CN115619012A - Method for calculating traffic capacity of confluence area of mixed traffic flow highway with special lane - Google Patents
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Abstract
The invention relates to a method for calculating the traffic capacity of a confluence area of a mixed traffic flow highway with a special lane, which comprises the steps of firstly, considering the demand of an automatic driving vehicle and the traffic capacity of the automatic driving special lane, and distributing the automatic driving vehicle to obtain the traffic demand of each lane; secondly, an objective function is provided according to the maximum traffic capacity as an optimization objective; simultaneously, constraint conditions of traffic flow in the confluence region are given; and finally, establishing a confluence area traffic capacity model according to the objective function and the constraint condition, and solving the confluence area traffic capacity model through mathematical programming to obtain the confluence area traffic capacity. According to the method, under the condition that the mixed traffic flow containing the special lane, the automatic driving vehicles and the manual automatic driving vehicles is in consideration of the automatic driving vehicle requirements and the automatic driving special lane traffic capacity, the traffic capacity of the confluence area is quantified through the distribution of the automatic driving vehicles and the constraint conditions to be followed by the traffic flow in the confluence area, and the method has guiding significance for the control of the man-machine mixed driving traffic flow containing the automatic driving special lane in the future.
Description
Technical Field
The invention belongs to the technical field of automatic driving, and particularly relates to a method for calculating the traffic capacity of a confluence area of a mixed traffic flow highway with a special lane.
Background
With the rapid development of informatization technology, a foundation is provided for the rapid development of automatic driving technology, compared with a manual-driving vehicle (HV), the automatic driving vehicle (CAV) has the characteristic of objectively judging road conditions and rational driving, and driving behaviors are not influenced by subjective factors such as driver psychological states, driving habits and the like, so that the automatic driving vehicle has the advantages of short reaction time, large speed change range and capability of obtaining smaller distance between heads compared with common vehicles, and theoretically, the maximum service flow rate and traffic capacity of man-machine hybrid traffic flow can be improved. In consideration of the basic national conditions and the difference of regional development in China, the hybrid driving state of the automatic driving vehicle and the manual driving vehicle exists in the urban road traffic system in China for a long time. In a man-machine hybrid driving environment, mutual interference between a manually driven vehicle and an automatically driven vehicle can reduce the running efficiency of the manually driven vehicle and the automatically driven vehicle, and the confluent region has complex vehicle behaviors and high conflict rate, increases driving difficulty and causes the traffic accident rate to rise.
High Occupant (HOV) lanes, bus exclusive lanes, have been widely implemented in traffic systems, while demonstrating the feasibility of setting exclusive lanes. The special lanes provide reference for the automatic driving special lanes, the lanes are spatially separated by the aid of the automatic driving special lanes, mutual interference between automatic driving vehicles and manual driving vehicles can be remarkably reduced, advantages of energy conservation and environmental protection, intelligent sharing, networking cooperation and the like of the automatic driving vehicles are fully exerted, benefits of the automatic driving vehicles can be improved by the aid of the automatic driving special lanes, and popularization of the automatic driving vehicles is facilitated.
The existing literature has limited research on the traffic capacity of the confluence area under the mixed traffic flow, and the research on the traffic capacity of the confluence area after the special automatic driving lane is arranged is still blank, so that the influence of commercial automatic driving vehicles on the traffic capacity of the confluence area in the future cannot be obtained, and reference cannot be provided for planning the special automatic driving lane.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to solve the technical problem of providing a method for calculating the traffic capacity of a confluence area of a mixed traffic flow highway with a special lane.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating the traffic capacity of a confluence area of a mixed traffic flow highway with a special lane is disclosed, wherein the special lane is an automatic driving special lane adjacent to a central green belt of the highway, namely a lane farthest from an entrance ramp and an exit ramp of the confluence area; the method comprises the following steps:
step one, considering the requirements of the automatic driving vehicles and the traffic capacity of the special automatic driving lanes, distributing the automatic driving vehicles to obtain the traffic requirements of all lanes, wherein the traffic requirements comprise the following situations:
1) When the demand of the automatic driving vehicles is smaller than the traffic capacity of the automatic driving special lane, all the automatic driving vehicles are distributed to the automatic driving special lane, and at the moment, the traffic demands of all lanes of the main road and the automatic driving special lane meet the following formula:
