CN111402605B - Traffic capacity model optimization-based signal control method for borrowing left turn of opposite lane - Google Patents

Traffic capacity model optimization-based signal control method for borrowing left turn of opposite lane Download PDF

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CN111402605B
CN111402605B CN202010215384.4A CN202010215384A CN111402605B CN 111402605 B CN111402605 B CN 111402605B CN 202010215384 A CN202010215384 A CN 202010215384A CN 111402605 B CN111402605 B CN 111402605B
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lane
turn
phase
signal
vehicles
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CN111402605A (en
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童蔚苹
袁诗琳
刘志远
王健
徐志红
潘晓玮
沈学芳
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Southeast University
CCDI Suzhou Exploration and Design Consultant Co Ltd
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CCDI Suzhou Exploration and Design Consultant Co Ltd
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    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/07—Controlling traffic signals
    • G08G1/08—Controlling traffic signals according to detected number or speed of vehicles
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G08G1/0129—Traffic data processing for creating historical data or processing based on historical data
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G08G1/0133—Traffic data processing for classifying traffic situation
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0137—Measuring and analyzing of parameters relative to traffic conditions for specific applications
    • G08G1/0145—Measuring and analyzing of parameters relative to traffic conditions for specific applications for active traffic flow control
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/065—Traffic control systems for road vehicles by counting the vehicles in a section of the road or in a parking area, i.e. comparing incoming count with outgoing count
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention discloses a traffic capacity model optimization-based signal control method for borrowing left turn of a lane, which comprises the following steps: step 1: performing canalization design and signal control scheme design on the intersection for left turning by lane; step 2: on the basis of step1, the lane length L for turning left of the opposite lane is usedcAnd selecting the signal duration of the pre-signal phase P1, establishing an optimization model with the maximum traffic capacity as a target, and finding the length L of the left-turn lane of the borrowed lane with the maximum traffic capacity of the intersection under the schemecAnd the signal duration of P1. The invention can improve the traffic capacity of the left-turning motor vehicle, reduce the delay of the entrance lane and improve the overall operation efficiency of the intersection.

Description

Traffic capacity model optimization-based signal control method for borrowing left turn of opposite lane
The technical field is as follows:
the invention relates to a traffic capacity model optimization-based signal control method for borrowing left turn of a lane, belonging to the technical field of traffic management and control.
Background art:
as a key node and a bottleneck of an urban road, the traffic capacity of the intersection determines and restricts the traffic efficiency of an urban road network. In a limited intersection facility space, traffic flow is guided and evacuated, space-time resources are reasonably distributed, the supply capacity of the intersection is improved, and the urban traffic transportation management system is urgent.
In the intersection, the conflict between the left-turn traffic flow and the opposite-direction straight-going traffic flow as well as the adjacent-direction straight-going traffic flow is an important factor influencing the running efficiency of the whole intersection, and particularly at the intersection with large left-turn traffic flow, the traffic flow conflict and the queuing congestion caused by vehicle detention seriously restrict the traffic capacity of the intersection. In response to the above, management departments and research scholars propose irregular countermeasures to reduce the conflict between the left-turn traffic and the straight-going traffic or reorganize the traffic right of each direction, thereby improving the traffic capacity and service level at the intersection. Esawey and the like summarize the advantages, the disadvantages, the applicability, the research status and the evaluation methods of the channelized modes of more than ten unconventional main line intersections such as the traditional U-shaped lane (MUT), the special U-shaped lane, the super middle lane (SSM), the loop-shaped lane, the pot-shaped lane and the like, and indicate that delay analysis and safety analysis are the most common evaluation modes in intersection optimization research. The adult, Bie Y and the like propose a hook-shaped bend design at the intersection of the tramcar and optimization based on delay analysis, and a traffic organization method for completing turning by a left-turn car through a right-side entrance lane is adopted, so that the space-time separation of the left-turn motor vehicle, a straight-going motor vehicle and the tramcar is realized, and the conflict among the types of traffic flows is avoided. The lane-borrowing left turn is a traffic organization mode which can ensure that more left-turn vehicles can quickly pass through the intersection and turn left to an exit lane under the condition that the existing lane arrangement of the intersection is basically unchanged, and is practically applied to the areas of Handan, peaceful and luxury, Kunming and the like in China in recent years. The method is suitable for intersections with special left-turn signal phases and large left-turn traffic flow, and improves available space-time resources of left-turn traffic in the intersections by arranging the variable lane openings between the pre-signal lamps and the inlet and outlet lanes. But the open lane by-pass lanes under study are not utilized to the maximum extent of time.
