CN108708238B - Traffic optimization design method for road intersection in construction period - Google Patents
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Abstract
The invention discloses a traffic optimization design method for a road intersection in a construction period, which comprises a geometric design step and a signal control step of the intersection, wherein in the geometric design step, a comprehensive function area is arranged at an inlet where a road occupying construction intersection is positioned, so that traffic flows in different flow directions can be used in different phases of a signal period, a pre-stop line is arranged at the upstream of the traffic flow in a construction area, and whether the traffic flow is allowed to enter the comprehensive function area or not is controlled; in the signal control step, the main signal at the intersection adopts the signal phase arrangement of the anticlockwise single-opening release, the traffic flow in the comprehensive function area is ensured to enter in advance before the signal phase begins and to be emptied after the signal phase ends, the pre-signal control is carried out on a pre-stop line, the starting time and the ending time of the traffic flow in the inlet direction entering the comprehensive function area are controlled, and the signal timing parameters of the main signal and the pre-signal control are optimized through a linear programming model. The method effectively improves the traffic capacity of the road intersection by optimizing the geometric arrangement and signal control of the intersection.
Description
Technical Field
The invention relates to a traffic optimization design method for a road intersection in a construction period.
Background
Plane intersections are bottleneck nodes of urban road traffic, but due to the reasons of road reconstruction, pipeline arrangement, underground engineering construction and the like, lane occupation construction is usually required to be carried out within the range of the intersections, so that the number of lanes at the intersections is reduced, and the traffic capacity is seriously influenced. However, in order to eliminate the influence caused by construction, the current design mainly treats the residual road space except for the construction occupied area as a conventional intersection, and divides the lane function again, and a targeted optimization design method is not proposed for the characteristic that the number of the imported lanes is less than that of the lanes on the road section under the condition that the imported lanes of the intersection occupy the lane construction.
At present, traffic optimization design methods related to construction periods of urban road intersections mainly comprise the following steps:
1. the method comprises the steps of performing conventional signal control on intersection geometric design and signal control, wherein the geometric design comprises intersection stop line position design, lane function division, intersection widening section length design and the like; the urban road intersection design specifications GB50647-2011, the urban road engineering design specifications CJJ 37-2012 and the urban road intersection design specifications CJJ152-2010 in China have relevant regulations; the signal control includes signal phase sequence, period duration, green light time distribution and the like, and representative documents include urban traffic control, traffic management and control and the like. The design method for the conventional signal control intersection has a mature technical scheme at present.
2. The method comprises the following steps of designing the geometry of an intersection and controlling signals in a construction period, adjusting the signal timing of the intersection in documents such as organization optimization and signal control research in the construction period of a single-point main road intersection, and relieving traffic jam in the construction period by combining measures such as forbidding left traffic and one-way traffic of the intersection; for the setting of the road marking in the construction period, relevant regulations are made in the technical specification JGJ348-2014 for setting the road marking in the construction site of the constructional engineering so as to ensure the traffic operation safety. The intersection in the construction period is designed from the middle-micro angle, wherein the intersection signal timing is mainly adjusted according to the traffic demand and the change of the number of lanes of the intersection in the construction period, and the adjusting method mainly adopts a conventional intersection signal control method; the measures of forbidding left and one-way traffic, etc. need to have a corresponding shunting path as a support for taking forbidding measures for certain flow directions, and will result in the increase of vehicle detour and road network total kilometers.
3. The regional traffic organization optimization in the construction period, documents such as a large municipal engineering construction period traffic organization research, a mountain city core region rail traffic construction period traffic organization and the like search for a diversion road section in a construction peripheral road network from the angle of the whole road network in an influence region range, redistribute the traffic flow in the region around a construction point of the engineering, improve the service level of the road network in the influence region range while meeting the urban traffic demand of the urban road network, and reduce the negative influence on the peripheral region traffic caused by the construction to the maximum extent. The construction influence area range is optimized by adopting traffic organization from the road network layer, and the traffic flow of the area around the construction point of the project is redistributed by searching and optimizing the shunting road sections, so that the traffic pressure of the area around the construction point is reduced.
The technical scheme does not consider the characteristic that the number of the lanes at the intersection is less than that of the lanes on the road section under the lane occupying construction condition of the intersection, and the residual road space except the construction occupied area is used as the conventional intersection for treatment. The number of lanes at the intersection is obviously reduced due to the construction occupation, and meanwhile, due to the lack of targeted measures, the traffic capacity of the intersection is greatly influenced by the construction occupation, and the traffic capacity of the intersection is seriously influenced.