in the formula (1), Q i 、Q c Traffic demands of a main road i lane and an automatic driving special lane are respectively, i =1, 2.. Multidot.s, s is the number of mixed lanes, the automatic driving special lane is removed, the other lanes are mixed lanes, and the mixed lanes are sequentially marked as a main road 1 lane, a main road 2 lane, \\ 8230and a main road s lane along the direction from a confluence area to the automatic driving special lane;
traffic flow rates for main road i lane and autopilot lane, respectively; q. q.s rf The traffic flow rate of the ramp driving into the lane 1 of the main road; p is the market penetration rate of the automatic driving vehicle, p is more than or equal to 0 and less than or equal to 1, p = p '+ p', p 'is the automatic driving vehicle mixing rate of the automatic driving special lane, and p' is the automatic driving vehicle mixing rate of the mixed lane; d is main road traffic demand, namely the total traffic demand of all main road lanes; phi is the traffic demand of the ramp, BFC' is the single-lane traffic capacity of the automatic driving special lane;
2) When the autonomous vehicle demand is greater than the autonomous-only lane capacity, allocating a portion of the autonomous vehicles to the hybrid lane, where the traffic demand of the main lane and the autonomous-only lane should satisfy the following equation:
in the formulas (1) and (2), the main road traffic demand D is less than or equal to BFC' +2BFC, BFC is the single lane traffic capacity of a mixed lane, and the ramp traffic demand phi is less than or equal to C max ，C max For vehicles merging into the main roadThe maximum influx is related to the traffic demand of the lane 1 of the main road;
3) Before the ramp vehicles converge into the main road, the mixing rate of the automatic driving vehicles in the automatic driving special lane and the automatic driving mixed lane is determined by an automatic driving vehicle distribution strategy, which specifically comprises the following steps:
in the formula (3), p' is less than or equal to p
4) After the vehicles on the ramp converge into the main road, the mixing rate of the automatically driven vehicles in the automatic driving special lane and the automatic driving mixed lane is also influenced by the merging behavior of the ramp, so that the number of the automatically driven vehicles on each main road lane is changed to a certain extent, and the method specifically comprises the following two situations:
(1) the traffic flow of the automatic driving special lane is composed of automatic driving vehicles which originally run on the automatic driving special lane and automatic driving vehicles which change lanes from the main road s lane to the automatic driving special lane, and the mixing rate of the automatic driving vehicles of the automatic driving special lane is as follows:
in the formula (I), the compound is shown in the specification,
the traffic flow rate for the main s lane change lane merging into the autodrive-only lane,
for the traffic flow rate of the non-changed lane of the autopilot-specific lane directly through the confluence,
the traffic flow rate converging into a main road i +1 lane for a main road i lane change lane;
the traffic flow rate of the I lanes of the main road, which are not changed, directly passing through the confluence area;
(2) regarding all the mixed lanes as a whole, the mixing rate of the automatic driving vehicles in the mixed lanes is:
step two, establishing a traffic capacity model of the confluence area, and solving the traffic capacity model of the confluence area to obtain the traffic capacity of the confluence area of the mixed traffic flow highway with the special lane;
firstly, an objective function is proposed according to the maximum traffic capacity optimization objective; the traffic capacity of the highway confluence area containing the special lane under the man-machine mixed driving condition is the sum of the main road traffic volume passing through the confluence area in unit time and the maximum traffic volume of the main road converging into the confluence area by the ramp, so that the objective function is as follows:
in the formula (6), C is the traffic capacity of the confluence area;
secondly, the traffic flow in the confluence region must comply with certain constraint conditions, which specifically include:
1) The traffic capacity of each lane in the confluence area cannot exceed the traffic capacity of the basic road section under the same condition, and the following conditions are provided:
wherein the content of the first and second substances,
the traffic flow rate of the main road 1 which is the lane-unchanging lane directly passes through the confluence area,
the traffic flow rate of the non-changed lane of the main lane i +1 directly passing through the confluence area;
2) Each variable in the equation (6) cannot exceed the maximum influx of the corresponding lane, and then:
q rf ≤C max (12)
in the formula (II) C' max The maximum influx of the vehicles in the i lane of the main road into the i +1 lane of the main road is related to the traffic demand of the i +1 lane of the main road; c ″ max The maximum influx for importing into the driveway dedicated for automatic driving is related to the traffic demand of the driveway dedicated for automatic driving;
3) The mixing rate of the automatic driving vehicles of each lane in the merging area is not more than the market penetration rate p of the automatic driving vehicles, and the mixing rate comprises the following steps:
according to the objective function and the constraint condition, obtaining a confluence area traffic capacity model as follows:
and (3) solving the optimization model of the formula (17) through mathematical programming, and calculating the traffic capacity of the confluence area of the mixed traffic flow highway with the special lane.