Generally speaking, most of the current researches on the left turn-by-lane are on the level of applicability and practicability, and the design of a signal control scheme is mostly based on the traditional intersection signal control scheme, so that the pre-signal is numerically adjusted, and scientific basis is lacked.
The invention content is as follows:
the invention aims to provide a left-turn signal control method for a borrowing lane based on traffic capacity model optimization, aiming at carrying out signal control under a left-turn organization scheme for the borrowing lane at an intersection, optimizing a signal timing scheme by taking the maximum traffic capacity of the intersection as a target, and finally carrying out result verification through a VISSIM simulation experiment to verify the optimization effect of the control method.
The above object of the present invention can be achieved by the following technical solutions:
a signal control method for borrowing a left turn of a lane based on traffic capacity model optimization comprises the following steps:
step 1: performing canalization design and signal control scheme design on the intersection for left turning by lane;
step 2: on the basis of step1, the lane length L for turning left of the opposite lane is usedcAnd selecting the signal duration of the pre-signal phase P1, establishing an optimization model with the maximum traffic capacity as a target, and finding the length L of the left-turn lane of the borrowed lane with the maximum traffic capacity of the intersection under the schemecAnd the signal duration of P1.
The traffic capacity model optimization-based signal control method for left-turn lane borrowing comprises the following specific steps of 1:
setting the inner lane of the exit lane in the south-north direction as a variable borrowing left-turning lane, setting a pre-signal lamp at the upstream of the entrance lane in the south-north direction to control left-turning vehicles to enter the opposite lane, and enabling the opening of the lane to be away from a stop line LcThe existing timing scheme is used for main signal phase timing: the phase sequence is as follows: m1 is a left-turn phase in the north-south direction, M2 is a straight-going phase in the north-south direction, M3 is a left-turn phase in the east-west direction, M4 is a special phase for buses in the north-south direction, M5 is a straight-going phase in the east-west direction, a pre-signal P1 is started when gamma seconds remain in the later stage of the special phase M4 for the buses, the left-turn vehicles are allowed to run into and use an opposite lane by taking 2 seconds from the full red time of the phase M4, and the left-turn vehicles in the left-turn lane and the left-turn lane of the original entrance lane are both used for realizing left turn in the main signal left-turn phase M1; prenoticeThe phase P1 should be x seconds earlier than the main signal phase M1.
The method for controlling the signal for the left turn of the borrowed lane based on the optimization of the traffic capacity model comprises the steps of establishing the optimization model with the maximum traffic capacity as the target in the step2, and finding out the length L of the left turn lane of the borrowed lane with the maximum traffic capacity at the intersection under the schemecAnd P1 are the following specific methods:
step 2.1: the traffic capacity of the single lane group of the intersection entrance way is obtained by the following formula:
ci＝si*Ge/C (1)
wherein s isiRepresenting the saturation flow rate of the lane group i in units of veh/h/ln; geThe unit of the effective green light time representing the signal phase of the lane group steering is s; c represents the total signal period of the intersection, and the unit is s;
in the intersection, the straight lane group and the bus lane group are not influenced by the setting of the left-turn lane of the borrowed lane and are directly calculated by the formula; the traffic capacity of the left-turn lane group consists of an original left-turn lane and a left-turn lane for borrowing, and the traffic capacity calculation expression is as follows:
cl＝cl0+cl1 (2)
wherein c isl0The capacity of the original left-turn lane is cl1The lane left-turn traffic capacity is borrowed;
the traffic capacity of the original left-turn lane is calculated by an HCM formula:
cl0＝sl0*Gle/C (3)
wherein s isl0Representing the saturated flow rate of the original left-turn lane, and the unit is veh/h/ln; gleThe effective green time, in units of s, represents the phase of the left turn signal.
