An intersection space-time resource dynamic regulation method based on mixed integer linear programming

Abstract

The application discloses a kind of intersection space-time resource dynamic regulation and control method based on mixed integer linear programming.The method establishes mixed integer linear programming model according to measured real-time traffic demand data, and dynamically optimizes signal timing scheme at intersection and each import channel's channelization scheme in time period.In order to reduce the discomfort brought by too large channelization scheme change to driver and the security hidden danger generated thereby, from the vehicle lane changing angle, the channelization limit constraint of previous and subsequent time period is established.The optimal channelization scheme of previous time period and measured real-time traffic demand data will be as the common input of subsequent mixed integer linear programming model, so as to realize the rolling optimization of space-time resource in control period.The method finally realizes the goal of designing signal timing scheme and smooth channelization scheme for intersection in different control time period.

Description

TECHNICAL FIELD

[0001] The application relates to a crossroad space-time resource dynamic regulation method for cooperatively optimizing a signal timing scheme and a lane channelization scheme at a crossroad under dynamic traffic demand and belongs to the field of traffic control. BACKGROUND

[0002] For the optimization problem of a crossroad space-time resource configuration scheme, a traditional method is to solve the problem in two steps: first, lane channelization is performed, and then signal timing is calculated. In the application process of the configuration scheme, the channelization scheme is always kept unchanged, and only the signal timing scheme is adjusted. Such space-time resource configuration is difficult to adapt to the changing traffic demand, and sometimes the space-time resource is wasted. Although many scholars have realized this problem and have proposed many solutions, such as setting a variable guide lane and dynamically selecting a channelization preplan in different time periods. However, these methods cannot fundamentally realize the optimization of lane resource and time resource configuration, and cannot well adapt to dynamic traffic changes. Based on this, the method adopts a mixed integer linear programming model to obtain the lane channelization and signal timing scheme according to real-time traffic demand data obtained by a crossroad detector, and gives a rolling cooperative optimization framework of the two under dynamic traffic conditions. SUMMARY

[0003] The application aims to provide a crossroad space-time resource dynamic regulation method based on a mixed integer linear programming. The core idea of the method is to establish a mixed integer linear programming model according to measured real-time traffic demand data, and dynamically optimize the signal timing scheme and the channelization scheme of each entrance lane of the crossroad in different time periods. In order to reduce the discomfort and safety hazards caused by the great change of the channelization scheme to the driver, a channelization change limit constraint is established from the perspective of vehicle lane changing. The optimal channelization scheme of the previous time period and the measured real-time traffic demand data will be used as the common input of the mixed integer linear programming model of the next time period, so as to realize the rolling optimization of the space-time resource in the control period. The ultimate goal of the method is to design a signal timing scheme and a smoothly changed channelization scheme for the crossroad in different control time periods.

[0004] The technical scheme adopted by the application is as follows:

[0005] A crossroad space-time resource dynamic regulation method based on a mixed integer linear programming comprises the following steps:

[0006] C0, collect relevant information of a signal crossroad, including the number R of entrance directions and exit directions, the number U of entrance lanes contained in each entrance a and the number L of exit lanes a; wherein the import direction, the export direction and the import lane are numbered in clockwise order from small to large, wherein: a e A = {1, 2,..., R} is the import number, c e C a = {1, 2,..., U a} is the import lane number, and correspondingly, the export direction number b e B = {1, 2,..., R} ;

[0007] C1, investigate the actual situation of the scene and select various model parameters, the maximum and minimum values of the signal light period p max , p min , the maximum and minimum values of the green light time g max , g min , the maximum acceptable saturation of each lane υ a,c , the emptying time of all conflict traffic flows α a,b,d,f , the green light compensation time Θ, the conversion coefficient of different flow directions ε a,b , the conversion coefficient increased by the left and right traffic flows on the shared lane The flow Q a,b of each import in each period;

[0008] C2, input the flow data Q a,b of each import in each period into the model, obtain the lane channelization scheme, traffic distribution scheme and signal timing scheme of each period of the intersection through a set of mixed integer linear programming models constructed with the objective of minimizing the common multiplier and combined with the channelization restriction constraint, and realize the rolling collaborative optimization of the space-time resources of the intersection; the mixed integer linear programming model specifically includes lane channelization constraints, traffic distribution constraints, signal timing constraints and objective functions.