Disclosure of Invention
The invention aims to solve the technical problem of providing a traffic optimization design method for a road intersection in the construction period.
In order to solve the technical problems, the traffic optimization design method for the construction period of the road intersection comprises a geometric design step and a signal control step, wherein in the geometric design step, an integrated function area is arranged at an inlet of the intersection of a road occupying construction area, the integrated function area is used by traffic flows in different flow directions in different phases of a signal period, a pre-stop line is arranged at the upstream of the traffic flow of the construction area, and whether the traffic flow is allowed to enter the integrated function area or not is controlled; in the signal control step, the main signal at the intersection adopts the signal phase arrangement of the anticlockwise single-opening release, the traffic flow in the comprehensive function area is ensured to enter in advance before the signal phase begins and to be emptied after the signal phase ends, the start and end time of the traffic flow in the inlet direction entering the comprehensive function area is controlled by pre-signal control of a pre-stop line, and the signal timing parameters of the main signal and the pre-signal control are optimized through a linear programming model.
Further, the geometric design step comprises setting the number of lanes in the comprehensive function area, the length of the comprehensive function area and the functional division of lanes at the intersection;
the number of lanes in the comprehensive function area is the sum of available lanes at the entrance of the occupied road construction intersection minus 1, and the reserved lanes are special exit lanes for right-turning vehicles which enter the entrance and pass through the intersection;
the length of the comprehensive functional area is the sum of the length of the occupied construction area and the length of the lane gradient section, and is calculated according to the formula (1),
Li=lwi+lci(1)
in the formula: i is an intersection number, such as that i ═ 1 represents an east inlet, i ═ 2 represents a north inlet, i ═ 3 represents a west inlet, and i ═ 4 represents a south inlet; l isiFor the length of the integrated functional region, /)wiFor occupying the length of the construction area, /)ciThe length of a lane gradient section;
wherein: the length of the lane transition section is calculated according to the formula (2),
in the formula: v is the design vehicle speed, WiThe width of the lane is changed transversely;
and the intersection lane function is divided, when the comprehensive function area is used as an entrance lane, the lane function is divided by adopting lane driving direction signs, and n is respectively arranged from left to rightiELA left-turn lane, a straight left-mixed lane, niETA straight special lane, a straight right mixed lane, niERA right-turn lane, wherein: n isiEL、niET、niERCalculated by the formulas (3) to (5) respectively,
in the formula: n isiEL、niET、niERThe number of lanes dedicated for left turn, the number of lanes dedicated for straight run and the number of lanes dedicated for right turn, qiL、qiT、qiRTraffic volumes of left turn, straight run and right turn, qiTotal traffic at the inlet of the ith fork of the intersection, niThe number of lanes in the comprehensive functional area is the number of the lanes in the occupied construction site, and the number of the lanes in the import non-occupied construction site is the number of the lanes in the import construction site.
Further, the optimization target of the linear programming model during signal timing is that the intersection has the maximum vehicle throughput, which is expressed by the formula (6),
in the formula: z is the maximum throughput of vehicles at the intersection, mu is the flow coefficient of the intersection, q is the flow coefficient of the intersectioniThe total traffic volume of the inlet of the ith fork of the intersection;
the constraint conditions of the signal timing linear programming model comprise signal period duration, main signal timing, pre-signal timing and intersection saturation constraint;
the signal period duration constraint requires that the main signal and the pre-signal period duration are the same, and in a reasonable maximum and minimum signal period duration range, in order to ensure that the established model is a linear model, the reciprocal of the period is adopted for representation, as shown in a formula (7);
wherein ξ is the reciprocal of the signal period duration, CmaxAnd CminMaximum and minimum signal cycle durations, respectively;
the main signal timing is in a phase sequence of single-port release in the counterclockwise direction, and the green light starting time and the green signal ratio of each inlet of the main signal meet the requirements of formulas (8) to (10);
in the formula: giThe starting moment of the green light at the inlet of the ith branch of the main signal at the intersection is expressed by relative time in one signal period and is a number between 0 and 1; lambda [ alpha ]iThe green signal ratio of the ith fork inlet of the main signal at the intersection; i is the interval time of the green light;
the pre-signal timing is coordinated with the main signal, the traffic flow in any inlet direction can enter the comprehensive function area after the opposite straight traffic flow completely passes through the comprehensive function area, and the formula (11) is satisfied,
in the formula:the starting moment of the pre-signal green light for the ith fork entrance of the intersection is expressed by relative time in one signal period and is a number between 0 and 1, and LiThe length of the comprehensive functional area is shown, and V is the design vehicle speed;
the traffic flow in any direction of the inlet ensures that the vehicles entering the comprehensive function area pass through the intersection during the period of the green light of the main signal, and the main signal traffic capacity is larger than the pre-signal traffic capacity, namely the formula (12) is satisfied,
in the formula:for the i-th branch inlet of the intersection, the pre-signal green ratio, siThe main signal saturation flow rate is the inlet of the ith branch at the intersection,pre-signal saturation flow rate for the ith fork entry at the junction;
the vehicle passing the pre-stop line at the end of the pre-signal green light passes through the intersection before the end of the main signal green light, and equation (13) is satisfied,
the intersection saturation constraint requires that each inlet saturation does not exceed the maximum saturation limit and satisfies the equations (14) - (15),
in the formula: dmaxIs a maximum saturation limit.
