection, and solving the model by adopting an MSA algorithm, wherein the steps are as follows:

initializing Step 0, initializing parameters, searching a feasible path set between any two points in a road network based on a graph traversal algorithm of a network topology to obtain an effective path set R of any OD to 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 an accumulated foreground value of the path, and carrying out one-time Lobitmode random network loading on the fixed passenger flow demand between OD pairs in the network to obtain the initial flow volume of the pathAnd initial road section flown＝1；

Step 2, updating the foreground value of the path, updating the impedance of the path according to the cross-section flow, and updating the foreground value of the path

Step 3, determining an updating direction and based on a path foreground valueFor traffic demand q^uLoading in the road network to obtain the auxiliary path flowFurther obtain the path flow updating directionWherein

Step 4, updating the path and the road section flow:obtaining road section flow from path incidence matrix

Step 5 convergence test: when in useAnd (4) ending the algorithm, otherwise, returning to Step 1.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

Fig. 2 is a graph of the classification of web-traffic at certain time intervals.

Detailed description of the preferred embodiments

Analysis of influence of short-time interruption on travel of rail transit passengers

The urban rail transit system comprises a plurality of subsystems, including equipment systems such as vehicles, rails, signals and stations, a power supply system and the like, and when any part of the system breaks down to cause an emergency operation event of rail transit, the urban rail transit system can affect the operation system to different degrees, such as train delay, line interruption and the like, and the operation efficiency, passenger trip efficiency and safety of the rail transit are affected.

Through statistical analysis of recent sudden operation events, the definition of the short-time interruption event is mainly divided into the following categories:

the first type is mainly events with large weight loss of life and property caused by force-ineligibility factors, such as natural disasters, terrorist events and the like, the occurrence probability is small, and when the emergencies occur, the space for passengers to make trip decisions independently is small. The second kind of emergency caused by great activity has predictability, and the operation management department can take corresponding measures in advance. According to statistics, the proportion of the emergency caused by the equipment failure of the vehicle and the unsafe behavior of passengers is large, when the emergency occurs, the passengers need to make a prejudgment according to the situation of the emergency, the traveling routes of part of the passengers are influenced, and the traveling plan needs to be changed, so that the network passenger flow state is influenced.

1. Path selection impact factor analysis

(1) Travel time factor

In a rail transit system, travel time is the primary factor considered by passengers, and a small number of passengers see the transfer times in a path and the comfort degree during riding. The travel time is the time of passengers in the rail transit system and is the whole process time from card swiping station entering to card swiping station exiting of the initial station.

(2) Service factor

1) Degree of congestion

When the passenger takes the bus for more than 20min, most passengers consider the degree of congestion when taking the bus. In the rail transit system operated in a net formation mode, the traveling time of most passengers exceeds 20min, so the degree of congestion affects the traveling of most passengers, and the degree of congestion reflects the riding comfort. When a passenger gets on or off the bus in a crowded environment, the time for the passenger to get on or off the bus is increased, and the safety of the passenger in traveling is influenced.

2) Convenience of transfer

The transfer refers to the behavior of taking a car from one route to another route at one station in order to reach a destination during the travel of the rail transit passengers. In the passenger routing process, the time taken for transfer in the route and the number of transfers are mainly considered. The transfer time is related to factors such as a platform structure, train departure interval and the like, when passengers are transferred, the psychological perception time of the passengers is correspondingly increased, and the probability of path selection is reduced due to the increase of transfer times of paths between the same OD pairs.

(3) Other factors

1) Passenger's own factors

The difference of passenger's self factor, like sex, age, occupation etc. leads to the passenger to the key point of paying close attention to in the trip process to be different, and the travelling comfort of its trip is paid close attention to more to the passenger of age, and the commuter passenger can pay close attention to the time of trip to they are the important component of rush hour passenger flow, and the comfort requirement of riding a car can be lower relatively speaking. Gender, women are relatively more comfortable in a ride 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, and the passengers familiar with the road network can have more comprehensive knowledge of the travel and can select a riding route according to the requirements of the passengers. Passengers unfamiliar with the road network need to know the relevant information of the road network by other ways, and usually select a riding route with the shortest theoretical travel time.

