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CN112906179B - Urban rail transit passenger flow control optimization method based on fluid queuing network - Google Patents

Urban rail transit passenger flow control optimization method based on fluid queuing network Download PDF

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CN112906179B
CN112906179B CN202011355014.7A CN202011355014A CN112906179B CN 112906179 B CN112906179 B CN 112906179B CN 202011355014 A CN202011355014 A CN 202011355014A CN 112906179 B CN112906179 B CN 112906179B
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刘珺
胡路
蒋阳升
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Chengdu Jiaoda Big Data Technology Co ltd
Southwest Jiaotong University
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Abstract

The invention discloses an urban rail transit passenger flow control optimization method based on a fluid queuing network, which comprises the following steps: s1, establishing an urban rail transit passenger flow control optimization model based on a fluid queuing network, comprising the following steps: s11, obtaining passenger travel OD data and subway line parameters; s12, constructing an urban rail transit fluid queuing network model; s13, determining passenger flow control decision variables; s14, determining passenger flow control constraint conditions; s15, constructing an optimization objective function; s2, solving the optimization model, comprising the following steps: s21, calculating a population individual target function; s22, judging whether the individual fitness meets a termination condition; if yes, ending; otherwise, carrying out the next step; and S23, selecting, crossing and mutating. On the basis of the urban rail transit passenger flow control scheme, the invention establishes a passenger flow control optimization model by combining a fluid queuing network model, and reduces the possibility of platform queuing overflow and queuing explosion.

Description

Urban rail transit passenger flow control optimization method based on fluid queuing network
Technical Field
The invention belongs to the technical field of traffic engineering, and particularly relates to an urban rail transit passenger flow control optimization method based on a fluid queuing network.
Background
With the continuous acceleration of urbanization process in China, population density in cities is higher and higher. With the development of social economy, the travel demand of the population is continuously increased, and in order to meet the increasing transportation demand, a diversified traffic system in the city is continuously perfected. And just because the demand and the dependence of passengers on urban rail transit are gradually increased, the mismatch between the transport capacity and the transport demand is increasingly sharp. The peak passenger flow congestion belongs to typical periodic congestion, and compared with sporadic congestion, the time, the place and the intensity of the peak passenger flow congestion are stable and closely related to travel demands. The net peak hour traffic is primarily for commuting purposes, constrained by its time characteristics, and therefore results in a high concentration of passengers during that time period. The overcrowding not only increases the travel time cost of passengers, but also brings great challenges to the operation management of urban rail transit.
At present, most of the current limiting modes adopted by daily operators of urban rail transit are from the perspective of safety level in stations. The system is based on personal subjective experience, depends on professional knowledge and working experience, has no theoretical support of a system, lacks reasonable calculation standards and lacks consideration on the service level of passengers during traveling; although the results of passenger flow control optimization in recent years increase at home and abroad, detailed analysis on passenger flow characteristics is mostly lacked. The control means is a simplified trend, and all the control means are directly used for the off-station passenger flow in consideration of the passenger travel OD.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a passenger flow control optimization model which is established by combining a fluid queuing network model on the basis of a passenger flow control scheme of urban rail transit; by optimizing the passenger flow control and departure interval, the problem of service rate reduction caused by the system state is solved, and the possibility of queue overflow and queue explosion of the platform can be reduced.
The purpose of the invention is realized by the following technical scheme: a method for controlling and optimizing urban rail transit passenger flow based on a fluid queuing network comprises the following steps:
s1, establishing an urban rail transit passenger flow control optimization model based on a fluid queuing network, which specifically comprises the following steps:
s11, obtaining passenger travel OD data, the station number of subway lines, the station mileage, the train number and the subway station platform capacity parameters;
s12, describing the trains on the subway line and the channels and platform systems in the stations according to the data acquired in the step S11, abstracting to corresponding fluid queuing models, and constructing an urban rail transit fluid queuing network model;
s13, determining a passenger flow control decision variable according to the passenger travel OD data;
s14, determining passenger flow control constraint conditions according to the passenger flow control decision variables and the queuing network model output indexes;
s15, constructing a passenger flow control optimization objective function by taking the minimum passenger travel time as a target according to the passenger flow control constraint condition;
s2, solving the urban rail transit passenger flow control optimization model based on the fluid queuing network, which comprises the following steps:
s21, processing the passenger flow control decision variable by using a real number coding method to generate a parent population, and calculating a population individual objective function;
s22, judging whether the population individual target function meets a preset termination condition; if so, ending the operation to obtain an optimal individual; if not, performing the next step;
s23, selecting the population by adopting a roulette method, and carrying out crossing and mutation treatment on the population by utilizing an IAGA crossing probability method and a self-adaptive mutation probability method;
s24, the optimal storage strategy is implemented to the group, and the step returns to the step S22.