[0009] Further, the west import is numbered as 1, and the other imports are numbered in clockwise order as 2, 3,..., R; at the same time, the west export is numbered as 1, and the other exports are numbered in clockwise order as 2, 3,..., R.

[0010] Further, the lane channelization constraint includes:

[0011]

[0012]

[0013]

[0014]

[0015] In the formula:

[0016] B is the number set of the export, b e B, b1 e B, b2 e B;

[0017] C a Let C be the set of numbers for the entrance lanes. a ;

[0018] U a This represents the maximum number for the entrance lane.

[0019] λ a,b,c This is a binary variable representing whether lane c is allowed for traffic flow (a, b). A value of 1 indicates that lane c is allowed.

[0020] It is allowed to be used, but not allowed when the value is 0; (a,b) represents the direction of traffic flow;

[0021] E Γ(a,b) Let (a, b) be the number of exit lanes for traffic flow (a, b).

[0022] It is a binary variable used to determine whether lane c is allowed to flow traffic.

[0023] Lanes (a, b1) and (a, b2) share the same lane. A value of 1 indicates that both traffic flows can travel on lane c, meaning lane c is...

[0024] A shared lane for two traffic flows; the opposite occurs when the value is 0.

[0025] M is a large number;

[0026] C a / {U a} represents the set of entry lane numbers excluding the maximum value among the entry lane numbers;

[0027] Among them, constraint (1) ensures that at least one traffic flow leaves through lane c;

[0028] Constraint (2) restricts the distribution of different lanes, namely, the left-turn lane must be on the left side of the straight lane and the right-turn lane must be on the right side of the straight lane;

[0029] Constraint (3) means that for each traffic flow (a,b), the number of its inbound lanes should be less than the number of its outbound lanes, Γ(a,b)=b, which represents the number of outbound lanes;

[0030] Constraint (4) is used to determine whether traffic flows (a,b1) and (a,b2) can travel in the same lane, that is, to determine whether lane c is a shared lane for the two traffic flows.

[0031] Furthermore, the traffic flow distribution constraints include:

[0032] q a,b,c ≤Mλ a,b,c a∈A, b∈B, c∈C a (5)

[0033]

[0034]

[0035] wherein:

[0036] q a,b,c is the flow of traffic flow (a, b) on lane c, (a, b) denotes the direction of the traffic flow;

[0037] Q a,b is the total traffic demand of traffic flow (a, b);

[0038] Ω is a common multiplier, and also the objective function in this module;

[0039] ε a,b is the conversion factor needed to convert the turning traffic flow into the equivalent straight traffic flow, ε a,b = 1 + 1.5 / d a,b , d a,b is the turning

[0040] radius;

[0041] denotes the conversion factor for the additional traffic flow (a, b1) on the same lane as (a, b2) which is affected by the traffic flow (a, b2) in the direction of (a, b1);

[0042] ζ a,c denotes the capacity of the entrance a lane c;

[0043] Constraint (5) ensures that the traffic flow (a, b) can only leave the intersection through the permitted lane c;

[0044] Constraint (6) ensures that the sum of the flows of traffic flows (a, b) distributed on different entrance lanes is equal to the total demand of the flow direction;

[0045] Constraint (7) ensures that the distribution of traffic flows on each permitted lane obeys the queuing theory, i.e. the saturation degree is equal, wherein denotes the equivalent straight traffic flow of the turning traffic flow in a certain flow direction, denotes the equivalent flow of the traffic flow (a, b1) on lane c which is affected by the traffic flow (a, b2).