3) Travel cost

The trip fee is expressed as a fare in rail transit. Under the support of government, the travel cost is relatively low, the selection of the passenger is less influenced, and therefore, the influence of the fare on the travel of the passenger is not considered.

4) Personal preferences of passengers

The selection preference of passengers for routes and stations is difficult to quantitatively analyze, and has more influence factors, no rule can be followed, such as station layout, service facilities, service personnel and the like, and when the passengers select the routes, the factors are rarely considered, so the influence of the preference of the passengers is generally ignored.

2. Path selection analysis under short-time interrupt condition

In an uncertain environment, people do decisions differently than in a deterministic environment, and may be prone to risk and safety. There are many factors that influence people's decision making in an uncertain environment, but decision theorists believe that it is mainly determined by two factors: first, the value of different behavioral outcomes; the second is the probability of each outcome occurring. Therefore, in an uncertain environment, we focus on two issues: the method comprises the steps of judging the value of different behavior results, and evaluating the possibility of different behavior results. These two problems are related to the cognitive and psychological factors of people in the decision making context.

When the rail transit system has an emergency, the decision environment of the passenger changes, and compared with the path decision of the passenger under the normal operation condition, the uncertainty is stronger. Meanwhile, under the condition of an emergency, a passenger may generate certain psychological pressure, which is different from a completely rational decision-making behavior under a normal road network environment, and a general theory assumes that the passenger is in a completely rational state when performing path selection, so that the passenger can make a decision under the condition of limited rationality in the path selection behavior of the passenger in the emergency.

Aiming at the analysis of passenger decision behaviors in an emergency, the selection of passengers is adjusted on the basis of the original selection, and the passengers are likely to leave the relevant area of the emergency, so that the influence caused by the emergency is reduced as much as possible, and the trip process is hopefully completed quickly and reliably.

3. Determination of rail traffic network and its effective path set

The urban rail transit road network mainly comprises two parts, namely a station and a route, and the construction of the station comprehensively considers factors in all aspects, such as: geographical position, passenger demand and the like, wherein the station is mainly a facility for passengers to take a bus, wait for the bus and distribute the passengers; the line is a facility for connecting each station, and the line forms a framework of a traffic network; the stations and lines form an urban traffic network.

(1) Definition of efficient paths

In urban rail transit systems, there are usually multiple routes between OD pairs for passengers to choose from, but not every one of these possible routes is chosen by the passenger. When a passenger goes out, the passenger always selects the path which is considered to have the maximum traveling utility, and the passenger cannot select the path which has repeated road sections, repeated stations, excessive transfer times and overlong time consumption in the actual traveling process. Therefore, it is necessary to further determine the route searched between the OD pairs, and whether the route is within the selection range of the passenger, which may be selected by the passenger, is called an effective route.

(2) Passenger travel impedance calculation

When the rail transit passenger selects the path, the path selection is influenced by a plurality of factors, and the abstract expression of the factors is the path impedance of the passenger. The path impedance is a criterion for routing passengers and has an important role in passenger flow distribution. By analyzing the influence factors of passenger routing and the passenger routing behavior under the condition of short-term interruption of rush hour, the passengers going out at the time interval pay more attention to the time of going out, and meanwhile, due to the fact that the rail transit is locally interrupted for a short time, the passengers tend to leave the accident influence area rapidly, the passenger flow distribution state changes, and the passengers are influenced in going out. In summary, when the path traveling impedance of the passenger is calculated, the path impedance function of the passenger is established mainly by considering the traveling 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 is set {1,2,3 …, I } which is a set of nodes and represents a station, and A is { a ═ a₁,a₂,a₃,…,a_nThe set of directed arcs represents a road section, a set of all OD point pairs on a U road network and one OD point pair on a U road network, and U belongs to U and R^u＝{r₁,r₂,…,r_kIndicates the set of all valid paths between OD pairs u, explored with the kth path between u.