Further, the obtaining step of the fluid queuing model in step S12 is as follows:
s121, establishing a platform waiting queuing model: for the boarding queuing system with the capacity of C in the boarding and landing area, passengers become a passenger flow input source in the boarding and landing area after passing through the entrance gate; the arrival process of passengers follows a time-varying poisson distribution Mt(ii) a The waiting time of passengers is distributed randomly, and the influence of the state of the system on the service process is considered, and is recorded as G (x), wherein x is the system state of the boarding queuing system in the boarding and alighting area, namely the number of passengers in the system; if the number of passengers in the system is larger than the capacity of the system, the passengers will overflow and stay in the station hall, the capacity of the station hall is infinity, and the number of passengers is marked as M according to a Kendall notation methodt/G(x)/C/C+∞；
At any time t, the state of the waiting queuing system is that the i-th station u is in the direction (the u is an uplink when the u is 1, and the u is a downlink when the u is 2)
Figure GDA0002980285190000021
Comprises the following steps: initial state of system
Figure GDA0002980285190000022
Plus the number of passengers entering minus passengers exiting, i.e.:
Figure GDA0002980285190000023
the rate of change of system state is:
Figure GDA0002980285190000024
wherein
Figure GDA0002980285190000025
The arrival rate of passengers is determined by the arrival rate of passengers at the time t in the u direction of the station i; the arrival of passengers follows Poisson distribution, so the arrival rate of the passengers at the time t in the u direction of the station i is recorded as
Figure GDA0002980285190000026
The input rate of passengers getting on the train from the passengers at the stationThe rate of arrival is decided, and since the capacity is infinite, the blocking probability is not considered, so:
Figure GDA0002980285190000027
output rate of passengers based on speed of passengers affected by system state
Figure GDA0002980285190000028
And (3) calculating:
Figure GDA0002980285190000031
wherein PT is the probability of train stop, and PT is 1, and is the train stop; l represents the station length; passenger speed in u-direction waiting queuing model of ith station
Figure GDA0002980285190000032
The calculation formula is as follows:
Figure GDA0002980285190000033
wherein:
Figure GDA0002980285190000034
given by historical data
Figure GDA0002980285190000035
Calibrating three standard points to calculate speed
Figure GDA0002980285190000036
Probability of being idle of system
Figure GDA0002980285190000037
And the system state changes, the output rate of the system occupant is therefore:
Figure GDA0002980285190000038
obtained according to the PSFFA method
Figure GDA0002980285190000039
The calculation formula of (a) is as follows:
Figure GDA00029802851900000310
wherein:
Figure GDA00029802851900000311
also given by historical data
Figure GDA00029802851900000312
Calibrating the three standard points to obtain the three standard points;
three dynamic performance indexes are established: respectively the real-time output rate of the system
Figure GDA00029802851900000313
Average occupied space
Figure GDA00029802851900000314
Mean residence time
Figure GDA00029802851900000315
The calculation formula is as follows:
Figure GDA00029802851900000316
Figure GDA00029802851900000317
Figure GDA00029802851900000318
y is residence time;
s122, train queuing model: the train is used as a carrier for passenger transportation, acts as a transportation task, a queuing phenomenon appears in each train, and a queuing system for train service is abstracted into a single virtual service desk M _ t/G (x)/1/C queuing model; according to the concept of fluid queuing, at the time t, the system state calculation formula of the kth train in the u direction is as follows:
Figure GDA0002980285190000041
wherein
Figure GDA0002980285190000042
Arrival rate of k-th train passenger in u-direction at time t
Figure GDA0002980285190000043
Output rate of waiting queuing model
Figure GDA0002980285190000044
And the connection probability PT between the station and the traini，k(t) determining:
Figure GDA0002980285190000045
TR is a train set;
output rate for train passengers getting off
Figure GDA0002980285190000046
Figure GDA0002980285190000047
Wherein
Figure GDA0002980285190000048
twAlighting passengersTime, ηk，u，j(t) is the proportion of passengers getting off the train at the j station of the kth train, and is determined by the OD data obtained by the S11;
the three dynamic performance indexes of the train queuing model are respectively the system output rate at any moment
Figure GDA0002980285190000049
Passengers occupying system space
Figure GDA00029802851900000410
Mean residence time of passengers
Figure GDA00029802851900000411
The calculation formula is as follows:
Figure GDA00029802851900000412
Figure GDA00029802851900000413
Figure GDA00029802851900000414
where CT represents the capacity of the train.