The traffic capacity of a left-turn lane consists of two parts: maximum number of vehicles N queued in advance in the lane and dispersed in the left-turn phase of the main signal1Maximum number of vehicles entering the lane and leaving at the dissipation speed N within the left-turn phase of the main signal2；
The maximum number of vehicles which enter the lane in advance and are queued up and dispersed in the main signal left-turn phase is:
Figure BDA0002422969470000031
wherein q iscThe number of vehicles which can be accommodated at most in the entrance lane of the left-turn lane of the lane borrowing, namely the number of vehicles which can be accommodated from the stop line to the left-turn opening of the lane borrowing in the original left-turn lane, is represented by LcIt is decided that,
Figure BDA0002422969470000032
Q1the number of left-turn vehicles which reach the intersection before the left-turn main signal lamp is started; q. q.ssThe number of left-turn vehicles staying in the original left-turn lane in the previous period is counted;
the number of left-turn vehicles which reach the intersection after the left-turn main signal lamp is started is Q2The maximum number of vehicles entering the left-turn lane of the lane loaning and leaving at the dissipation speed in the left-turn phase of the main signal is as follows:
Figure BDA0002422969470000033
wherein χ is the time that the pre-signal phase of the left-turn lane is earlier than the main phase, and the unit is s; scRepresenting the saturated flow rate of the left-turn lane by the lane, and the unit is veh/h/ln;
based on equation (3), the total capacity of the left-turn lane can be calculated by the following expression:
Figure BDA0002422969470000034
Figure BDA0002422969470000035
Figure BDA0002422969470000036
wherein p is1Is qc-qs＜Q1＜2qc-qsProbability of p2Is Q1＞2qc-qsThe probability of (d); p is a radical of3Is Q2＜sl0*Gle+sc*(Gle-x) probability, p4Is Q2＞sl0*Gle+sc*(Gle-a probability of χ); p is a radical of1、p2And p3、p4Calculating by Poisson distribution probability density function according to actual conditions, Q1＜qc-qsNeglecting the probability of p1+p2Equal to 1; p is a radical of3+p4Equal to 1, the above equation (8) is further simplified to:
Figure BDA0002422969470000041
step 2.2: establishing a traffic capacity maximization model:
in order to ensure that all vehicles entering the left-turn lane of the borrowed lane can be emptied before the left-turn phase of the main signal is finished, and the operation of other phases is not influenced, the following constraint conditions are required to be met:
qc≥p1*(Q1-qc+qs)+p2*qc (10)
sc*Gle≥qc+sc*(Gle-χ) (11)
the formula (10) ensures that the vehicles entering the left-turn lane of the borrowed road are queued and cannot overflow, and the formula (11) ensures that the vehicles entering the left-turn lane of the borrowed road can be completely emptied in time;
let the number of left-turn vehicles that can pass through the left-turn lane in one signal period in equation (9) be Z, then Z satisfies:
Figure BDA0002422969470000042
then P (x), P (y) are calculated by Poisson distribution probability density function formula:
Figure BDA0002422969470000043
wherein λ is an expected value of a left turn vehicle arrival rate;
the probability density function is taken into equation (12):
Figure BDA0002422969470000044
the traffic capacity maximization problem can be converted into a solving problem of solving the Z maximum value under the condition that the formula (14) is used as an objective function and the constraints of the formulas (10) and (11) are met, and under the lane borrowing left-turn scheme, left-turn vehicles staying in the original left-turn lane in the previous period can be emptied in a preset mode, namely q is equal to qsWhen 0, Z satisfies the following relationship:
Figure BDA0002422969470000051
the formula (10) can be collated as follows:
Figure BDA0002422969470000052
the formula (11) can be obtained by arranging:
sc*χ≥qc (17)
therefore, Z must also satisfy the following relationship:
Figure BDA0002422969470000053
maximum value of Z is given by sc*(Gle- χ) is a variable, the algorithm for maximizing the formula (18) is solved, and Z is solved by an iterative algorithm, wherein the specific iterative steps are as follows:
step 1: initializing, namely substituting parameters such as a left-turn vehicle arrival rate, a left-turn lane saturation flow rate and a signal control scheme into a formula (18), and enabling the iteration number n to be 1;
step 2: python is used to call the gradient descent extreme function and solve s which maximizes the equation (18)c*(Gle- χ) and ZmaxLet Zmax＝Zn；
Step 3: according to formula (17), Z is obtainedmaxQ in case ofcA maximum value;
step 4: verifying whether the constraints in the formulas (10) and (11) are met, and if so, determining a balanced solution; if not, let n be n +1, return to Step 2.
Has the advantages that:
the invention provides a left-turn lane borrowing improvement scheme and a corresponding signal control scheme. The left-turn traffic capacity is disassembled by analyzing and setting the arrival rule of left-turn vehicles at the left-turn intersection of the borrowed lane, and a universal left-turn lane traffic capacity formula of the single-entrance lane of the left-turn intersection of the borrowed lane is established. Then, in order to ensure that the traffic capacity of the left-turn lane is maximized and the influence on other lanes is avoided, a left-turn lane traffic capacity maximization model based on the length of the left-turn lane and the time length of the left-turn phase of the lane is established. And finally, by combining the examples, the formula and the model are verified by solving the model and developing a simulation experiment. The result shows that the lane-borrowing left-turn scheme has better applicability at the intersection with larger left-turn flow, has obvious effect of improving the traffic capacity, has less influence on other lanes and the entrance lane, and is an intersection traffic signal control means easy to implement.