The method for optimally designing the traffic during the construction period of the road intersection adopts the technical scheme, namely the method comprises a geometric design step and a signal control step of the intersection, wherein in the geometric design step, a comprehensive function area is arranged at an inlet of the intersection in a road occupying construction area, the comprehensive function area is used by traffic flows in different flow directions in different phases of a signal period, and a pre-stop line is arranged at the upstream of the traffic flow in the construction area to control whether the traffic flow is allowed to enter the comprehensive function area; in the signal control step, the main signal at the intersection adopts signal phase arrangement of single-port release in the anticlockwise direction, the traffic flow in the comprehensive function area is ensured to enter in advance before the signal phase begins and to be emptied after the signal phase ends, the start time and the end time of the traffic flow in the inlet direction entering the comprehensive function area are controlled by pre-signal control of a pre-stop line, and signal timing parameters of the main signal and the pre-signal control are optimized through a linear programming model. Aiming at the situation that part of lanes at the intersection are occupied, the method utilizes the characteristic that the number of lanes on a road section is not influenced by the occupied lane construction, optimizes the geometric arrangement and signal control of the intersection, and effectively improves the traffic capacity of the intersection on the basis of ensuring traffic safety.
Drawings
The invention is described in further detail below with reference to the following figures and embodiments:
FIG. 1 is a schematic diagram of a road intersection in the traffic optimization design method for the construction period of the road intersection;
FIG. 2 is a schematic diagram of geometrical conditions of an intersection of a road occupying construction road in practical application of the method.
Detailed Description
The embodiment is shown in figure 1, the traffic optimization design method for the construction period of the road intersection comprises a geometric design step and a signal control step of the intersection, wherein in the geometric design step, a comprehensive function area 2 is arranged at an entrance where the intersection of a road occupying construction area 1 is located, the comprehensive function area 2 is used by traffic flows in different flow directions in different phases of a signal period, a pre-stop line 3 is arranged at the upstream of the traffic flow of the construction area 1, and whether the traffic flow is allowed to enter the comprehensive function area 2 or not is controlled; in the signal control step, the main signal at the intersection adopts the signal phase arrangement of the anticlockwise single-opening release, the traffic flow in the comprehensive function area 2 is ensured to enter in advance before the signal phase begins and to be emptied after the signal phase ends, the signal control is performed on the pre-stop line 3, the starting time and the ending time of the traffic flow in the inlet direction entering the comprehensive function area 2 are controlled, and the signal timing parameters of the main signal and the pre-signal control are optimized through a linear programming model.