Further, the passenger flow control decision variable determined in the step S13 is the proportion of inbound passenger flow at each time t
Figure GDA00029802851900000415
And departure interval H of the k-th train in the u directionk，u(ii) a The passenger flow control decision variables satisfy the following constraints:
Figure GDA00029802851900000416
Figure GDA00029802851900000417
wherein HlbAnd HubRespectively the minimum value and the maximum value of the departure interval; Δ is the step length of each time step, S is a station set, a station i belongs to S ═ 1, 2.., N }, and N is the total number of stations; TR is a train set, a train k belongs to TR ═ 1, 2.., M }, and M is the total train amount; u is a set of train running directions, and belongs to U, wherein U belongs to {1 (uplink), 2 (downlink) };
Figure GDA00029802851900000418
time step sequence index for time set
Figure GDA00029802851900000419
Further, the passenger flow control constraint condition determined in step S14 is:
Figure GDA0002980285190000051
Figure GDA0002980285190000052
Figure GDA0002980285190000053
Figure GDA0002980285190000054
Figure GDA0002980285190000055
Figure GDA0002980285190000056
Figure GDA0002980285190000057
Figure GDA0002980285190000058
mi，u(n.DELTA.0 or 1
Figure GDA0002980285190000059
Wherein m isi，u(n Δ) is a variable from 0 to 1, and when m is 1, the number of people in the system is greater than the system capacity; m is a real number; fBCalculating formula for queuing overflow times
Figure GDA00029802851900000510
Not allowing the maximum number of overflows to be exceeded
Figure GDA00029802851900000511
Figure GDA00029802851900000512
The number of people staying at the platform is not allowed to exceed the maximum number of people staying
Figure GDA00029802851900000513
Under the passenger flow control scheme, the time-varying arrival rate of passengers in the direction of i station u is calculated by the following formula:
Figure GDA00029802851900000514
wherein,
Figure GDA00029802851900000515
indicating a normal time-varying arrival rate.
Further, the passenger flow control objective function determined in step S15 is:
Figure GDA00029802851900000516
wherein T isSThe sum of the time spent by the passengers on trips.
Further, the calculation formula of the IAGA cross probability operator and the mutation probability algorithm in step S23 is specifically as follows:
Figure GDA00029802851900000517
Figure GDA0002980285190000061
wherein, PcAnd PmRespectively cross probability and mutation probability, PcmaxAnd PcminUpper and lower limits of the crossover probability, P, respectivelymmaxAnd PmminUpper and lower limits of the probability of variation, FavgAnd FmaxRespectively are the average fitness value and the maximum fitness value in the current population, F is the fitness value in the crossed individual, and A is an arbitrary constant.
Further, the step S24 of implementing the optimal storage policy on the population specifically includes:
traversing individuals with highest fitness and individuals with lowest fitness in the current group, and judging whether the fitness of the individuals with highest fitness in the current group is higher than the highest fitness of the individuals in all the groups; if so, taking the best individual in the current group as the individual with the highest fitness in all generation groups; and if not, replacing the individuals with the highest fitness in all the generation groups with the individuals with the lowest fitness in the current generation group.
The invention has the beneficial effects that: the invention overcomes the problem that the traditional passenger flow control scheme is dependent on subjective experience and lacks of systematic and scientific theoretical support, and establishes a passenger flow control optimization model by combining a fluid queuing network model on the basis of the urban rail transit passenger flow control scheme and fully considering the safety, the service level and the trip time cost of passengers. By optimizing the passenger flow control and departure interval, the problem of service rate reduction caused by the system state is basically eliminated, the departure interval time is reduced in the passenger flow arrival peak period, the train transport capacity in unit time is improved, and the possibility of platform queue overflow and queue explosion is reduced. Compared with the traditional passenger flow control optimization method, the model effectively reduces the travel time cost of passengers, reduces the congestion condition in the urban rail transit network, and effectively improves the service level of the system.