Description of the drawings:
fig. 1 is a layout and phase allowance diagram of an intersection, wherein the intersection after left-turning of a borrowed lane is arranged in the current intersection in fig. 1(a) and fig. 1 (b).
Fig. 2 is a left turn vehicle arrival-departure space-time diagram.
FIG. 3 is a graph showing the results of the calculation.
Fig. 4 is a diagram of an intersection control simulation experiment process in the embodiment of the present invention, in which fig. 4(a) is a simulation interface of an original intersection, and fig. 4(b) is a simulation interface of an intersection after a left-turn lane is set.
The specific implementation mode is as follows:
the invention is described in further detail below with reference to the figures and the specific embodiments.
As shown in fig. 1, the traffic capacity model optimization-based signal control method for borrowing left turn of lanes of the invention is described by taking a national road-ten catalpic street intersection in the ministry of the Suzhou city, wherein the national road in the south and north direction of the intersection is a main road, the bidirectional seven lanes are provided, the outermost side of the intersection is a bus lane, and the intersection is shared by the right turn social vehicles; the east-west direction is a secondary trunk road, five bidirectional lanes are arranged, and machine-non separation belts are arranged in four directions. The intersection current layout is shown in fig. 1 (a). The current traffic flow survey shows that the traffic flow of the south-north entrance way exceeds 1000pcu/h during the peak time of the intersection, and the traffic flow of the south-entrance way turning left is up to 351 pcu/h. In the current signal scheme, as shown in fig. 1(a) and table 1, under control, the saturation of the lane turning left from south to north is high, and queuing often occurs; intersection service level is lower, and vehicle delay is great. In addition, the buses in the north-south direction have a special signal phase M5, but since the buses which go straight and turn left share a lane with the traffic flow of the right turn, the buses which go straight and turn left can influence the social vehicles which turn right, and the social vehicles which turn right can also occupy the phase resource of M5. Based on the current operation state, the method comprises the following steps:
step 1: performing canalization design and signal control scheme design on the intersection for left turning by lane;
as shown in fig. 1(b), the lane at the inner side of the exit lane in the north-south direction is set as a variable-loaning left-turn lane, a pre-signal lamp is arranged at the upstream of the entrance lane to control left-turn vehicles to enter an opposite lane, and the opening of the lane is far away from a stop line Lc. As shown in FIG. 1(b), to fully utilize the signal phase resource, the pre-signal P1 is turned on when the gamma seconds remain in the later phase M4 dedicated for buses, allowing the left-turn vehicle to enter and use the opposite lane, the left-turn lane and the original lane
Left-turning vehicles entering the left-turning lane collectively make a left turn within the master signal left-turn phase M1. In order to avoid the influence of the left-turn traffic staying in the lane on the oncoming straight traffic, the pre-signal phase P1 should be earlier than the main signal phase M1 by x seconds. Because the running conditions of other flow-direction traffic flows except the left-turn traffic flow of the north-south approach are still available, the existing timing scheme is used for main signal phase timing, and only the phase sequence is adjusted (see table 1). The main signal phase timing adopts the existing timing scheme (M1 is a straight phase in the north-south direction and has the duration of 65 seconds, M2 is a left-turn phase in the north-south direction and has the duration of 30 seconds, M3 is a straight phase in the east-west direction and has the duration of 45 seconds, M4 is a left-turn phase in the east-west direction and has the duration of 30 seconds, M5 is a special phase for buses in the north-south direction and has the duration of 10 seconds), and only the phase sequence is adjusted to be: m1 is the left turn phase in the north-south direction, M2 is the straight phase in the north-south direction, M3 is the left turn phase in the east-west direction, M4 is the bus-dedicated phase in the north-south direction, and M5 is the straight phase in the east-west direction. The pre-signal P1 is turned on when γ seconds remain in the later phase of the bus-specific phase M4 (the full red time of the phase M4 can be used, and γ takes 2 seconds).
TABLE 1 intersection early peak timing scheme
Phase position M1 M2 M3 M4 M5 Period of time
Duration(s) 65 30 45 30 10 180
Step 2: on the basis of step1, the lane length L for turning left of the opposite lane is usedcAnd selecting the signal duration of the pre-signal phase P1, establishing an optimization model with the maximum traffic capacity as a target, and finding the length L of the left-turn lane of the borrowed lane with the maximum traffic capacity of the intersection under the schemecAnd the signal duration of P1.