[0046] Further, the signal timing constraints include:

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] wherein:

[0057] σ is the inverse of the cycle length;

[0058] p max is the maximum cycle length;

[0059] p min is the minimum cycle length;

[0060] ψ a,b is the green time length corresponding to the traffic flow (a, b) in units of cycle length 1 / σ, (a, b) represents the flow direction of the traffic flow;

[0061] g max is the maximum green time length;

[0062] g min is the minimum green time length;

[0063] δ a,b is the green start time corresponding to the traffic flow (a, b) in units of cycle length 1 / σ;

[0064] Δ a,c is the green start time corresponding to the lane c of the import a in units of cycle length 1 / σ;

[0065] Ψ a,c is the green time length corresponding to the lane c of the import a in units of cycle length 1 / σ;

[0066] γ a,b,d,f is a binary variable representing the precedence order of the conflicting traffic flow; if γ a,b,d,f = 0, it means that the green signal of the traffic flow (a, b) precedes the green signal of the conflicting traffic flow (d, f), otherwise the traffic flow (d, f) precedes;

[0067] α a,b,d,f is the clearance time, including the yellow light time and the all-red time;

[0068] υa,c maximal acceptable saturation of the import a-lane c;

[0069] Θ is the effective green light compensation time; Λ is the set of all conflicting traffic flows;

[0070] Constraint (8) limits the range of the reciprocal of the cycle length to

[0071] Constraint (9) limits the range of the green light time to [g min σ, g max σ];

[0072] Constraint (10) indicates that the start time of the green light is greater than 0;

[0073] Constraint (11) limits the end time of the green light to be less than 1;

[0074] Constraint (12) indicates that different traffic flows running in the same lane have the same green light start time;

[0075] Constraint (13) indicates that different traffic flows running in the same lane have the same green light length;

[0076] Constraints (14) and (15) separate the conflicting traffic flows by the phase sequence;

[0077] Constraint (16) limits the saturation of all lanes to be less than the maximal acceptable saturation.

[0078] Further, let Constraints (7) and (16) are rewritten as constraints (17) and (18), respectively; and Constraints (19)-(22) are used to linearize the constraints as follows:

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085] Further, the following constraints are used to ensure that the vehicle only needs to change lanes once to complete the normal driving task under the two calculated channeling schemes, and the constraints are specifically:

[0086] Definition Ξ n,a,b,c is a binary variable, when the nth iteration gets lane c to allow traffic flow (a, b) to use, then Ξ n,a,b,c is equal to 1, and Ξ n,a,b,c is equal to 0; c a,b,min , c a,b,max are the minimum and maximum values of the lane numbers that allow traffic flow (a, b) to use in the last iteration, respectively;

[0087] If c a,b,max + 2 ≤ U a , then make

[0088]

[0089] This constraint means that only lane c a,b,max + 1 can be added to the drivable lanes of traffic flow (a, b), and further lanes cannot be allowed to pass through traffic flow (a, b);

[0090] When c a,b,max + 2 > U a , no additional constraints are needed;

[0091] If c a,b,min - 2 ≥ 1, then make

[0092]

[0093] This constraint means that only lane c a,b,min - 1 can be added to the drivable lanes of traffic flow (a, b), and further lanes cannot be allowed to pass through traffic flow (a, b);

[0094] When c a,b,min - 2 < 1, no additional constraints are needed;

[0095] Constraints (23) and (24) control the tendency of different turning lanes to increase outward, and for the same traffic flow (a, b), the next calculation of the available lanes to be added is limited to the adjacent lanes of the last time the lane is channeled;

[0096] If (a, b) is a left-turn traffic flow, and c a,b,min ≠ c a,b,max , then make

[0097]

[0098] This constraint means that if there are at least two lanes that allow left-turn traffic flow (a, b) to pass in the last stage of optimization results, then the next stage of optimization needs to ensure that the c a,b,min + 1thlane allows traffic flow (a, b) to pass;

[0099] If (a, b) is a right-turn traffic flow, and c a,b,min ≠ c a,b,max , then make sure that

[0100]

[0101] The constraint means that there are at least two lanes in the last stage optimization result that allow the right-turn traffic flow (a, b) to pass, so the c a,b,max -1thlane is allowed to pass the traffic flow (a, b) in the next stage optimization;

[0102] If (a, b) is a straight traffic flow, and there are two lanes allowing straight, that is, c a,b,max -c a,b,min = 1, then make sure that

[0103] The constraint means that the two lanes allowing straight in the last stage are still allowed to straight in the next stage optimization;

[0104] If (a, b) is a straight traffic flow, and there are three or more lanes allowing straight, that is, c a,b,max -c a,b,min > 1, then make sure that

[0105] The constraint means that among the lanes allowing straight in the last stage, except for the outermost two lanes, the other lanes are still allowed to straight in the next stage optimization.