Preferably, the geometric design step comprises the steps of setting the number of lanes in the comprehensive function area 2, the length of the comprehensive function area 2 and the functional division of lanes at the intersection;
the number of lanes in the comprehensive function area 2 is the sum of available lanes at the entrance of the occupied road construction intersection minus 1, and the reserved lanes are special exit lanes for right-turning vehicles which enter the entrance and pass through the intersection;
the length of the comprehensive function area 2 is the sum of the length of the occupied construction area 1 and the length of the lane gradient section, and is calculated according to the formula (1),
Li=lwi+lci(1)
in the formula: i is an intersection number, such as that i ═ 1 represents an east inlet, i ═ 2 represents a north inlet, i ═ 3 represents a west inlet, and i ═ 4 represents a south inlet; l isiFor the length of the integrated functional region, /)wiFor occupying the length of the construction area, /)ciThe length of a lane gradient section;
wherein: the length of the lane transition section is calculated according to the formula (2),
in the formula: v is the design vehicle speed, WiThe width of the lane is changed transversely;
and the intersection lane function is divided, when the comprehensive function area 2 is used as an entrance lane, the lane function is divided by adopting lane driving direction signs, and n is respectively arranged from left to rightiELA left-turn lane, a straight left-mixed lane, niETA straight special lane, a straight right mixed lane, niERA right-turn lane, wherein: n isiEL、niET、niERCalculated by the formulas (3) to (5) respectively,
in the formula: n isiEL、niET、niERThe number of lanes dedicated for left turn, the number of lanes dedicated for straight run and the number of lanes dedicated for right turn, qiL、qiT、qiRTraffic volumes of left turn, straight run and right turn, qiTotal traffic at the inlet of the ith fork of the intersection, niThe number of lanes in the comprehensive functional area is the number of the lanes in the occupied construction site, and the number of the lanes in the import non-occupied construction site is the number of the lanes in the import construction site.
Preferably, the optimization goal of the linear programming model during signal timing is that the intersection has the maximum vehicle throughput, which is expressed by the formula (6),
in the formula: z is the maximum throughput of vehicles at the intersection, mu is the flow coefficient of the intersection, q is the flow coefficient of the intersectioniThe total traffic volume of the inlet of the ith fork of the intersection;
the constraint conditions of the signal timing linear programming model comprise signal period duration, main signal timing, pre-signal timing and intersection saturation constraint;
the signal period duration constraint requires that the main signal and the pre-signal period duration are the same, and in a reasonable maximum and minimum signal period duration range, in order to ensure that the established model is a linear model, the reciprocal of the period is adopted for representation, as shown in a formula (7);
wherein ξ is the reciprocal of the signal period duration, CmaxAnd CminMaximum and minimum signal cycle durations, respectively;
the main signal timing is in a phase sequence of single-port release in the counterclockwise direction, and the green light starting time and the green signal ratio of each inlet of the main signal meet the requirements of formulas (8) to (10);
in the formula: giThe starting moment of the green light at the inlet of the ith branch of the main signal at the intersection is expressed by relative time in one signal period and is a number between 0 and 1; lambda [ alpha ]iThe green signal ratio of the ith fork inlet of the main signal at the intersection; i is the interval time of the green light;
the pre-signal timing is coordinated with the main signal, the traffic flow in any inlet direction can enter the comprehensive function area 2 only after the opposite straight traffic flow completely passes through the comprehensive function area 2, and the formula (11) is satisfied,
in the formula:the starting moment of the pre-signal green light for the ith fork entrance of the intersection is expressed by relative time in one signal period and is a number between 0 and 1, and LiThe length of the comprehensive function area 2 is shown, and V is the design vehicle speed;
the traffic flow in any direction of the inlet ensures that the vehicles entering the comprehensive function area 2 pass through the intersection during the green period of the main signal, and the main signal traffic capacity is larger than the pre-signal traffic capacity, namely the formula (12) is satisfied,
in the formula:for the i-th branch inlet of the intersection, the pre-signal green ratio, siThe main signal saturation flow rate is the inlet of the ith branch at the intersection,pre-signal saturation flow rate for the ith fork entry at the junction;
the vehicle passing the pre-stop line at the end of the pre-signal green light passes through the intersection before the end of the main signal green light, and equation (13) is satisfied,
the intersection saturation constraint requires that each inlet saturation does not exceed the maximum saturation limit and satisfies the equations (14) - (15),
in the formula: dmaxIs a maximum saturation limit.