2.1, establishing a traffic capacity model:
according to the american manual for road capacity (HCM), the capacity of a single lane group at an intersection entrance lane can be obtained by the following formula:
ci＝si*Ge/C (1)
wherein s isiRepresenting the saturation flow rate of the lane group i in units of veh/h/ln; geThe unit of the effective green light time representing the signal phase of the lane group steering is s; and C represents the total signal period of the intersection and has the unit of s.
In the intersection, the straight lane group and the bus lane group are not influenced by the setting of the left-turn lane of the borrowed lane and can be directly calculated by the formula; the traffic capacity of the left-turn lane group consists of an original left-turn lane and a left-turn lane for borrowing, and the traffic capacity calculation expression is as follows:
cl＝cl0+cl1 (2)
wherein c isl0The capacity of the original left-turn lane is cl1The lane-borrowing left-turn lane traffic capacity.
As shown in the upper left-turn vehicle arrival-departure space-time diagram (limited by the space of the diagram, only the queuing case is shown), each polyline represents the trajectory of one vehicle. For the original left-turn lane, the vehicle stops for waiting after reaching the stop line and propagates backwards to form a queue; before a pre-signal lamp of a left-turn lane is turned on, vehicles queue in the original left-turn lane, after the pre-signal lamp is turned on, the vehicles after the opening of the left-turn lane are started, the queue dissipates, enter the left-turn lane and stop after reaching a stop line, and then stop for waiting to form a queue; after the main left-turning signal lamp is turned on, all left-turning vehicles are started to leave, and the queue dissipates. Therefore, the traffic capacity of the original left-turn lane is less influenced by the left-turn lane of the lane borrowing, and can be approximately calculated by an HCM formula:
cl0＝sl0*Gle/C (3)
wherein s isl0Representing the saturated flow rate of the original left-turn lane, and the unit is veh/h/ln; gleThe effective green time, in units of s, represents the phase of the left turn signal.
The left-turn lane uses part of the special phases of the buses and the east-west straight phases to enable the vehicles to enter the original opposite approach lane, and the dissipation rate is dissipated during the green light period of the left-turn phase of the main signal, and the dissipation rate can be approximately equivalent to the saturation flow rate of the original left-turn lane. However, in order to ensure timely dissipation of the left-turn vehicle on the loaning lane and prevent the vehicle from being detained to influence the straight-ahead vehicles in the north-south direction, the pre-signal of the left-turn lane on the loaning lane should be ended in advance and the length L of the entrance lane of the left-turn lane on the loaning lane is limitedcAnd all vehicles entering the lane can be ensured to be emptied before the south-north straight-driving phase is started. Thus, the capacity of a left-turn lane by lane consists of two parts: maximum number of vehicles N queued in advance in the lane and dispersed in the left-turn phase of the main signal1Maximum number of vehicles entering the lane and leaving at the dissipation speed N within the left-turn phase of the main signal2。
As lane change is required once when entering the borrowing left-turn lane, the left-turn vehicles can preferentially select the original left-turn lane for queuing by default under the condition that the original left-turn lane is not full of queues; and in the free dissipation stage, the original left-turn lane and the left-turn lane for borrowing are uniformly selected. The maximum number of vehicles which enter the lane in advance and are queued up and dispersed in the main signal left-turn phase is:
Figure BDA0002422969470000081
wherein q iscThe number of vehicles which can be accommodated in the entrance lane of the left-turn lane of the lane borrowing at most (namely the number of vehicles which can be accommodated from the stop line to the opening of the left-turn lane of the lane borrowing in the original left-turn lane is LcIt is decided that,
Figure BDA0002422969470000082
)；Q1the number of left-turn vehicles which reach the intersection before the left-turn main signal lamp is started; q. q.ssThe number of left turn vehicles left in the original left turn lane for the previous cycle.
The number of left-turn vehicles which reach the intersection after the left-turn main signal lamp is started is Q2The maximum number of vehicles entering the left-turn lane of the lane loaning and leaving at the dissipation speed in the left-turn phase of the main signal is as follows:
Figure BDA0002422969470000083
wherein χ is the time that the pre-signal phase of the left-turn lane is earlier than the main phase, and the unit is s; scRepresents the saturation flow rate of the left-turn lane by the lane, and has the unit of veh/h/ln.