According to the travel process of passengers, the time is divided into three parts: riding time, transfer time and station entering and exiting time.

1) Length of ride

The time of the passengers on the train in the traveling process comprises the following steps: the train running time and the station stopping time.

Wherein, t_ij-the length of time of travel of the section (i, j);

t_ithe stop time of the train station i is usually a fixed value.

2) Congestion coefficient

Passenger perception riding time is related to train crowding degree, crowded ridingThe environment not only reduces the comfort level, increases passenger's the time of getting on or off the bus and perception trip time, increases passenger's trip risk simultaneously. When a short interruption occurs during a peak period, the distribution state of the traffic in the road network changes, and the impedance is different when the passenger selects a route. Reference Wuxiangyun et al^[14]The proposed congestion function with too long sensing time caused by congestion of the carriage has the following expression:

wherein x is_ij-section (i, j) section traffic;

a-overhead coefficient of general congestion;

b-overcrowded overhead factor;

z is the number of seats of the train;

c-train rated passenger capacity.

Therefore, the link travel time considering the congestion degree is:

when the passenger selects the rail transit trip, the riding time length of the kth route considering the congestion degree between the OD and the u is as follows:

the ride time of the kth path between the OD and the u is long;

3) length of transfer

The transfer time includes the traveling time from one line to another line, and the waiting time after transfer. Due to different structures of the stations, transfer distances are different, and traveling time is different. Therefore, the transfer travel time needs to be obtained by actual investigation. And in the peak period, the passenger flow is large, the passengers arrive approximately in uniform distribution in the arrival interval of the train, and the waiting time is 1/2 of the departure interval.

Thus, the transfer time when a passenger makes a transfer at a transfer station can be expressed as:

wherein the content of the first and second substances,-the time that station j transfers from line m to n;

-station j transfers the travel time from line m to n;

station j transfers the latency from line m to n.

Through going out the action and the psychology to the passenger and analyzing, the perception trip time that the transfer can increase the passenger consequently, enlarge passenger's transfer time, promptly:

wherein, H is train departure interval;

λ -transfer penalty coefficient.

The passenger trip path may need to be changed for a plurality of times, so the path change time is the sum of the plurality of times of change time, and the change punishment is carried out.

Wherein the content of the first and second substances,the transfer duration of the k path between OD and u.

4) Number of transfers

Along with the network-forming operation of rail transit, the number of times of transfer is greater than one in the traveling process of passengers, and the perception time of the passengers is increased due to the increase of the number of times of transfer.

Wherein the content of the first and second substances,-the number of transfers of the k path between OD and u;

omega-transfer times penalty coefficient;

5) length of time to go in and out of station

The passenger arrival time comprises the traveling time and the waiting time of arrival, similar to transfer, the layout and the structure of each station are different, the traveling time is different, and the waiting time is half of the departure interval.

Wherein r is^aEntering stationThe running time of the point a;

w^a-waiting time at ingress point a;

r^b-travel time to station b;

-the length of time for the k path between the OD pair u to enter and exit;

-the length of the arrival time of the kth path between OD pair u;

the length of outbound time of the k-th route between OD pairs u.

In summary, the travel time of the k-th path between OD and u is:

in the invention, the operation time of the train in the interval is mainly obtained according to the ratio of the distance between the stations to the average operation speed of the train; the train stop time is obtained through investigation; the transfer time is obtained by investigating each transfer station.

(II) passenger flow distribution method based on accumulated foreground theory

Conventional passenger flow distribution methods are generally based on an ideal situation, that is, assuming that passengers can grasp information of the entire road network, which is not the case. Under the condition that an emergency occurs, the path decision state of a passenger is different from that under the normal condition, the invention considers the incomplete rationality of the passenger when the passenger makes the path decision under the condition, and applies the accumulated prospect theory to analyze the path decision behavior of the passenger and establish a random user equilibrium model.