When the method is applied specifically, if a road-occupying construction area is arranged at an east inlet of a road intersection, the construction area 1 occupies 3 lanes, the length is 50m, the traffic volume of each flow direction of the intersection is shown in table 1, and the geometric conditions are shown in fig. 2. The method is applied to carry out geometric design and signal control optimization on the composite material, and is compared with the traditional design scheme. The design input parameters are as follows: maximum and minimum signal cycle duration CmaxAnd CminRespectively taking 120s and 60 s; taking the green light interval time I for 4 s; the main signal and pre-signal single lane saturation flow rates are 1800 veh/h; maximum saturation limit dmaxTaking 1.0; the width of each lane is 3.5 m; the design vehicle speed V is 30 km/h;
TABLE 1
The specific process is briefly described as follows:
step one, determining the number of lanes in an integrated function area 2 according to the geometric design steps of the method, wherein the east inlet is the inlet where the occupied construction area is located, the total number of available lanes is 5, the number of lanes in the integrated function area 2 is 4, and the leftmost lane is a special outlet lane for a left-side inlet right-turning vehicle;
step two, calculating the length of the comprehensive function area 2 according to the formula (1) and the formula (2), wherein the length of the comprehensive function area 2 is 110 m;
Li=lwi+lci(1)
wherein: l iswiThe length of the construction area is 50m, V is 30, Wi is 3 lanes and 3.5m wide lanes are 10.5, and the formula (2) is substituted, and L isci=302× 10.5.5/155 ═ 60.9m, where the integer is 60, then Li ═ 50+60 ═ 110.
Thirdly, dividing lane functions and respectively setting niELA left-turn lane, 1 left straight lane, niETA straight lane, 1 straight right lane, niERStraight lane, niEL、niET、niERCalculated by the formulas (3) to (5), respectively; the lane function division calculation result is shown in table 2, and the geometric design optimization result is shown in fig. 2;
TABLE 2
Number of lanes | Left-turn lane | Left straight lane | Straight special lane | Straight right lane | Special lane for right turn |
East import | 0 | 1 | 2 | 1 | 0 |
West imported goods | 0 | 1 | 2 | 1 | 0 |
|
1 | 1 | 0 | 1 | 0 |
|
1 | 1 | 0 | 1 | 0 |
Step four, carrying out signal timing according to the signal control step of the method, substituting the input parameter into formula (6) as an optimization target, using formulas (7) to (15) as a linear programming model of a constraint condition, and solving by adopting a simplex method or mathematical software (such as LINGO) to obtain a signal control scheme shown in table 3;
TABLE 3
Step five, evaluating a design scheme, namely comparing the traditional design scheme with the method by taking the maximum throughput of the motor vehicles at the intersection as an evaluation index; in the traditional design scheme, two signal timing modes of single-port amplification and double-loop control are adopted, and the calculation result is shown in a table 4; the method optimizes the geometric design and signal control of the intersection, improves the maximum throughput of motor vehicles at the intersection by 23.6 percent and 9.1 percent respectively compared with two signal timing methods of single-opening discharge and double-loop control, and improves the traffic efficiency of vehicles at the intersection.
TABLE 4
Compared with the prior art, the method has the following advantages and beneficial effects:
1. the invention provides a geometric design and signal control method aiming at the construction condition that one or more inlet roads occupy the lane at an intersection;
2. the invention can fully utilize the remaining lanes except the lanes occupied by construction at the intersection, and almost all the lanes are used as the import lanes through the dynamic control of the lanes, thereby improving the traffic capacity;
3. the invention ensures the early entering of the traffic flow before the phase begins and the emptying of the traffic flow after the phase ends in the comprehensive function area through reasonable signal control, reduces the loss time and ensures the traffic safety.
The above detailed description of the application of the method is provided to enable one of ordinary skill in the art to fully understand and apply the method, and it is readily apparent to those skilled in the art that various modifications can be made to the method and the generic principles of the method can be applied to other embodiments without the use of inventive faculty. Therefore, the present invention is not limited to the above-mentioned embodiments, and those skilled in the art should make improvements and modifications within the scope of the present invention according to the disclosure of the present invention.