Drawings
FIG. 1 is a schematic flow chart of an urban rail transit passenger flow control optimization method based on a fluid queuing network;
FIG. 2 is a schematic diagram of the queuing network structure of the station floor and train of the present invention;
FIG. 3 is an optimized track of a case solving process of a metropolis subway in the embodiment of the present invention;
FIG. 4 is a comparison graph before and after optimization of an off-site current limit control scheme in an embodiment of the present invention;
FIG. 5 is an early peak train operation diagram of the first line of optimized Chengdu subway in the embodiment of the invention;
FIG. 6 is a diagram illustrating a comparison of the state of an optimized pre-and post-waiting queuing system in accordance with an embodiment of the present invention;
fig. 7 is a comparison diagram of the dynamic process of optimizing the passenger carrying of the front, rear, upper and lower 10 th trains in the embodiment of the invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, the method for controlling and optimizing urban rail transit passenger flow based on the fluid queuing network of the invention comprises the following steps:
s1, establishing an urban rail transit passenger flow control optimization model based on a fluid queuing network, which specifically comprises the following steps:
s11, obtaining passenger travel OD data, the station number of subway lines, the station mileage, the train number and the subway station platform capacity parameters;
s12, describing the trains on the subway line and the channels and platform systems in the stations according to the data acquired in the step S11, abstracting to corresponding fluid queuing models, and constructing an urban rail transit fluid queuing network model;
as shown in fig. 2, which is a schematic diagram of a queuing network structure of a station layer and a train, the steps of constructing a fluid queuing model according to the parameters obtained in S11 are as follows:
s121, establishing a platform waiting queuing model: for the boarding queuing system with the capacity of C in the boarding and landing area, passengers become a passenger flow input source in the boarding and landing area after passing through the entrance gate; the arrival process of passengers follows a time-varying poisson distribution Mt(ii) a The waiting time of passengers is distributed randomly, and the influence of the state of the system on the service process is considered, and is recorded as G (x), wherein x is the system state of the boarding queuing system in the boarding and alighting area, namely the number of passengers in the system; if the number of passengers in the system is larger than the capacity of the system, the passengers will overflow and stay in the station hall, the capacity of the station hall is infinity, and the number of passengers is marked as M according to a Kendall notation methodt/G(x)/C/C+∞；
At any time t, the state of the waiting queuing system is that the i-th station u is in the direction (the u is an uplink when the u is 1, and the u is a downlink when the u is 2)
Figure GDA0002980285190000071
Comprises the following steps: initial state of system
Figure GDA0002980285190000072
Plus the number of passengers entering minus passengers exiting, i.e.:
Figure GDA0002980285190000073
the rate of change of system state is:
Figure GDA0002980285190000074
wherein
Figure GDA0002980285190000075
Driven by I vehicleThe arrival rate of passengers in the direction t of the station u is determined; the arrival of passengers follows Poisson distribution, so the arrival rate of the passengers at the time t in the u direction of the station i is recorded as
Figure GDA0002980285190000076
The input rate of passengers getting on the train in the landing zone is determined by the passenger arrival rate at the station, and because the capacity is infinite, the blocking probability is not considered, so that:
Figure GDA0002980285190000077
output rate of passengers based on speed of passengers affected by system state
Figure GDA0002980285190000078
And (3) calculating:
Figure GDA0002980285190000079
wherein PT is the probability of train stop, and PT is 1, and is the train stop; l represents the station length; passenger speed in u-direction waiting queuing model of ith station
Figure GDA00029802851900000710
The calculation formula is as follows:
Figure GDA0002980285190000081
wherein:
Figure GDA0002980285190000082
given by historical data
Figure GDA0002980285190000083
Calibrating three standard points to calculate speed
Figure GDA0002980285190000084
Probability of being idle of system
Figure GDA0002980285190000085
And the system state changes, the output rate of the system occupant is therefore:
Figure GDA0002980285190000086
obtained according to the PSFFA method
Figure GDA0002980285190000087
The calculation formula of (a) is as follows:
Figure GDA0002980285190000088