The vehicle arrival at the intersection is distributed in a discrete mode, and Poisson distribution fitting is generally adopted empirically[17]. Therefore, based on equation (3), the total capacity of the left-turn lane can be calculated by the following expression:
Figure BDA0002422969470000091
Figure BDA0002422969470000092
Figure BDA0002422969470000093
wherein p is1Is qc-qs＜Q1＜2qc-qsThe probability of (a) of (b) being,p2is Q1＞2qc-qsThe probability of (d); p is a radical of3Is Q2＜sl0*Gle+sc*(Gle-x) probability, p4Is Q2＞sl0*Gle+sc*(Gle- χ). p is a radical of1、p2And p3、p4Can be calculated by a poisson distribution probability density function. Normally, the left-turn traffic flow at the intersection is large, and therefore, Q is1＜qc-qsHas a negligible probability of p1+p2Approximately equal to 1; p is a radical of3+p4Equal to 1. The above equation (8) can be further simplified as:
Figure BDA0002422969470000094
2.2, establishing a traffic capacity maximization model:
through the analysis of the left-turn traffic capacity, the main parameter for determining the traffic capacity is the number q of vehicles which can be accommodated by the entrance lane of the left-turn lane at most under the premise of determining the main signal control schemecAnd the time χ that the pre-signal phase of the left-turn lane is earlier than the main phase, and the vehicle emptying rule of the left-turn lane is also for qcAnd χ are limited. In order to ensure that all vehicles entering the left-turn lane of the borrowed lane can be emptied before the left-turn phase of the main signal is finished, and the operation of other phases is not influenced, the following constraint conditions are required to be met:
qc≥p1*(Q1-qc+qs)+p2*qc (10)
sc*Gle≥qc+sc*(Gle-χ) (11)
the formula (10) ensures that the vehicles entering the left-turn lane can not overflow, and the formula (10) ensures that the vehicles entering the left-turn lane can be completely emptied in time.
Let the number of left-turn vehicles that can pass through the left-turn lane in one signal period in equation (9) be Z, then Z satisfies:
Figure BDA0002422969470000095
assuming that the arrival of the vehicles turning left at the intersection obeys the poisson distribution, p (x), p (y) can be calculated by poisson distribution probability density function formulas:
Figure BDA0002422969470000101
where λ is the expected value for the left turn vehicle arrival rate.
The probability density function is taken into equation (12):
Figure BDA0002422969470000102
the traffic capacity maximization problem can be converted into a solving problem of solving the Z maximum value under the condition that the formula (14) is used as an objective function and the constraints of the formulas (10) and (11) are met. Under the lane borrowing left-turn scheme, it is preset that left-turn vehicles staying in the original left-turn lane in the previous period can be emptied, namely qsWhen 0, Z satisfies the following relationship:
Figure BDA0002422969470000103
the formula (9) can be obtained by arranging:
Figure BDA0002422969470000104
the formula (10) can be collated as follows:
sc*χ≥qc (17)
therefore, Z must also satisfy the following relationship:
Figure BDA0002422969470000105
Figure BDA0002422969470000111
based on the above discussion, the maximum value of Z can be determined by dividing by sc*(Gleχ) is a variable, and the algorithm that maximizes equation (18) is solved. The method adopts an iterative algorithm to solve, and the specific iterative steps are as follows:
step 1: initializing, namely substituting parameters such as a left-turn vehicle arrival rate, a left-turn lane saturation flow rate and a signal control scheme into a formula (17), and enabling the iteration number n to be 1;
step 2: python is used to call the gradient descent extreme function and solve s which maximizes the equation (18)c*(Gle- χ) and ZmaxLet Zmax＝Zn；
Step 3: according to formula (17), Z is obtainedmaxQ in case ofcA maximum value;
step 4: verifying whether the constraints in the formulas (10) and (11) are met, and if so, determining a balanced solution; if not, let n be n +1, return to Step 2.
In the intersection example of the present embodiment, sl0＝0.4(veh/s)，C＝180s，Gle＝25s，sc＝0.4(veh/s)，λ＝10pcu/min，
Figure BDA0002422969470000112
Substituting the parameters into equation (18) and solving the parameters by an algorithm can obtain s shown in the following figurec*(Gle-χ)-ZmaxRelationship diagram, ZmaxWith sc*(Gle- χ) increases and then decreases, at sc*(Gle-x) is 6, where x is 10s, qc≤scAnd x is 0.4 x 10 x 4, and the constraint condition is satisfied, namely the final solution of the model.