Specifically, the calculation of the traffic capacity of the basic highway section comprises the following contents:
1) The single lane traffic capacity BFC of the mixed lane is as follows:
in the formula, t cc For desired headway between autonomous vehicles, t cm For a desired headway, t, between autonomous and manually driven vehicles mm A desired headway between manually driven vehicles;
2) The single lane traffic capacity BFC of the automatic driving special lane is as follows:
based on the acceptable clearance theory and probability theory, the maximum amount of traffic lane influx includes the following two situations:
(1) maximum influx of mixed lanes
Taking the example of the ramp merging into the main road 1 lane, assume that the critical gap of a k (k =1, 2) type vehicle is t ck Where k is 1 for autonomous driving and k is 2 for manual drivingVehicle with time interval t fk (ii) a Headway of lane 1 on main road
According to the theory of acceptable clearance, when
Allowing a k-shaped vehicle to converge into a main road 1 lane from a ramp; when in use
Allowing a k-type vehicle on the ramp to be arranged at the head and the other vehicle following the k-type vehicle to converge into the main road 1 lane; in general, when
When the vehicle is running, the head of a k-type vehicle on the ramp is allowed to be arranged and the rear part of the k-type vehicle is followed by r 1 Vehicle driven manually, r 2 The automatic driving vehicle converges into a main road 1 lane;
because the random events of searching proper gaps and merging into the main road by manually driven vehicles and automatically driven vehicles in the ramp traffic flow are mutually independent, the queuing configuration and the probability of the ramp vehicles which possibly appear are researched, and the maximum merging amount of the ramp traffic lane into the main road 1 traffic lane is calculated according to the queuing configuration and the probability;
when the captain is 1, the queuing forms are 2, and respectively use manually driven vehicles and automatically driven vehicles as the head of the queuing;
when the captain is 2, the queue configurations are 4, namely manually driven vehicles-manually driven vehicles, manually driven vehicles-automatically driven vehicles, automatically driven vehicles-manually driven vehicles and automatically driven vehicles-automatically driven vehicles; the probabilities of these four queue configurations are: (1-p) 2 P (1-p), p (1-p) and p 2 The sum of the four probability values is 1;
generally, the queue configuration when the captain is r is: the k-type vehicles are arranged at the head of the queue, and r is arranged in the queue configuration with the rear queue length of r-1 1 Vehicle manually driven, r 2 Common to different queue configurations of autonomous vehicles
Wherein r is 1 +r 2 = r-1; the k-type vehicles are positioned at the head of the queue, and r is arranged in the queue configuration with the rear queue length of r-1 1 Vehicle manually driven, r 2 The probability that the vehicle is automatically driving the vehicle is:
p k representing the probability of a k-type vehicle; if the sum of the probability values is also 1, then:
the time headway of the main road 1 lane obeys second-order Alron distribution, and the probability distribution function is as follows:
in the formula, lambda is a vehicle arrival rate, m represents an order, and t represents a head time distance between two vehicles;
the head-hour distance of the main road 1 lane can pass through the ramp, the k-type vehicles are positioned at the head of the queue, and r is arranged in the queue configuration with the rear queue length of r-1 1 Vehicle manually driven, r 2 The probability that the vehicle is automatically driving the vehicle is:
the head time distance of the lane 1 on the main road can ensure that the vehicles pass through the ramp at one time, the k-type vehicles are positioned at the head of a queuing formation, and r is arranged in a queuing formation with the rear formation length of r-1 1 Vehicle driven manually, r 2 The probability of the vehicle automatically driving the vehicle is:
the probability that the vehicle head time distance of the main road 1 lane can guarantee that the vehicles pass through the r ramp roads at one time is as follows:
the mathematical expectation that the mixed traffic flow of the inner ramp of the lane gap of the main road 1 can be converged into the main road is as follows:
suppose traffic demand of 1 lane of main road is Q 1 I.e. main 1 lane has Q 1 And if the gap is small, the maximum input amount of the ramp vehicle to the main road is as follows:
wherein, t c1 、t c2 Critical gap, t, for autonomous and manually driven vehicles, respectively f1 、t f2 The time intervals on the vehicle are respectively the time intervals of the automatic driving vehicle and the manual driving vehicle;
suppose traffic demand of i +1 lanes of main road is Q i+1 Similarly, the maximum amount of traffic C 'that vehicles in the lane i of the main road merge into the lane i +1 of the main road' max Comprises the following steps:
wherein Q is 2 Traffic demand for the primary 2 lanes;
(2) maximum influx C' of driveway for automatic driving max
From the above, it can be seen that only the autonomous vehicle has an incentive to enter the lane dedicated for autonomous driving, at which time the time interval t for the autonomous vehicle f1 And a critical gap t c1 The maximum influx C' into the driveway special for automatic driving is changed because the vehicle is not driven manually max The calculation process of (2) is as follows:
according to the theory of acceptable clearance, when
Allowing an autonomous vehicle to merge into an autonomous dedicated lane; when in use
Allowing n automatic driving vehicles to merge into an automatic driving special lane;
probability P that n automatic driving vehicles converge into automatic driving special lane in main road s lane in one headway n Comprises the following steps:
traffic demand of the automatic driving exclusive lane is Q c That is, the total number of head time on the driveway for automatic driving is Q c (ii) a Suppose that the main road s is capable of accommodating at most o vehicles in a queue on the lane, wherein the queue appears
Number of times of (1) is P n Q c Is present and present
The number of times of
Therefore, the total number of vehicles allowed to enter the automatic driving special lane from the main lane s in 1h is as follows:
let o → ∞ obtain the maximum amount of the main road s lane to merge into the lane dedicated for automatic drivingC″ max Comprises the following steps:
compared with the prior art, the invention has the beneficial effects that:
1. the method is characterized in that a confluence area traffic capacity model is established based on a linear optimization idea, the confluence area traffic capacity model is an optimization target with the maximum traffic capacity, an objective function is provided, and the condition that the confluence area contains a special lane and the automatic driving vehicle and the manual automatic driving vehicle run in a mixed mode is considered, under the condition, the automatic driving vehicle converged on a ramp can continuously change lanes and converge into the automatic driving special lane, and the traffic flow running of all lanes of a main road is directly influenced.