1. Passenger flow distribution method

The passenger flow distribution is a process of distributing passenger travel demands among OD pairs in the urban rail transit system to a road network. The travel time of passengers is converted into generalized travel cost, effective path searching is carried out according to the network structure of the rail transit system, and the demand between OD pairs in the network is reasonably distributed according to a distribution model. This chapter mainly introduces the random user equilibrium allocation method.

The user balance model considers that a traveler can grasp information of the entire road network and know the condition of the road network in real time to obtain the impedance of a path in the road network, which is difficult to realize in actual situations. The random user equilibrium model is based on the cognition of a traveler 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 the kth path between OD pairs u.

The above conditions may be equivalent to the following unconstrained model.

Wherein the content of the first and second substances,

in the formula:period of the travelerThe impedance is perceived;

c^u(x) The actual impedance between OD and u;

-the perceived impedance of the kth path.

Because the passengers cannot completely master the road network information, the invention takes the travel impedance of the rail transit passengers in the network as a random variable, and therefore, the invention selects a random user balancing method to distribute the passenger flow.

2. Time characteristic analysis for travel of rail transit passengers

(1) Passenger travel time fluctuation characteristics

According to the method, the trip time of the passengers in the rail transit is statistically analyzed through AFC card swiping data, so that the fact that the trip origin and destination are the same, the trip time of the passengers is different under the condition that the trip time periods are close, the trip time of different passengers at the same station fluctuates within a certain range, and the fluctuation of the trip time of the passengers is related to the self-factors of the passengers and the road network state.

Taking Beijing subway as an example, the travel time of passengers in rail transit and the fluctuation situation of the travel time of the passengers are analyzed through AFC card swiping data of the passengers. The AFC card swiping data records relevant information of passengers in the traveling process, mainly comprises station entering and exiting and time, and cannot record the passenger path selection process.

According to the method, AFC card swiping data of passengers in 17:00-19:00 late peak time periods when a rail transit network normally operates on a certain working day in 2019 and 2 are selected, and traveling time of the passengers is subjected to statistical analysis. By screening card swiping data of late peak 17:00-19:00 and counting travel origin-destination points of passengers, the origin-destination points with higher travel frequency in peak period are screened as west two flags-vertical water bridge, west two flags-tiantong yuan, morning sun gate-grass house and Haihe yellow village-vertical water bridge, the invention analyzes the track traffic travel time of the passengers at the origin-destination points, as shown in table 1:

TABLE 1 OD travel time statistics

As can be seen from table 1, the travel times for different passengers between the same OD pair are different and fluctuate within a certain range. The west two flags-water standing bridge and the rising sun gate-grass house are two OD point pairs on the same line, a passenger generally does not select the line needing to be transferred when going out, O and D of the west two flags-tiantong yuan and Haihe Huangzhuang-water standing bridge are positioned on different lines, and the passenger needs to be transferred at least once when going out. As can be seen from the table, in the passenger traveling process, the standard deviation of the traveling time of the OD point pair requiring transfer is greater than the route not requiring transfer, which indicates that the passenger traveling process increases the fluctuation of the traveling time due to the transfer behavior. Thus, the data show that the number of transfers increases the volatility of the passenger travel time.

And according to the fluctuation characteristics of the travel time of the passengers between different OD points, assuming the distribution of the travel time, and carrying out fitting inspection. Therefore, the method selects normal distribution to fit the rail transit travel time of the passengers, and the fitting result is shown in table 2.

TABLE 2 Normal fitting Single sample K-S test

a. The distribution was checked as normal.

b. And calculating according to the data.

The Kolmogorov-Smirnov test was performed on the assumption that the rail transit travel time of passengers was normally distributed using SPSS, and the results are shown in table 2. As can be seen from the test results of the table, the bilateral significance of the K-S test is greater than 0.05, and the results show that the fitting of the fluctuation characteristics of the passenger rail transit travel time by utilizing normal distribution is acceptable.