[0106] The beneficial effects of the present application are:

[0107] The present application provides a dynamic regulation method for intersection space-time resources based on mixed integer linear programming. Considering the layout requirements of each flow direction lane, the distribution requirements of traffic flow between lanes, and the matching relationship between signals and lanes, etc., a set of mixed integer linear programming model is established as the basic optimization model for signal timing and lane channelization. Then from the perspective of vehicle lane changing, a constraint of channelization change limitation between the front and rear time periods is established, and combined with the basic optimization model, an updated mixed integer linear programming model is established to support the rolling collaborative optimization of signal timing and lane channelization. The method realizes the dynamic regulation of intersection space-time resources, and on the basis of fully utilizing the intersection space-time resources, ensures that the driver will not feel unadapted due to the large change of channelization scheme, and ensures the driving safety. In addition, the scale of the mixed integer linear programming model constructed by the method is small, and after inputting the real-time traffic demand data, it can be directly and quickly solved by the existing solver. BRIEF DESCRIPTION OF DRAWINGS

[0108] Figure 1 A schematic diagram of a four-lane intersection entrance and entrance lane numbering;

[0109] Figure 2 Rolling optimization constraint module schematic Figure 1 ;

[0110] Figure 3 Rolling optimization constraint module schematic Figure 2 ;

[0111] Figure 4 Rolling optimization constraint module schematic Figure 3 ;

[0112] Figure 4 Rolling optimization constraint module schematic Figure 6 ;

[0113] Figure 5 Rolling optimization constraint module schematic Figure 7 ;

[0114] Figure 8 Rolling optimization workflow diagram

[0115] Figure 9 Lane channeling scheme obtained by solving stage one

[0116] Figure 10 Lane channeling scheme obtained by solving stage two

[0117] Figure 11 Lane channeling scheme obtained by solving stage three

[0118] Figure 12 Lane channeling scheme obtained by solving stage four

[0119] Figure 13 Signal timing scheme obtained by solving stage one

[0120] Figure 14 Signal timing scheme obtained by solving stage two

[0121] Figure 15 Signal timing scheme obtained by solving stage three

[0122] Figure 2 Signal timing scheme obtained by solving stage four DETAILED DESCRIPTION

[0123] The application provides an intersection space-time resource dynamic regulation method based on mixed integer linear programming, C1, a basic optimization module

[0124] The module constructs a mixed integer linear programming model for coordinating optimization of signal timing scheme and lane channelization scheme. The module contains five parts, which are lane channelization constraints (1)-(4), traffic flow distribution constraints (5)-(7), signal timing constraints (8)-(16), linearization processing of constraints (17)-(22) and objective function-maximization of intersection capacity Ω.

[0125] C11, lane channelization constraint

[0126]

[0127]

[0128]

[0129]

[0130] In the formula:

[0131] B is a set of numbers of exits, b∈B, b1∈B, b2∈B;

[0132] C a is a set of numbers of import lanes, c∈C a ;

[0133] U a is a maximum value of numbers of import lanes;

[0134] λ a,b,c is a binary variable, which represents whether the lane c is allowed to be used by the traffic flow (a, b), and when the value is 1, it represents that the lane c is allowed to be used, and when the value is 0, it represents that the lane c is not allowed to be used;

[0135] E Γ(a,b) is the number of exit lanes of the traffic flow (a, b);

[0136] is a binary variable, which is used to judge whether the lane c is allowed to be used by the traffic flows (a, b1) and (a, b2) to pass through together, and when the value is 1, it represents that the two traffic flows can drive on the lane c, that is, the lane c is a shared lane of the two traffic flows, and when the value is 0, it is opposite;

[0137] M is a large number, which is far greater than the final objective function value according to the specific circumstances of the problem, and in the present application, it is equal to 10000.