2. Since each variable in the objective function cannot exceed the maximum influx of the corresponding lane, the maximum influx of the lane is calculated based on the acceptable clearance theory and the probability theory. The maximum influx of the mixed lane takes different queuing configurations of two vehicle types into consideration, the maximum influx is calculated by utilizing probability theory and acceptable gap theory, and the possible queuing configurations of vehicles on the ramp are more comprehensively considered, so that the calculation result of the maximum influx of the mixed lane is closer to the actual situation. And calculating the maximum influx of the automatic driving special lane according to the acceptable clearance theory.
Drawings
FIG. 1 is a schematic view of a merge area with a dedicated lane under a mixed traffic flow;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a graph of the cut-in rate of autonomous vehicles versus the capacity of the merge area;
FIG. 4 is a graph of the maximum merging amount of a mixed lane and the mixing rate of an autonomous vehicle under different main road traffic demands;
FIG. 5 is a graph of maximum importation of autonomous driving lanes versus blending rate of autonomous driving vehicles for different main road traffic demands.
Detailed Description
The technical solutions of the present invention are described in detail below with reference to the accompanying drawings and specific embodiments, but the scope of the present invention is not limited thereto.
As shown in FIG. 1, the CAV exclusive lane is adjacent to the central green belt of the expressway (i.e. the lane farthest from the entrance ramp and the exit ramp of the confluence region), the other lanes are mixed lanes, and the mixed lanes are marked as a main road 1 lane, a main road 2 lane, \8230anda main road s lane in sequence along the direction from the confluence region to the CAV exclusive lane; in this embodiment, a one-way three-lane highway is taken as an example to describe the method for calculating the traffic capacity of the confluence area of the highway with the mixed traffic flow including the special lane, so s =2, which specifically includes the following steps:
step one, considering the requirement of an automatic driving vehicle and the traffic capacity of a special automatic driving lane, and distributing the automatic driving vehicle; the demand allocation principle of the automatic driving vehicle is as follows: the automatic driving special lane is preferred, automatic driving vehicles are distributed by adopting a fixed traffic flow management principle, and on the premise that the total number of the automatic driving vehicles distributed to the automatic driving special lane is not more than the traffic capacity of the automatic driving special lane, more automatic driving vehicles are distributed to the automatic driving special lane as much as possible;
1) When the demand of the automatic driving vehicles is smaller than the traffic capacity of the automatic driving special lane, all the automatic driving vehicles are distributed to the automatic driving special lane, and the traffic demands of the main road 1 lane, the main road 2 lane and the automatic driving special lane are obtained according to the formula (1), namely the traffic volume is as follows:
in formula (31), Q 1 Traffic demand for lane 1 of the main road, Q 2 Traffic demand of 2 lanes on the main road, q f1 Traffic flow rate of 1 lane of main road, q f2 Traffic flow rate for the primary 2 lanes; p is the market penetration rate of the automatic driving vehicle, p is more than or equal to 0 and less than or equal to 1, p = p '+ p', p 'is the automatic driving vehicle mixing rate of the automatic driving special lane, and p' is the automatic driving vehicle mixing rate of the mixed lane; d is main road traffic demand, namely the total traffic demand of all main road lanes; phi is the traffic demand of the ramp, BFC' is the single lane traffic capacity of the automatic driving special lane;
2) When the demand of the automatic driving vehicles is larger than the traffic capacity of the automatic driving special lane, some automatic driving vehicles are distributed to the mixed lane, and the traffic demands of the main road 1 lane, the main road 2 lane and the automatic driving special lane are obtained according to the formula (2):
in the formulas (31) and (32), the main road traffic demand D is less than or equal to BFC' +2BFC, BFC is the single lane traffic capacity of the mixed lane, and the ramp traffic demand phi is less than or equal to C max ，C max The maximum afflux amount of the ramp vehicles afflux to the main road;
3) Before the ramp vehicles converge into the main road, the mixing rate of the automatic driving vehicles of the automatic driving special lane and the automatic driving mixed lane is shown in the formula (3);