In addition, as can be seen from the graph, the change rate of the target function on the left side of the extreme point is smaller, and the change rate on the right side is larger, which indicates that when the time χ for early breaking of the phase of the pre-signal is larger, and even approaches the time for turning left to green light of the main signal, the left-turning traffic capacity is not greatly influenced by the time χ, and can be kept in a more stable level; when the pre-signal phase is early and late, the left turn traffic capacity is significantly negatively affected. The method is consistent with the actual running rule of the left-turn lane, and the left-turn lane mainly shares the queuing pressure of left-turn vehicles in the original left-turn lane, provides space-time resources for dissipating a motorcade, and provides a traffic service in a free flow stage or mainly takes the original left-turn lane as a main part.
In order to verify the lifting effect of the lane borrowing left-turn scheme on the running condition of the intersection, a signal control scheme before and after the lane borrowing left-turn is set at the intersection, traffic flow data and intersection facility data are input into a simulation experiment, simulation running parameters are output, the simulation environment is VISSIM 11.0, and the simulation time is 10 min.
The simulation output results are shown in table 2, and the main evaluation indexes are vehicle average delay and queue length. It can be seen that the south entrance of the original intersection has a greater delay than the north entrance due to the greater left-turn traffic flow, resulting in a serious queue. By arranging the left-turn lane, the delay of vehicles at the south entrance lane is obviously reduced, the queuing condition is obviously improved, and the method accords with the expectation. In addition, the embodiment only carries out the left turn modification on the south inlet channel, and the simulation result shows that the scheme has little influence on the north inlet channel without the left turn modification on the channel.
TABLE 2 simulation results
Figure BDA0002422969470000121
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.

Claims (2)

1. A traffic capacity model optimization-based signal control method for borrowing a left turn of a lane is characterized by comprising the following steps: the method comprises the following steps:
step 1: performing canalization design and signal control scheme design on the intersection for left turning by lane;
step 2: on the basis of step1, the lane length L for turning left of the opposite lane is usedcAnd selecting the signal duration of the pre-signal phase P1, establishing an optimization model with the maximum traffic capacity as a target, and finding the length L of the left-turn lane of the borrowed lane with the maximum traffic capacity of the intersection under the schemecAnd signal duration of P1;
establishing an optimization model with the maximum traffic capacity as a target in the step2, and finding out the length L of the left-turn lane of the borrowed lane with the maximum traffic capacity of the intersection under the schemecAnd P1 are the following specific methods:
step 2.1: the traffic capacity of the single lane group of the intersection entrance way is obtained by the following formula:
ci＝si*Ge/C (1)
wherein s isiRepresenting the saturation flow rate of the lane group i in units of veh/h/ln; geThe unit of the effective green light time representing the signal phase of the lane group steering is s; c represents the total signal period of the intersection, and the unit is s;
in the intersection, the straight lane group and the bus lane group are not influenced by the setting of the left-turn lane of the borrowed lane and are directly calculated by the formula; the traffic capacity of the left-turn lane group consists of an original left-turn lane and a left-turn lane for borrowing, and the traffic capacity calculation expression is as follows:
cl＝cl0+cl1 (2)
wherein c isl0The capacity of the original left-turn lane is cl1The lane left-turn traffic capacity is borrowed;
the traffic capacity of the original left-turn lane is calculated by an HCM formula:
cl0＝sl0*Gle/C (3)
wherein s isl0Representing the saturated flow rate of the original left-turn lane, and the unit is veh/h/ln; gleAn effective green time, in units of s, representing the phase of the left turn signal;
the traffic capacity of a left-turn lane consists of two parts: maximum number of vehicles N queued in advance in the lane and dispersed in the left-turn phase of the main signal1Maximum number of vehicles entering the lane and leaving at the dissipation speed N within the left-turn phase of the main signal2；
The maximum number of vehicles which enter the lane in advance and are queued up and dispersed in the main signal left-turn phase is:
Figure FDA0002975616610000021
wherein q iscThe number of vehicles which can be accommodated at most in the entrance lane of the left-turn lane of the lane borrowing, namely the number of vehicles which can be accommodated from the stop line to the left-turn opening of the lane borrowing in the original left-turn lane, is represented by LcIt is decided that,
Figure FDA0002975616610000022
Q1the number of left-turn vehicles which reach the intersection before the left-turn main signal lamp is started; q. q.ssThe number of left-turn vehicles staying in the original left-turn lane in the previous period is counted;