[0138] Constraint (1) guarantees that at least one traffic stream leaves the intersection through lane c; constraint (2) restricts the distribution of different lanes, i.e. left-turn lanes must be on the left side of straight lanes and right-turn lanes must be on the right side of straight lanes; constraint (3) indicates that for each traffic stream (a, b), the number of its import lanes should be less than the number of its export lanes, Γ(a, b) = L b , represents the number of export lanes; constraint (4) is used to determine whether traffic streams (a, b1) and (a, b2) can run on the same lane, i.e. to determine whether lane c is a shared lane for the two traffic streams.

[0139] C12, traffic stream distribution constraint

[0140] q a,b,c ≤ Mλ a,b,c a e A, b e B, c e C a (5)

[0141]

[0142]

[0143] wherein:

[0144] q a,b,c is the flow of traffic stream (a, b) on lane c;

[0145] Q a,b is the total traffic demand of traffic stream (a, b);

[0146] Ω is a common multiplier and also the objective function in this module;

[0147] ε a,b is the conversion factor needed to convert the turning traffic flow into the equivalent straight traffic flow, ε a,b = 1 + 1.5 / d a,b , d a,b is the turning radius;

[0148] η a,b1,b2 means the additional conversion factor of traffic stream (a, b1) affected by traffic stream (a, b2) running on the same lane;

[0149] ζ a,c represents the capacity of import a lane c;

[0150] Constraint (5) guarantees that traffic stream (a, b) can only leave the intersection through the allowed lane c; constraint (6) guarantees that the sum of the flows of traffic streams (a, b) distributed on different import lanes is equal to the total demand of the flow direction; constraint (7) guarantees that the traffic stream distribution of each permitted lane complies with the queuing theory, i.e. the saturation degree is equal, wherein This represents the equivalent of a straight-through traffic flow for a given direction of traffic turning. This represents the equivalent flow increase in traffic flow (a,b1) on lane c due to the influence of traffic flow (a,b2).

[0151] C13, Signal Timing Constraints

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158]

[0159]

[0160]

[0161] In the formula:

[0162] σ is the reciprocal of the period duration;

[0163] p max This is the maximum cycle duration;

[0164] p min Minimum cycle duration;

[0165] ψ a,b The green light duration corresponding to traffic flow (a,b) is expressed in units of cycle length 1 / σ.

[0166] g max This is the maximum green light duration;

[0167] g min This is the minimum green light duration;

[0168] δ a,b The starting time of the green light for traffic flow (a,b) is expressed in terms of cycle duration 1 / σ.

[0169] Δ a,c The starting time of the green light for lane c of import a is expressed in units of cycle duration 1 / σ.

[0170] Ψ a,c The green light duration for lane c of import lane a is expressed in units of cycle duration 1 / σ.

[0171] γ a,b,d,f is a binary variable, indicating the precedence of the conflicting traffic flow. If γ a,b,d,f = 0, it means that the green signal of traffic flow (a, b) precedes the green signal of the conflicting traffic flow (d, f), and vice versa;

[0172] α a,b,d,f is the clearance time, including the yellow light time and the all-red time;

[0173] υ a,c is the maximum acceptable saturation of the import lane c of traffic flow a;

[0174] Θ is the effective green compensation time;

[0175] Λ is the set of all conflicting traffic flows.

[0176] Constraint (8) limits the range of the reciprocal of the cycle length to be Constraint (9) limits the range of the green time to be [g min σ, g max σ]; Constraint (10) means that the start time of the green light should be greater than 0; Constraint (11) limits the end time of the green light to be less than 1; Constraint (12) means that different traffic flows running on the same lane have the same green start time; Constraint (13) means that different traffic flows running on the same lane have the same green time; Constraints (14) and (15) separate the conflicting traffic flows by the signal phase sequence; Constraint (16) limits the saturation of all lanes to be less than the maximum acceptable saturation.