(2) Time distribution rule of rail transit trip

According to the analysis of the fluctuation characteristics of the passenger rail transit travel time, the travel time of passengers is assumed to be subjected to normal distribution, the assumption is verified by SPSS, and the verification result shows that the normal distribution can be used for fitting the fluctuation characteristics of the passenger rail transit travel time.

Under the condition of rail transit network formation operation, each OD pair has a plurality of feasible paths, and when a passenger selects the same path between the OD pairs to go out, the traveling time of the passenger is different and fluctuates within a certain range. The fluctuation of the travel time of passengers on the same path between the OD pairs is influenced by various factors, and the difference is shown as different walking speeds of different passengers when the passengers walk on an inbound passage, a transfer passage and an outbound passage, uncertainty of the arrival waiting time and the transfer waiting time of the passengers, and unpredictable factors such as increase of the riding time caused by congestion, train faults and the like.

For the same path between OD point pairs, because the rail transit train operates according to the plan of the train operation diagram, the riding time is relatively fixed, so the average value of the riding time of the passengers is the same, and the variance is 0, namely:

therefore, the mean and variance of the ride time for the kth path between OD pair u is:

for the transfer time of the passengers at the transfer station, the transfer time is composed of the transfer traveling time of the passengers at the transfer station and the waiting time after the transfer, the transfer traveling time is determined by the transfer distance and the walking speed of the passengers, and the waiting time after the transfer is related to the departure interval H of the line where the passengers are. In the peak period, the passenger flow is large, the transfer passengers are approximately distributed uniformly according to [0, H ] in the arrival interval of the train, and the passenger transfer traveling time is different fixed values according to different station structures. Thus, the mean and variance are:

thus, the mean and variance of the transfer time for the kth path between OD and u is:

in general, the arrival of passengers at the station is random, but in the peak period, the arrival volume of passengers is larger and presents a smoother distribution characteristic, the arrival of passengers at the station is also approximately uniformly distributed in [0, H ], and the traveling time of the passengers entering and leaving the station is constant. Thus, the mean and variance of the inbound and outbound time are:

in summary, the time mean and variance of the kth path between OD and u are:

therefore, the travel time of the k-th path passenger between OD and u follows the following normal distribution,

wherein the content of the first and second substances,OD to the k-th path between u.

(3) Path selection strategy based on accumulated foreground theory

Under the condition of short-time interruption, the network structure of rail transit is changed, the traveling of passengers is influenced, and the instability in the traveling process is enhanced, so that the path decision behavior under the short-time interruption condition can be analyzed by applying an accumulation prospect theory, and the path adjustment decision process of the passengers is divided into an editing stage and an evaluation stage. In the editing stage, the path impedance of the passenger is converted into subjective value according to the selected reference point, and the probability root of the selected path is converted into subjective probability; and in the evaluation stage, obtaining the accumulated foreground value of each travel scheme.

1) Reliability of travel time of passengers

Reliability refers to the likelihood that a system will accomplish a desired goal at a particular time and under particular conditions. The method mainly aims at a certain specific travel route between OD pairs, and researches the reliability of the rail transit travel time of passengers.

Therefore, the reliability of the k-th path between OD and u is defined as:

u∈U

wherein, U is the set of all OD pairs in the road network;

-the reliable trip impedance of the path at confidence β;

the trip impedance of the kth path between OD and u.

2) Reference point selection based on time reliability

In the "editing" 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 a passenger is determined, a reference point is selected at first, the reference point is an important concept in the accumulated prospect theory, and the passenger compares 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 has no unified and specified standard, and relevant scholars have studied the reference point, and the reference point is mainly divided into two categories: exogenous 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 is relatively wide in application. The endogenous reference point is a dynamic reference point, which means that the reference point changes along with the change of the decision condition, and the same decision condition is different for different decision makers, and the type of reference point is more consistent with the actual condition, therefore, the endogenous reference point is selected as the reference standard by the method.