4) After the ramp vehicles merge into the main road, the mixing rate of the automatic driving vehicles of the automatic driving special lane and the automatic driving mixed lane is also influenced by the merging behavior of the ramp, the number of the automatic driving vehicles of each lane is changed to a certain extent, and the method specifically comprises the following steps:
(1) the traffic flow of the automatic driving special lane is composed of automatic driving vehicles originally running on the special lane and automatic driving vehicles changing lanes from the main road 2 lane to the automatic driving special lane, and the mixing rate of the automatic driving vehicles of the automatic driving special lane obtained according to the formula (4) is as follows:
in the formula, q rf The traffic flow rate of the ramp entering the lane of the main road 1,
the traffic flow rate for main lane 1 lane change lanes merging into main lane 2 lane,
the traffic flow rate for main lane 2 lane change lanes merging into the autodrive-only lanes,
the traffic flow rate of the main road 1 which is the lane-unchanging lane directly passes through the confluence area,
the traffic flow rate of the main road 2 which is the lane-unchanging lane directly passes through the confluence area,
the traffic flow rate of the non-changed lane of the automatic driving special lane directly passing through the confluence area;
(2) regarding the lane of the main road 1 and the lane of the main road 2 as a whole, the mixing rate of the automatic driving vehicle in the mixed lane is obtained according to the formula (5) as follows:
step two, establishing a traffic capacity model of the confluence area, and solving the traffic capacity model of the confluence area to obtain the traffic capacity of the confluence area of the mixed traffic flow highway with the special lane;
firstly, an objective function is proposed according to the maximum traffic capacity optimization objective; the traffic capacity of the highway confluence area containing the special lane under the man-machine mixed driving condition is the sum of the main road traffic volume passing through the confluence area in unit time and the maximum traffic volume of the main road converging into the confluence area by the ramp, and an objective function is obtained according to the formula (6) and is as follows:
in the formula, C is the traffic capacity of a confluence area;
secondly, the traffic flow in the confluence area must comply with certain constraint conditions, which are specifically as follows:
1) The traffic capacity of each lane in the confluence area cannot exceed the basic road section traffic capacity under the same conditions, namely:
2) Each variable in equation (35) cannot exceed the maximum influx for the corresponding lane, i.e.:
q rf ≤C max (12)
3) The autonomous vehicle mixing rate of each lane in the merging area must not exceed the market penetration rate p of the autonomous vehicle according to equations (15) and (16):
according to the objective function and the constraint conditions, the obtained confluence area traffic capacity model of the embodiment is as follows:
equation (44) is solved to obtain the merge region throughput capacity of this example.
Calculating the traffic capacity of the basic sections of the expressway, comprising the following steps:
1) The single lane traffic capacity BFC of the mixed lane is as follows:
in the formula, t cc Taking 0.6s for the expected headway of the automatic driving vehicle; t is t cm 1.2s is taken for the expected headway time between the automatic driving vehicle and the manual driving vehicle; t is t mm 1.8s is taken for the expected headway of the manually driven vehicle;
2) The single lane traffic capacity BFC of the autopilot-specific lane is:
based on the acceptable clearance theory and probability theory, the maximum amount of traffic lane influx includes the following two situations:
1) Maximum influx of mixed lanes
When a ramp vehicle merges into the main lane 1, let the critical gap of a k (k =1, 2) type vehicle be t ck Where k is 1 for an autonomous vehicle, k is 2 for an autonomous vehicle, and the time-dependent distance of the k-type vehicle is t fk (ii) a Headway of lane 1 on main road
According to the theory of acceptable clearance, when
When the vehicle runs on the main road 1, allowing a k-type vehicle to flow into the ramp; when in use
When the vehicle is on the main road 1, allowing a k-type vehicle on the ramp to be arranged at the head and the other vehicle behind the k-type vehicle to converge into the main road 1; in general, when
Allowing a k-type vehicle on the ramp to be arranged at the head and followed by r 1 Vehicle driven manually, r 2 The automatic driving vehicle converges into a main road 1 lane;
because the random events of searching proper gaps and merging into the main road by manually driven vehicles and automatically driven vehicles in the ramp traffic flow are mutually independent, the queuing configuration and the probability of the ramp vehicles which possibly appear are researched, and the maximum merging amount of the ramp traffic lane into the main road 1 traffic lane is calculated according to the queuing configuration and the probability;