wherein:
Figure GDA0002980285190000089
also given by historical data
Figure GDA00029802851900000810
Calibrating the three standard points to obtain the three standard points;
three dynamic performance indexes are established: respectively the real-time output rate of the system
Figure GDA00029802851900000811
Average occupied space
Figure GDA00029802851900000812
Mean residence time
Figure GDA00029802851900000813
The calculation formula is as follows:
Figure GDA00029802851900000814
Figure GDA00029802851900000815
Figure GDA00029802851900000816
y is residence time;
s122, train queuing model: the train is used as a carrier for passenger transportation, acts as a transportation task, a queuing phenomenon appears in each train, and a queuing system for train service is abstracted into a single virtual service desk M _ t/G (x)/1/C queuing model; according to the concept of fluid queuing, at the time t, the system state calculation formula of the kth train in the u direction is as follows:
Figure GDA00029802851900000817
wherein
Figure GDA00029802851900000818
Arrival rate of k-th train passenger in u-direction at time t
Figure GDA00029802851900000819
Output rate of waiting queuing model
Figure GDA0002980285190000091
And the connection probability PT between the station and the traini，k(t) determining:
Figure GDA0002980285190000092
TR is a train set;
output rate for train passengers getting off
Figure GDA0002980285190000093
Figure GDA0002980285190000094
Wherein
Figure GDA0002980285190000095
twTime of alighting for passengers, ηk，u，j(t) is the proportion of passengers getting off the train at the j station of the kth train, and is determined by the OD data obtained by the S11;
the three dynamic performance indexes of the train queuing model are respectively the system output rate at any moment
Figure GDA0002980285190000096
Passengers occupying system space
Figure GDA0002980285190000097
Mean residence time of passengers
Figure GDA0002980285190000098
The calculation formula is as follows:
Figure GDA0002980285190000099
Figure GDA00029802851900000910
Figure GDA00029802851900000911
where CT represents the capacity of the train.
S13, determining a passenger flow control decision variable according to the passenger travel OD data; the passenger flow control decision variable determined in the step is the proportion of the passenger flow entering the station at each time t
Figure GDA00029802851900000912
And departure interval H of the k-th train in the u directionk，u(ii) a The passenger flow control decision variables satisfy the following constraints:
Figure GDA00029802851900000913
Figure GDA00029802851900000914
wherein HlbAnd HubRespectively the minimum value and the maximum value of the departure interval; Δ is the step length of each time step, S is a station set, a station i belongs to S ═ 1, 2.., N }, and N is the total number of stations; TR is a train set, a train k belongs to TR ═ 1, 2.., M }, and M is the total train amount; u is a set of train running directions, and belongs to U, wherein U belongs to {1 (uplink), 2 (downlink) };
Figure GDA00029802851900000915
time step sequence index for time set
Figure GDA00029802851900000916
In the present invention t is discrete and is therefore represented here in the form of n x.
S14, determining passenger flow control constraint conditions according to the passenger flow control decision variables and the queuing network model output indexes; the passenger flow control constraint conditions determined in the step are as follows:
Figure GDA00029802851900000917
Figure GDA0002980285190000101
Figure GDA0002980285190000102
Figure GDA0002980285190000103
Figure GDA0002980285190000104
Figure GDA0002980285190000105
Figure GDA0002980285190000106
Figure GDA0002980285190000107
mi，u(n.DELTA.0 or 1
Figure GDA0002980285190000108
Wherein m isi，u(n Δ) is a variable from 0 to 1, and when m is 1, the number of people in the system is greater than the system capacity; m is a real number; fBCalculating formula for queuing overflow times
Figure GDA0002980285190000109
Not allowing the maximum number of overflows to be exceeded
Figure GDA00029802851900001010
Figure GDA00029802851900001011
The number of people staying at the platform is not allowed to exceed the maximum number of people staying
Figure GDA00029802851900001012
Under the passenger flow control scheme, the time-varying arrival rate of passengers in the direction of i station u is calculated by the following formula:
Figure GDA00029802851900001013
wherein,
Figure GDA00029802851900001014
indicating a normal time-varying arrival rate.
S15, constructing a passenger flow control optimization objective function by taking the minimum passenger travel time as a target according to the passenger flow control constraint condition; the determined passenger flow control objective function is:
Figure GDA00029802851900001015
wherein T isSThe sum of the time spent by the passengers on trips.