[0177] C14, Linearization of constraints

[0178] In order to facilitate the solution, the term in constraint (7) and (16) needs to be linearized to make the final model a mixed integer linear programming model. Let Constraints (7) and (16) can be rewritten as constraints (17) and (18), respectively. In addition, for itself, linearization of constraints (19)-(22) is also needed.

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] C15, Objective function of the base optimization model

[0186] The objective function is to maximize the capacity of the intersection. If it is assumed that the demand matrix of all turning traffic flows is proportionally increased, then maximizing the capacity of the intersection is equivalent to maximizing the common multiplier in constraint (6).

[0187] That is, the objective function is: maxΩ.

[0188] Further, the present application also comprises a rolling optimization constraint module:

[0189] C2. Rolling optimization constraint module

[0190] The function of the module is to avoid the situation that the channelization schemes obtained by the two consecutive calculations in the rolling optimization process differ too much, reduce the discomfort of the driver caused by the too large dynamic change of the lane channelization, and improve the driving safety.

[0191] In the present application, the "too large difference" is defined as: due to the change of the channelization schemes obtained by the two consecutive calculations, the situation that the vehicle needs to change two or more lanes to complete the normal driving task occurs.

[0192] The rolling optimization constraint module avoids the situation that the channelization schemes obtained by the two consecutive calculations differ too much through constraints (23)-(28), that is, the vehicle only needs to change lanes once to complete the normal driving task under the channelization schemes obtained by the two consecutive calculations, which maximally reduces the discomfort of the driver caused by the change of the channelization schemes and improves the driving safety.

[0193] In addition, the present application considers that the driver is less sensitive to the dynamic change of the signal timing, and therefore does not add additional constraints thereto.

[0194] Definition Ξ n,a,b,c is a binary variable, when the lane c is allowed to be used by the traffic flow (a, b) obtained in the nth iteration, then Ξ n,a,b,c takes the value 1, and if not allowed, then Ξ n,a,b,c takes the value 0; c a,b,min , c a,b,max are the minimum value and the maximum value of the lane number allowed to be used by the traffic flow (a, b) obtained by the last iteration calculation, respectively.

[0195] If c a,b,max +2≤U a , then make

[0196]

[0197] This constraint means that only the lane numbered c a,b,max +1 can be added as a drivable lane for traffic flow (a, b), and no further lane can be allowed for traffic flow (a, b).

[0198] When c a,b,max +2 > U a , no additional constraint is needed.

[0199] If c a,b,min -2 > 1, then make c

[0200]

[0201] This constraint means that only the lane numbered c a,b,min -1 can be added as a drivable lane for traffic flow (a, b), and no further lane can be allowed for traffic flow (a, b).

[0202] When c a,b,min -2 < 1, no additional constraint is needed.

[0203] The purpose of constraints (23) and (24) is to control the tendency of adding lanes outwardly. For the same traffic flow (a, b), the candidate lanes that can be added in the next optimization are limited to the adjacent lanes of the last added lanes. For example, for the six-lane intersection in Figure 3 , if lanes 3 and 4 are allowed for straight traffic in the last optimization, then in the next optimization, the straight lanes can be added at most to lanes 2 and 5.

[0204] If (a, b) is a left-turn traffic flow and c a,b,min ≠ c a,b,max , then make c

[0205]

[0206] This constraint means that if there are at least two lanes allowed for left-turn traffic (a, b) in the last optimization, then in the next optimization, the c a,b,min +1thlane should be allowed for traffic flow (a, b). The purpose of constraint (25) is to control the tendency of reducing left-turn lanes from right to left. In the next optimization, at most one left-turn lane on the right can be reduced. For example, for the four-lane intersection in Figure 4 , if lanes 2, 3, and 4 are allowed for left-turn in the last optimization, then in the next optimization, lanes 3 and 4 should still be allowed for left-turn, and at most one lane 2 can be reduced.