when the queue length is 1, the queue configurations are 2, and manual driving vehicles and automatic driving vehicles are respectively used as the head of the queue;
when the queue length is 2, the queue configuration is 4,respectively a manually driven vehicle to a manually driven vehicle, a manually driven vehicle to an automatically driven vehicle, an automatically driven vehicle to a manually driven vehicle, and an automatically driven vehicle to an automatically driven vehicle; the probabilities of these four queue configurations are: (1-p) 2 P (1-p), p (1-p) and p 2 The sum of the four probability values is 1;
generally, the queuing configuration when the queue length is r is: the k-type vehicles are positioned at the head of the queue, and r is arranged in the queue configuration with the rear queue length of r-1 1 Vehicle manually driven, r 2 For autonomous vehicles, different queuing configurations
Wherein r is 1 +r 2 = r-1; the k-type vehicles are positioned at the head of the queue, and r is arranged in the queue configuration with the rear queue length of r-1 1 Vehicle manually driven, r 2 The probability of the vehicle automatically driving the vehicle is:
p k representing the probability of a k-type vehicle; if the sum of the probability values is also 1, then:
the time headway of the main road 1 lane obeys second-order Alron distribution, and the probability distribution function is as follows:
in the formula, lambda is a vehicle arrival rate, m represents an order, and t represents a head time distance between two vehicles;
the time distance of the head of the main road 1 can pass through the ramp, the k-type vehicles are positioned at the head of the queue, and the rear queue length is r-1 1 Vehicle driven manually, r 2 The probability of the vehicle automatically driving the vehicle is:
in the formula (22), t c1 Take 2.4s,t c2 Taking for 3s;
the time distance between the head of the lane 1 on the main road can ensure that the vehicles can pass through the ramp once, the k-type vehicles are positioned at the head of a queuing formation, and r is arranged in the queuing formation with the rear formation length of r-1 1 Vehicle manually driven, r 2 The probability of the vehicle automatically driving the vehicle is:
the probability that the vehicle head time distance of the main road 1 lane can guarantee that the vehicles pass through the r ramp roads at one time is as follows:
the mathematical expectation that the mixed traffic flow of the inner ramp of the lane gap of the main road 1 can be converged into the main road is as follows:
suppose traffic demand of the main road 1 lane is Q 1 I.e. main 1 lane has Q 1 And if the gap is small, the maximum input amount of the ramp vehicle to the main road is as follows:
wherein, t c1 、t c2 Critical gap, t, for autonomous and manually driven vehicles, respectively f1 、t f2 The time intervals are the time intervals of the automatic driving vehicle and the manual driving vehicle;
suppose traffic demand of i +1 lanes of main road is Q i+1 The same principle can be obtained, main roadThe maximum afflux amount C 'of the vehicle in the i lane afflux to the main lane i +1 lane' max Comprises the following steps:
(3) maximum influx C' of driveway for automatic driving max
From the above, it can be seen that only the autonomous vehicle has an incentive to enter the autonomous-drive-dedicated lane, at which time the time-on-vehicle distance t of the autonomous vehicle f1 And critical gap t c1 The maximum influx C' into the driveway special for automatic driving is changed because the vehicle is not driven manually max The calculation process of (2) is as follows:
according to the theory of acceptable clearance, when
Allowing an autonomous vehicle to merge into an autonomous dedicated lane; when in use
Allowing n automatic driving vehicles to merge into an automatic driving special lane;
probability P that n automatic driving vehicles converge into automatic driving special lane in main road s lane in one headway n Comprises the following steps:
traffic demand of autodrive exclusive lane is Q c That is, the total number of head time on the driveway for automatic driving is Q c (ii) a Suppose that the main road s is able to accommodate at most o vehicles in a queue, where it appears
Number of times of (1) is P n Q c Is present and present
The number of times of
Therefore, the total number of vehicles allowed to enter the automatic driving special lane from the main lane s in 1h is as follows:
let o → ∞ obtain the maximum influx C ″' of the main road s lane into the lane special for automatic driving max Comprises the following steps:
in order to verify the effectiveness of the method, a traffic capacity model of the confluence area is solved through Matlab software, and the relation between the mixing rate of the automatic driving vehicles and the traffic capacity of the confluence area and the influence of different main road traffic demands and the mixing rate of the automatic driving vehicles on the maximum confluence amount are analyzed.