S2, solving the urban rail transit passenger flow control optimization model based on the fluid queuing network, which comprises the following steps:
s21, processing the passenger flow control decision variable by using a real number coding method to generate a parent population, and calculating a population individual objective function;
s22, judging whether the population individual target function meets a preset termination condition; if so, ending the operation to obtain an optimal individual; if not, performing the next step;
s23, selecting the population by adopting a roulette method, and carrying out crossing and mutation treatment on the population by utilizing an IAGA crossing probability method and a self-adaptive mutation probability method;
the calculation formula of the IAGA cross probability operator and the mutation probability algorithm is specifically as follows:
Figure GDA0002980285190000111
Figure GDA0002980285190000112
wherein, PcAnd PmRespectively cross probability and varianceProbability of anomaly, PcmaxAnd PcminUpper and lower limits of the crossover probability, P, respectivelymmaxAnd PmminUpper and lower limits of the probability of variation, FavgAnd FmaxRespectively are the average fitness value and the maximum fitness value in the current population, F is the fitness value in the crossed individual, and A is an arbitrary constant.
S24, implementing the optimal storage strategy for the group, and returning to the step S22; the implementation of the optimal storage strategy for the group specifically comprises the following steps:
traversing individuals with highest fitness and individuals with lowest fitness in the current group, and judging whether the fitness of the individuals with highest fitness in the current group is higher than the highest fitness of the individuals in all the groups; if so, taking the best individual in the current group as the individual with the highest fitness in all generation groups; and if not, replacing the individuals with the highest fitness in all the generation groups with the individuals with the lowest fitness in the current generation group.
The invention overcomes the problem that the traditional passenger flow control scheme is dependent on subjective experience and lacks of systematic and scientific theoretical support, and establishes a passenger flow control optimization model by combining a fluid queuing network model on the basis of the urban rail transit passenger flow control scheme and fully considering the safety, the service level and the trip time cost of passengers. Compared with the traditional passenger flow control optimization method, the model effectively reduces the travel time cost of passengers, reduces the congestion condition in the urban rail transit network, and effectively improves the service level of the system.
The analysis is performed by taking the urban rail transit network as an example, and the urban subway parameters are shown in table 1.
The train operation diagram is a technical file for representing the train operation in the section and the arrival, departure and passing time of the station, and is determined by departure interval time, stop time of different stations and section operation time. In this example, all train section running times, i.e., 15 time steps, stop times, i.e., 3 time steps, are set, and the initial departure interval is set to, i.e., 21 time steps. And generating an initial train operation diagram through the data.
TABLE 1 Chengdu subway case parameter calibration
Figure GDA0002980285190000113
Figure GDA0002980285190000121
According to the OD matrix of the passengers going out of the urban rail transit, combining the established fluid queuing network model and the passenger flow control optimization model, carrying out passenger flow control optimization on the urban rail transit network, wherein the population evolution process is shown in figure 3; after the total travel time of passengers is calculated, the results before and after optimization are compared and analyzed, the optimization before and after station external current limiting scheme pair is shown in fig. 4, and the optimization result of the train operation diagram is shown in fig. 5. Through analysis, the system state of the waiting queuing system on the platform before and after optimization and the queuing state on the train are respectively shown in fig. 6 and fig. 7, and the optimization result is shown in table 2.
TABLE 2 Chengdu subway case passenger flow control optimization results
Figure GDA0002980285190000122
According to the optimization result, the average waiting time in the uplink direction is reduced from 9.62min to 2.15min, 77.63% is optimized, and passengers who are not completely transported in the train set are eliminated. The average waiting time in the uplink direction is reduced from 2.16min to 1.89min, and the optimization is 12.49%. The average waiting time of passengers in the system is reduced to a lower level, the average waiting time of the passengers in the descending direction of the Tianfu wide-field station is reduced to 2.46min by 21.54min, the optimization effect is extremely obvious, the main reason is that the problem of service rate reduction caused by the system state is basically eliminated by optimizing the passenger flow control and departure interval, the departure interval time is reduced in the passenger flow arrival peak period, the train operation capacity in unit time is improved, and the possibility of platform queue overflow and queue explosion is reduced.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (7)

1. A method for controlling and optimizing urban rail transit passenger flow based on a fluid queuing network is characterized by comprising the following steps:
s1, establishing an urban rail transit passenger flow control optimization model based on a fluid queuing network, which specifically comprises the following steps:
s11, obtaining passenger travel OD data, the station number of subway lines, the station mileage, the train number and the subway station platform capacity parameters;
s12, describing the trains on the subway line and the channels and platform systems in the stations according to the data acquired in the step S11, abstracting to corresponding fluid queuing models, and constructing an urban rail transit fluid queuing network model;
s13, determining a passenger flow control decision variable according to the passenger travel OD data;
s14, determining passenger flow control constraint conditions according to the passenger flow control decision variables and the queuing network model output indexes;
s15, constructing a passenger flow control optimization objective function by taking the minimum passenger travel time as a target according to the passenger flow control constraint condition;
s2, solving the urban rail transit passenger flow control optimization model based on the fluid queuing network, which comprises the following steps:
s21, processing the passenger flow control decision variable by using a real number coding method to generate a parent population, and calculating a population individual objective function;
s22, judging whether the population individual target function meets a preset termination condition; if so, ending the operation to obtain an optimal individual; if not, performing the next step;
s23, selecting the population by adopting a roulette method, and carrying out crossing and mutation treatment on the population by utilizing an IAGA crossing probability method and a self-adaptive mutation probability method;
s24, the optimal storage strategy is implemented to the group, and the step returns to the step S22.