The background of the invention is the situation of short-time interruption of rail transit in a peak period, most passengers going out in the peak period are commuting passenger flows, the traveling purpose and regularity are strong, the traveling time is the main influence factor of the selected path, and the traveling time-space range is relatively fixed, so that the commuting passengers have certain planning on the traveling path and the traveling time before traveling.

Therefore, when calculating the value function of each alternative path, when a passenger selects any one OD to u for trip, the mean value and the variance of the trip impedance of the kth path between the OD selected by the passenger to u are calculated by combining the distribution of the impedance and the trip time of the passenger rail transit trip, and the distribution function of the path is obtained. According to the characteristics of commuting passenger flow and the reliability of the travel time of the passengers, the invention selects the probability budget time of the passengers for ensuring the expected punctual arrival as a reference point.

The budget time expression of OD to the kth path among u is as follows:

wherein the content of the first and second substances,-OD to the reference point of the kth path between u;

rho is a parameter of the passenger considering the reliability of travel time, and the larger the value of the parameter is, the greater the reliability of the path is, the higher the possibility that the passenger avoids the uncertain risk is.

For more than one feasible path between any OD pair, according to the selection mode of the endogenous reference point, the invention uses the selection mode of the reference point thereof and adopts the minimum budget time of each path between the OD pairs as the reference point, namely:

wherein, theta^uReference point of OD to u.

3) Subjective value determination

After the reference point for selecting the passenger path is determined, namely the minimum budget time of all feasible paths between the OD pairs is used as the reference point, the subjective value of each candidate path of the passenger can be further calculated. The cost function for the passenger routing alternatives is as follows:

wherein, alpha is the risk avoidance degree in income;

β -degree of risk bias at loss;

a-profit pursuit coefficient;

b-loss of aversion coefficient.

Wherein 0 < alpha, beta < 1, with larger values indicating more risk sensitivity of the passenger; a is more than 0 and less than b.

4) Accumulated foreground value

The decision function adopted by the invention is expressed as follows:

w(p)＝exp[-(-ln p)^γ],0＜γ＜1

the theory of accumulation is applied to rail transit, and passenger flow is generally regarded as a continuous flow. According to the travel time rule of the passengers in the rail transit, the travel time distribution of the passengers is given for each path of the OD pairs. When the passenger selects the path, the continuous function expression of the accumulated foreground value is as follows:

wherein the content of the first and second substances,being a variableThe distribution function of (2).

The travel time of the rail transit path of the passenger fluctuates within a certain range, when an emergency occurs in a rail transit system, the uncertainty of the road network condition cognition of the passenger is increased, and according to an accumulated prospect theory, after editing and evaluating different feasible paths between OD pairs, the passenger selects the path with the maximum accumulated prospect value to travel.

(4) Random equilibrium distribution model based on accumulated foreground value

1) Model building

The limit rationality of the passengers in the emergency state is considered by the accumulated prospect theory, the passenger trip path utility value is obtained by calculating through a value function and a decision weight function, and the cognitive deviation problem of the passengers is not considered. Even if the passengers select the same path, the reference points are the same, the normal distribution functions obeyed by the path are the same, the actual conditions of the passengers during traveling are different, and the distribution rule of the traveling time cannot be completely mastered due to the fluctuation condition of passenger flow, so that the passengers have different perceptions of the accumulated foreground values of the paths among the OD pairs.

Therefore, the method utilizes a random utility theory to establish a model, takes travel time as a random variable, divides the path utility of passengers into two parts for the perception deviation of the passengers, and accumulates the foreground value of one partAnother part is a random error termNamely:

in the formula:-the path accumulates the foreground actual observations;

-a path utility random error term;

assuming that random error terms are Gumbel variables which are independently and identically distributed, according to a random utility theory, the probability that any OD pair u-th path is selected is as follows:

where θ is a parameter reflecting the degree of familiarity of passengers with the road network. According to the random user theory, when the network reaches the random user equilibrium state, the following conditions should be satisfied:

q^u≥0

because the path accumulation foreground value function has asymmetry, the invention adopts a variational inequality to discuss the property of the random user equilibrium model solution.