Fig. 3 is a graph showing the relationship between the merging area traffic capacity and the mixing rate of the automatically driven vehicles, and it can be seen from fig. 3 that the merging area traffic capacity increases with the increase of the mixing rate of the automatically driven vehicles and finally reaches the limit of the carrying capacity of the road, which shows that the automatically driven vehicles can improve the traffic capacity of the road.
Fig. 4 is a graph showing a relationship between the maximum merging amount of the hybrid lane and the mix-in rate of the autonomous vehicle for different main road traffic demands, and it can be seen from fig. 4 that the maximum merging amount of the hybrid lane decreases as the mix-in rate of the autonomous vehicle increases at a low traffic demand (D =1800 to 3600 veh/h), because the traffic demand allocated to the hybrid lane decreases as the mix-in rate of the autonomous vehicle increases when the traffic demand does not exceed the basic traffic capacity of the autonomous lane. Under the medium traffic demand (D = 5400-12600 veh/h), the maximum influx of the mixed lane is in a trend of ascending first and descending later along with the increase of the mixing rate of the automatic driving vehicles, which shows that when the traffic demand is close to or greater than the basic traffic capacity of the automatic driving special lane, the distributed traffic demand of the mixed lane is increased along with the increase of the mixing rate of the automatic driving vehicles, but when the main road traffic demand reaches a certain value, the maximum influx of the mixed lane is reduced along with the increase of the main road traffic demand, and the result accords with the related research result. When the traffic demand is close to a saturated state (D =14400 veh/h), the main road traffic volume is basically saturated, and the maximum influx also slowly increases along with the increase of the mixing rate of the automatic driving vehicle, which indicates that the automatic driving vehicle has a certain positive influence on vehicle influx.
Fig. 5 is a graph of a relationship between a maximum influx into an autonomous driving dedicated lane and an autonomous driving vehicle mixing rate under different main road traffic demands, wherein under a certain traffic demand, the maximum influx into the autonomous driving dedicated lane decreases as the autonomous driving vehicle mixing rate increases, which shows that the maximum influx continuously decreases as the traffic volume of the autonomous driving dedicated lane increases, and conforms to relevant research conditions; when the traffic demand increases, the maximum influx is gradually reduced to 0, which indicates that the traffic volume of the automatic driving special lane reaches a saturated state at the moment, and the automatic driving vehicle of the mixed lane can not be converged into the special lane any more.
Nothing in this specification is said to apply to the prior art.
Claims (3)
1. A method for calculating the traffic capacity of a confluence area of a highway with mixed traffic flow containing a special lane is characterized in that the special lane is an automatic driving special lane adjacent to a central green belt of the highway; the method is characterized by comprising the following steps:
step one, considering the requirements of the automatic driving vehicles and the traffic capacity of the special automatic driving lanes, distributing the automatic driving vehicles to obtain the traffic requirements of all lanes, wherein the traffic requirements comprise the following situations:
1) When the autonomous vehicle demand is less than the autonomous-only lane capacity, all autonomous vehicles are assigned to the autonomous-only lanes, and at this time the traffic demand of each lane of the main road and the autonomous-only lanes should satisfy the following formula:
in the formula (1), Q i 、Q c Traffic demands of a main road i lane and an automatic driving special lane are respectively, i =1, 2.. Multidot.s, s is the number of mixed lanes, the automatic driving special lane is removed, the other lanes are mixed lanes, and the mixed lanes are sequentially marked as a main road 1 lane, a main road 2 lane, \\ 8230and a main road s lane along the direction from a confluence area to the automatic driving special lane;
traffic flow rates for the main i lane and the autopilot lane, respectively; q. q of rf The traffic flow rate of the ramp entering the lane 1 of the main road; p is the market penetration rate of the automatic driving vehicle, and p is more than or equal to 0 and less than or equal to 1; d is the main road traffic demand; phi is the traffic demand of the ramp, BFC' is the single lane traffic capacity of the automatic driving special lane;
2) When the autonomous vehicle demand is greater than the autonomous-only lane capacity, assigning a portion of the autonomous vehicles to the hybrid lane, where traffic demands of the main lane and the autonomous-only lane should satisfy the following equation:
in the formulas (1) and (2), the main road traffic demand D is less than or equal to BFC' +2BFC, BFC is the single lane traffic capacity of a mixed lane, and the ramp traffic demand phi is less than or equal to C max ，C max The maximum influx for vehicles on the ramp to converge into the main road is related to the traffic demand of the lane 1 on the main road; market penetration of autonomous vehicles p = p '+ p ", p' being an autonomous vehicle mix-in rate of an autonomous-only lane, p" being an autonomous vehicle mix-in rate of a hybrid lane;