2. The method for optimizing urban rail transit passenger flow control based on fluid queuing network according to claim 1, wherein the fluid queuing model is obtained by the following steps of step S12:
s121, establishing a platform waiting queuing model: for the boarding queuing system with the capacity of C in the boarding and landing area, passengers become a passenger flow input source in the boarding and landing area after passing through the entrance gate; the arrival process of passengers follows a time-varying poisson distribution Mt(ii) a The waiting time of passengers is distributed randomly, and the influence of the state of the system on the service process is considered, and is recorded as G (x), wherein x is the system state of the boarding queuing system in the boarding and alighting area, namely the number of passengers in the system; if the number of passengers in the system is larger than the capacity of the system, the passengers will overflow and stay in the station hall, the capacity of the station hall is infinity, and the number of passengers is marked as M according to a Kendall notation methodt/G(x)/C/C+∞；
For any time t, the u-direction waiting queuing system state of the ith station
Figure FDA0003516388800000011
Comprises the following steps: initial state of system
Figure FDA0003516388800000012
Plus the number of passengers entering minus passengers exiting, i.e.:
Figure FDA0003516388800000013
the rate of change of system state is:
Figure FDA0003516388800000021
wherein
Figure FDA0003516388800000022
The arrival rate of passengers is determined by the arrival rate of passengers at the time t in the u direction of the station i; when u is 1, the uplink is performed, and when u is 2, the downlink is performed; the arrival of passengers follows Poisson distribution, so the arrival rate of the passengers at the time t in the u direction of the station i is recorded as
Figure FDA0003516388800000023
The input rate of passengers getting on the train in the landing zone is determined by the passenger arrival rate at the station, and because the capacity is infinite, the blocking probability is not considered, so that:
Figure FDA0003516388800000024
output rate of passengers based on speed of passengers affected by system state
Figure FDA0003516388800000025
And (3) calculating:
Figure FDA0003516388800000026
wherein PT is the probability of train stop, and PT is 1, and is the train stop; l represents the station length; passenger speed in u-direction waiting queuing model of ith station
Figure FDA0003516388800000027
The calculation formula is as follows:
Figure FDA0003516388800000028
wherein:
Figure FDA0003516388800000029
given by historical data
Figure FDA00035163888000000210
Calibrating three standard points to calculate speed
Figure FDA00035163888000000211
Probability of being idle of system
Figure FDA00035163888000000212
And the system state changes, the output rate of the system occupant is therefore:
Figure FDA00035163888000000213
obtained according to the PSFFA method
Figure FDA00035163888000000214
The calculation formula of (a) is as follows:
Figure FDA00035163888000000215
wherein:
Figure FDA00035163888000000216
also given by historical data
Figure FDA00035163888000000217
Calibrating the three standard points to obtain the three standard points;
three dynamic performance indexes are established: respectively the real-time output rate of the system
Figure FDA00035163888000000218
Average occupied space
Figure FDA00035163888000000219
Mean residence time
Figure FDA00035163888000000220
The calculation formula is as follows:
Figure FDA0003516388800000031
Figure FDA0003516388800000032
Figure FDA0003516388800000033
y is residence time;
s122, train queuing model: the train is used as a carrier for passenger transportation, acts as a transportation task, a queuing phenomenon appears in each train, and a queuing system for train service is abstracted into a single virtual service desk M _ t/G (x)/1/C queuing model; according to the concept of fluid queuing, at the time t, the system state calculation formula of the kth train in the u direction is as follows:
Figure FDA0003516388800000034
wherein
Figure FDA0003516388800000035
Arrival rate of k-th train passenger in u-direction at time t
Figure FDA0003516388800000036
Output rate of waiting queuing model
Figure FDA0003516388800000037
And the connection probability PT between the station and the traini，k(t) determining:
Figure FDA0003516388800000038
TR is a train set;
output rate for train passengers getting off
Figure FDA0003516388800000039
Figure FDA00035163888000000310
Wherein
Figure FDA00035163888000000311
twTime of alighting for passengers, ηk，u，j(t) is the proportion of passengers getting off the train at the j station of the kth train, and is determined by the OD data obtained by the S11;
the three dynamic performance indexes of the train queuing model are respectively the system output rate at any moment
Figure FDA00035163888000000312
Passengers occupying system space
Figure FDA00035163888000000313
Mean residence time of passengers
Figure FDA00035163888000000314
The calculation formula is as follows:
Figure FDA00035163888000000315
Figure FDA00035163888000000316
Figure FDA00035163888000000317
where CT represents the capacity of the train.