the number of left-turn vehicles which reach the intersection after the left-turn main signal lamp is started is Q2The maximum number of vehicles entering the left-turn lane of the lane loaning and leaving at the dissipation speed in the left-turn phase of the main signal is as follows:
Figure FDA0002975616610000023
wherein χ is the time that the pre-signal phase of the left-turn lane is earlier than the main phase, and the unit is s; scRepresenting the saturated flow rate of the left-turn lane by the lane, and the unit is veh/h/ln;
based on equation (3), the total capacity of the left-turn lane can be calculated by the following expression:
Figure FDA0002975616610000024
Figure FDA0002975616610000025
Figure FDA0002975616610000026
wherein p is1Is qc-qs＜Q1＜2qc-qsProbability of p2Is Q1＞2qc-qsThe probability of (d); p is a radical of3Is Q2＜sl0*Gle+sc*(Gle-x) probability, p4Is Q2＞sl0*Gle+sc*(Gle-a probability of χ); p is a radical of1、p2And p3、p4Calculating by Poisson distribution probability density function according to actual conditions, Q1＜qc-qsNeglecting the probability of p1+p2Equal to 1; p is a radical of3+p4Equal to 1, the above equation (8) is further simplified to:
Figure FDA0002975616610000031
step 2.2: establishing a traffic capacity maximization model:
in order to ensure that all vehicles entering the left-turn lane of the borrowed lane can be emptied before the left-turn phase of the main signal is finished, and the operation of other phases is not influenced, the following constraint conditions are required to be met:
qc≥p1*(Q1-qc+qs)+p2*qc (10)
sc*Gle≥qc+sc*(Gle-χ) (11)
the formula (10) ensures that the vehicles entering the left-turn lane of the borrowed road are queued and cannot overflow, and the formula (11) ensures that the vehicles entering the left-turn lane of the borrowed road can be completely emptied in time;
let the number of left-turn vehicles that can pass through the left-turn lane in one signal period in equation (9) be Z, then Z satisfies:
Figure FDA0002975616610000032
then P (x), P (y) are calculated by Poisson distribution probability density function formula:
Figure FDA0002975616610000033
wherein λ is an expected value of a left turn vehicle arrival rate;
the probability density function is taken into equation (12):
Figure FDA0002975616610000034
the traffic capacity maximization problem can be converted into a solving problem of solving the Z maximum value under the condition that the formula (14) is used as an objective function and the constraints of the formulas (10) and (11) are met, and under the lane borrowing left-turn scheme, left-turn vehicles staying in the original left-turn lane in the previous period can be emptied in a preset mode, namely q is equal to qsWhen 0, Z satisfies the following relationship:
Figure FDA0002975616610000041
the formula (10) can be collated as follows:
Figure FDA0002975616610000042
the formula (11) can be obtained by arranging:
sc*χ≥qc (17)
therefore, Z must also satisfy the following relationship:
Figure FDA0002975616610000043
maximum value of Z is given by sc*(Gle- χ) is a variable, the algorithm for maximizing the formula (18) is solved, and Z is solved by an iterative algorithm, wherein the specific iterative steps are as follows:
step 1: initializing, namely substituting parameters such as a left-turn vehicle arrival rate, a left-turn lane saturation flow rate and a signal control scheme into a formula (18), and enabling the iteration number n to be 1;
step 2: python is used to call the gradient descent extreme function and solve s which maximizes the equation (18)c*(Gle- χ) and ZmaxLet Zmax＝Zn；
Step 3: according to formula (17), Z is obtainedmaxQ in case ofcA maximum value;
step 4: verifying whether the constraints in the formulas (10) and (11) are met, and if so, determining a balanced solution; if not, let n be n +1, and return to Step 2.
2. The traffic-capacity-model-optimized signal control method for borrowing a left turn to a lane according to claim 1, wherein: the concrete method for performing channelized design and signal control scheme design for left-turn lane borrowing at the intersection in the step1 comprises the following steps:
setting the inner lane of the exit lane in the south-north direction as a variable borrowing left-turning lane, setting a pre-signal lamp at the upstream of the entrance lane in the south-north direction to control left-turning vehicles to enter the opposite lane, and enabling the opening of the lane to be away from a stop line LcThe existing timing scheme is used for main signal phase timing: the phase sequence is as follows: m1 is the left-turn phase in the north-south direction, M2 is the straight-ahead phase in the north-south direction, M3 is the left-turn phase in the east-west direction,m4 is a special bus phase in the north-south direction, M5 is a straight-ahead phase in the east-west direction, a pre-signal phase P1 is started when gamma seconds remain in the later stage of the special bus phase M4, the full red time of the M4 phase is utilized, gamma is taken for 2 seconds, a left-turning vehicle is allowed to drive into and use an opposite lane, and the left-turning vehicle in a left-turning lane of a borrowed lane and a left-turning vehicle in a left-turning lane of an original entrance lane are turned left in the main signal left-turning phase M1; the pre-signal phase P1 should be x seconds earlier than the main signal phase M1.
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