First, the satisfaction function of passenger routing is defined as:

in the formula: v. of^uIs composed ofIs in the form of a vector ofAnd a continuous function of

When the passenger OD requirements are known, then the model is equivalent to finding a feasible path flow set f^*E Ω, Ω is the set of feasible path flow sets f, such thatThe following inequalities are satisfied:

(5) solving algorithm

1) Solving algorithm

And searching an effective path by using a graph traversal algorithm, calculating an accumulated foreground value of the path, and loading the passenger flow demand between OD pairs into the road network. Taking the accumulated foreground value of the traveler as the basis of path selection, and solving the model by adopting an MSA algorithm, wherein the steps are as follows:

step 0 is initialized. Initializing parameters, searching a feasible path set between any two points in a road network based on a graph traversal algorithm for a network topology structure, and obtaining an effective path set R of any OD to u^u；

Step 1 calculates the 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 according to the expressions (3-5) to (3-20), and calculating the accumulated foreground value of the path according to the expressions (3-23) to (3-28). The fixed passenger flow demand between OD pairs is subjected to random network loading in a Logit form in the network by adopting a formula (3-43), and the initial flow of a path is obtainedAnd initial road section flown＝1；

Step 2 updates the path foreground value. According to the cross-section flow, the path impedance is updated by the expressions (3-5) to (3-20), and the path foreground value is updated by the expressions (3-23) to (3-28)

Step 3 determines the update direction. Path-based foreground valuesFor traffic demand q^uLoading in the road network to obtain the auxiliary path flowFurther obtain the path flow updating directionWherein

Step 4, updating the path and the road section flow:obtaining road section flow from path incidence matrix

Step 5 convergence test: when in useAnd (4) ending the algorithm, otherwise, returning to Step 1.

2) Passenger flow matrix extraction method

The background of the research of the invention is a short-time interruption condition in a peak period, and the invention mainly aims at the distribution of the passenger flow in the short-time interruption time in the peak period, so that the on-line passenger flow in the period needs to be extracted, then converted into an OD passenger flow matrix, and distributed to an effective path, so as to research the passenger flow distribution condition in the interruption period in the peak period. The definition of online passenger flow refers to the sum of all passengers traveling on urban rail transit in a period of time.

The invention adopts a virtual start-stop point method to extract the online passenger flow in a certain time period, thereby obtaining the section passenger flow with higher accuracy. According to the time of passengers getting in and out of the station, the passenger flow on the network in a certain time period has 4 parts, as shown in figure 2, the class A passengers are passengers with card swiping time in the range of 18:00-18: 30; a class B passenger is a passenger who enters the station at 18:00-18:30 and leaves the station after 18: 30; the class C passengers are passengers who enter before 18:00 and exit at 18:00-18: 30; class D passengers are passengers that are 18:00 inbound and 18:30 later outbound.

In order to acquire accurate online passenger flow in a certain period of time, different classes of passengers need to be distinguished, and the online passenger flow is acquired by adopting a virtual starting and ending point method. Class a passengers, the actual OD being the effective OD; the class B passenger, the first half of the trip is in the time range, O is a valid starting point, the destination station D needs to be changed into a virtual station, and the most possible station of the passenger at 18:30 is presumed to be a D' point according to the arrival time of the passenger, the selected path and the time of the path; the second half of the class C passenger trip is in the time range, D is an effective destination station, and a starting point O needs to be changed into a virtual node O'; the class D passengers have the starting point and the ending point to become virtual nodes in the time range in the middle of the trip. Through the process, the online passenger flow of a certain period is obtained.