3. The method for optimizing urban rail transit passenger flow control based on fluid queuing network according to claim 2, wherein the passenger flow control decision variable determined in step S13 is the proportion of inbound passenger flow at each time t
Figure FDA0003516388800000041
And departure interval H of the k-th train in the u directionk，u(ii) a The passenger flow control decision variables satisfy the following constraints:
Figure FDA0003516388800000042
Figure FDA0003516388800000043
wherein HlbAnd HubRespectively the minimum value and the maximum value of the departure interval; Δ is the step length of each time step, S is a station set, a station i belongs to S ═ 1, 2.., N }, and N is the total number of stations; TR is a train set, a train k belongs to TR ═ 1, 2.., M }, and M is the total train amount; u is a set of train running directions, belongs to U which is {1, 2}, is an uplink when U is 1, and is a downlink when U is 2;
Figure FDA0003516388800000044
time step sequence index for time set
Figure FDA0003516388800000045
4. The method for optimizing urban rail transit passenger flow control based on fluid queuing network according to claim 3, wherein the passenger flow control constraint determined in step S14 is:
Figure FDA0003516388800000046
Figure FDA0003516388800000047
Figure FDA0003516388800000048
Figure FDA0003516388800000049
Figure FDA00035163888000000410
Figure FDA00035163888000000411
Figure FDA00035163888000000412
Figure FDA00035163888000000413
Figure FDA00035163888000000414
wherein m isi，u(n Δ) is a variable from 0 to 1, and when m is 1, the number of people in the system is greater than the system capacity; m is a real number; fBCalculating formula for queuing overflow times
Figure FDA00035163888000000415
Not allowing the maximum number of overflows to be exceeded
Figure FDA00035163888000000416
Figure FDA00035163888000000417
The number of people staying at the platform is not allowed to exceed the maximum number of people staying
Figure FDA00035163888000000418
Figure FDA00035163888000000419
Under the passenger flow control scheme, the time-varying arrival rate of passengers in the direction of i station u is calculated by the following formula:
Figure FDA00035163888000000420
wherein,
Figure FDA00035163888000000421
indicating a normal time-varying arrival rate.
5. The method for optimizing urban rail transit passenger flow control based on fluid queuing network according to claim 4, wherein the passenger flow control objective function determined in step S15 is:
Figure FDA0003516388800000051
wherein T isSThe sum of the time spent by the passengers on trips.
6. The urban rail transit passenger flow control optimization method based on the fluid queuing network as claimed in claim 1, wherein the calculation formula of the IAGA cross probability operator and the mutation probability algorithm in step S23 is specifically:
Figure FDA0003516388800000052
Figure FDA0003516388800000053
wherein, PcAnd PmRespectively cross probability and mutation probability, PcmaxAnd PcminUpper and lower limits of the crossover probability, P, respectivelymmaxAnd PmminUpper and lower limits of the probability of variation, FavgAnd FmaxRespectively are the average fitness value and the maximum fitness value in the current population, F is the fitness value of the individual in the cross population, and A is an arbitrary constant.
7. The urban rail transit passenger flow control optimization method based on the fluid queuing network as claimed in claim 1, wherein said step S24 of implementing the optimal conservation strategy for the group specifically comprises:
traversing individuals with highest fitness and individuals with lowest fitness in the current group, and judging whether the fitness of the individuals with highest fitness in the current group is higher than the highest fitness of the individuals in all the groups; if so, taking the best individual in the current group as the individual with the highest fitness in all generation groups; and if not, replacing the individuals with the highest fitness in all the generation groups with the individuals with the lowest fitness in the current generation group.
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