Claims (2)
1. A road intersection construction period traffic optimization design method comprises an intersection geometric design step and a signal control step, and is characterized in that: in the geometric design step, a comprehensive function area is arranged at an entrance of an intersection of a road occupying construction area, the comprehensive function area is used by traffic flows in different flow directions in different phases of a signal period, a pre-stop line is arranged at the upstream of the traffic flow in the construction area, and whether the traffic flow is allowed to enter the comprehensive function area is controlled; in the signal control step, a main signal at an intersection adopts signal phase arrangement of anticlockwise single-opening release, the traffic flow in a comprehensive function area is ensured to enter in advance before the signal phase begins and empty after the signal phase ends, the start time and the end time of the traffic flow in the inlet direction entering the comprehensive function area are controlled by pre-signal control of a pre-stop line, and signal timing parameters controlled by the main signal and the pre-signal are optimized through a linear programming model; the geometric design step comprises the steps of setting the number of lanes in the comprehensive function area, the length of the comprehensive function area and the functional division of lanes at the intersection;
the number of lanes in the comprehensive function area is the sum of available lanes at the entrance of the occupied road construction intersection minus 1, and the reserved lanes are special exit lanes for right-turning vehicles which enter the entrance and pass through the intersection;
the length of the comprehensive functional area is the sum of the length of the occupied construction area and the length of the lane gradient section, and is calculated according to the formula (1),
in the formula:inumbering intersections, e.g. for crossingsi=1 denotes eastern import,i=2 denotes north import,i=3 denotes western import,i=4 denotes south import;L i in order to integrate the length of the functional zones,l wi in order to take up the length of the construction area,l ci the length of a lane gradient section;
wherein: the length of the lane transition section is calculated according to the formula (2),
in the formula:Vin order to design the speed of the vehicle,W i the width of the lane is changed transversely;
and the intersection lane function division is that when the comprehensive function area is used as an entrance lane, lane functions are divided by adopting lane driving direction signs and are respectively arranged from left to rightn iEL A left-turn special lane, a straight left-mixed lane,n iET A straight special lane, a straight right mixed lane,n iER A right-turn lane, wherein:n iEL 、n iET 、n iER calculated by the formulas (3) to (5) respectively,
in the formula:n iEL 、n iET 、n iER are respectively asThe number of lanes dedicated for left turn, the number of lanes dedicated for straight run and the number of lanes dedicated for right turn,q iL 、q iT 、q iR traffic volumes of left turn, straight run and right turn respectively,q i is the first of the intersectioniThe total traffic volume at the inlet of the fork,n i the number of lanes in the comprehensive functional area is the number of the lanes in the occupied construction site, and the number of the lanes in the import non-occupied construction site is the number of the lanes in the import construction site.
2. The method of optimally designing traffic at a road intersection in construction period according to claim 1, characterized in that: the optimization target of the linear programming model during signal timing is that the intersection has the maximum vehicle throughput, which is expressed by the formula (6),
in the formula:Zin order to achieve the maximum throughput of vehicles at the intersection,μthe flow coefficient of the intersection is the flow coefficient,q i is the first of the intersectioniThe total traffic at the inlet of the fork;
the constraint conditions of the signal timing linear programming model comprise signal period duration, main signal timing, pre-signal timing and intersection saturation constraint;
the signal period duration constraint requires that the main signal and the pre-signal period duration are the same, and in a reasonable maximum and minimum signal period duration range, in order to ensure that the established model is a linear model, the reciprocal of the period is adopted for representation, as shown in a formula (7);
in the formula:ξis the inverse of the duration of the signal period,C maxandC minmaximum and minimum signal cycle durations, respectively;
the main signal timing is in a phase sequence of single-port release in the counterclockwise direction, and the green light starting time and the green signal ratio of each inlet of the main signal meet the requirements of formulas (8) to (10);
in the formula:g i is the main signal at the intersectioniThe starting moment of the green light at the fork entrance is a number between 0 and 1 in terms of relative time in one signal period;λ i is the main signal at the intersectioniThe split inlet split ratio;Ithe green light interval time;
the pre-signal timing is coordinated with the main signal, the traffic flow in any inlet direction can enter the comprehensive function area after the opposite straight traffic flow completely passes through the comprehensive function area, and the formula (11) is satisfied,
in the formula:g p i is the first of the intersectioniThe green light start time of the fork entry pre-signal, expressed in relative time in one signal cycle, is a number between 0 and 1,L i in order to integrate the length of the functional zones,Vdesigning the vehicle speed;
the traffic flow in any direction of the inlet ensures that the vehicles entering the comprehensive function area pass through the intersection during the period of the green light of the main signal, and the main signal traffic capacity is larger than the pre-signal traffic capacity, namely the formula (12) is satisfied,
in the formula:λ p i is the first of the intersectioniThe split inlet pre-signal green-to-signal ratio,s i is the first of the intersectioniThe main signal saturation flow rate at the fork inlet,s p i is the first of the intersectioniA fork inlet pre-signal saturation flow rate;
the vehicle passing the pre-stop line at the end of the pre-signal green light passes through the intersection before the end of the main signal green light, and equation (13) is satisfied,
the intersection saturation constraint requires that each inlet saturation does not exceed the maximum saturation limit and satisfies the equations (14) - (15),
in the formula:d maxis a maximum saturation limit.
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