before the ramp vehicles converge into the main road, the mixing rate of the automatic driving vehicles in the automatic driving special lane and the automatic driving mixed lane is as follows:
after the vehicles on the ramp merge into the main road, the mixing rate of the automatically-driven vehicles in the automatic driving special lane and the automatic driving mixed lane is influenced by the merging behavior of the vehicles on the ramp, and the mixing rate comprises the following two situations:
(1) the traffic flow of the automatic driving special lane is composed of automatic driving vehicles which originally run on the automatic driving special lane and automatic driving vehicles which change lanes from the main road s lane to the automatic driving special lane, and the mixing rate of the automatic driving vehicles of the automatic driving special lane is as follows:
in the formula (I), the compound is shown in the specification,
the traffic flow rate for the main road s lane change lane merging into the autopilot lane,
the traffic flow rate of the non-changed lane directly passing through the confluence area for the autopilot-only lane,
the traffic flow rate of the lane change lane of the main road i into the lane of the main road i + 1;
the traffic flow rate of the I lanes of the main road directly passing through the confluence area is the unchanged lanes of the i lanes of the main road;
(2) considering all the mixed lanes as a whole, the mixing rate of the autonomous vehicles in the mixed lanes is:
step two, establishing a confluence area traffic capacity model of the formula (17), and solving the confluence area traffic capacity model through mathematical programming to obtain the traffic capacity of the confluence area of the mixed traffic flow highway with the special lane;
in the formula (I), the compound is shown in the specification,
the traffic flow rate of the main road 1 which is the lane-unchanging lane directly passes through the confluence area,
the traffic flow rate of the non-converted lane of the i +1 lane of the main road directly passing through the confluence area; c' max The maximum influx of the vehicles in the i lane of the main road into the i +1 lane of the main road is related to the traffic demand of the i +1 lane of the main road; c ″ max The maximum amount of import to the autodrive-specific lane is related to the traffic demand of the autodrive-specific lane.
2. The method for calculating the traffic capacity of the confluence area of the expressway with mixed traffic flow including special lanes according to claim 1, wherein the maximum influx C of vehicles on the ramp merging into the main road max Comprises the following steps:
wherein Q is 1 Traffic demand for primary 1 lanes; k represents a k-type vehicle, k =1,2, k takes 1 to represent an autonomous vehicle, and k takes 2 to represent a manually driven vehicle; p is a radical of formula k Denotes the probability of a k-type vehicle, λ is the vehicle arrival rate, t ck Critical clearance, t, for a k-type vehicle c1 、t c2 Critical gaps for autonomous and manned vehicles, respectively; t is t fk Is k typeTime-to-day distance, t, of the vehicle f1 、t f2 The time intervals are the time intervals of the automatic driving vehicle and the manual driving vehicle;
maximum influx C 'for vehicles converging into main road i +1 lane' max Comprises the following steps:
wherein Q is i+1 Traffic demand for main i +1 lanes, Q 2 Traffic demand for the primary 2 lanes;
maximum influx C' into driveway for automatic driving max Comprises the following steps:
wherein Q is c For traffic demand of the driverless exclusive lane, m represents the order of the second order alvaran distribution, and n is the number of driverless vehicles allowed to merge into the driverless exclusive lane.
3. The method for calculating the traffic capacity of the confluence area of the mixed traffic flow highway with the special lane according to claim 1 or 2, wherein the single-lane traffic capacity BFC of the mixed lane is as follows:
in the formula, t cc For desired headway between autonomous vehicles, t cm For a desired headway, t, between autonomous and manually driven vehicles mm A desired headway between manually driven vehicles;
the single lane traffic capacity BFC of the automatic driving special lane is as follows:
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| CN116665442A (en) * | 2023-05-31 | 2023-08-29 | 东南大学 | Intelligent networking special lane design method considering mixed flow theoretical traffic capacity |
| CN117409572A (en) * | 2023-09-04 | 2024-01-16 | 河北渤思科技有限公司 | Road traffic flow data management method and system based on signal processing |
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| CN116665442A (en) * | 2023-05-31 | 2023-08-29 | 东南大学 | Intelligent networking special lane design method considering mixed flow theoretical traffic capacity |
| CN116665442B (en) * | 2023-05-31 | 2024-05-10 | 东南大学 | Intelligent networking special lane design method considering mixed flow theoretical traffic capacity |
| CN117409572A (en) * | 2023-09-04 | 2024-01-16 | 河北渤思科技有限公司 | Road traffic flow data management method and system based on signal processing |
| CN117409572B (en) * | 2023-09-04 | 2024-05-28 | 河北渤思科技有限公司 | Road traffic flow data management method and system based on signal processing |
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