[0207] If (a, b) is a right-turn traffic flow, and c a,b,min ≠ c a,b,max , then make sure that

[0208]

[0209] This constraint means that there are at least two lanes in the previous stage optimization result that allow the right-turn traffic flow (a, b) to pass, so in the next stage optimization, the c a,b,max -1thlane should be allowed for the traffic flow (a, b) to pass. The constraint (26) is set to control the tendency of the right-turn lanes to gradually decrease from left to right, and at most one right-turn lane on the left side can be reduced in the next stage optimization. For example, for the four-lane intersection in Figure 5 , if the 1st, 2nd, and 3rdlanes are allowed for right-turn in the previous stage, then in the next stage optimization, the 1stand 2ndlanes should still be allowed for right-turn, and at most one 3rdlane can be reduced.

[0210] If (a, b) is a straight traffic flow, and there are two lanes allowed for straight, i.e., c a,b,max -c a,b,min = 1, then make sure that

[0211]

[0212]

[0213] This constraint means that among the two lanes allowed for straight in the previous stage, at least one lane should still be allowed for straight in the next stage optimization. The constraint (27) ensures that under the channeling scheme obtained in the next stage, the vehicles on the original straight lanes only need to change lanes at most once to complete the driving task. For example, for the four-lane intersection in Figure 6 , if the 2ndand 3rdlanes are allowed for straight in the previous stage, then in the next stage optimization, at least one of the 2ndor 3rdlanes should still be allowed for straight, and at most one lane can be reduced.

[0214] If (a, b) is a straight traffic flow, and there are three or more lanes allowed for straight, i.e., c a,b,max -c a,b,min > 1, then make sure that

[0215]

[0216] This constraint means that among the lanes allowed for straight in the previous stage, except for the two outermost lanes, the other lanes should still be allowed for straight in the next stage optimization. The constraint (28) limits the lanes that can be reduced in the next stage optimization to the two outermost straight lanes. For example, for the four-lane intersection in Figure 7In a six-lane intersection, if lanes 2, 3, 4, and 5 were allowed to go straight in the previous stage, then in the next stage of optimization, it is necessary to ensure that lanes 3 and 4 are still allowed to go straight, and lanes 2 and 5 can be reduced at most.

[0217] The specific implementation process of rolling collaborative optimization based on the basic optimization module and the rolling optimization constraint module is as follows: Figure 1 The explanation is as follows:

[0218] (1) First, input the initial flow to enter the basic optimization module;

[0219] (2) The basic optimization module calculates the initial signal timing scheme and the initial lane channelization scheme based on the input traffic flow and outputs them;

[0220] (3) Input the initial lane channelization scheme into the rolling optimization constraint module to obtain the initial channelization constraint;

[0221] (4) Combine the channelization constraints with the basic optimization module to obtain an updated optimization module. Then input the newly collected traffic flow data into the updated optimization module to generate updated signal timing schemes and lane channelization schemes, and output the two schemes;

[0222] (5) Input the updated lane channelization scheme into the rolling optimization constraint module to obtain the updated channelization constraint;

[0223] (6) Determine whether the optimization time has reached the preset maximum value. If it has reached the maximum value, exit the calculation; otherwise, return to (4).

[0224] by Figures 8 to 11 The above method will be explained and verified using a typical four-lane signalized intersection as an example. In this case, the process of solving for the initial lane channelization scheme is called stage one, the process of solving for the second updated lane channelization scheme is called stage two, and stages three and four are similar.

[0225] The pre-setting parameters are as follows: Take the shortest period p of the signal. min The longest period is 60s, p. max Set the minimum green light time to 120 seconds (g). min The longest green light time is 6 seconds. max The maximum acceptable saturation υ for each lane in the model is 60 seconds. a,c The value is 0.9, and the clearing time α is [value missing] for all conflicting traffic flows. a,b,d,f All values ​​are set to 6 seconds, and the green light compensation time Θ is set to 3 seconds.

[0226] On a shared lane, traffic flow in one direction is affected by left and right turning traffic. We use a conversion coefficient. Quantifying this effect, it takes the value of 0.1 times the corresponding turning flow conversion factor ε a,b The additional effect of through flow on other turning flows is not considered. The conversion factors for different turning flows are shown in Table 1.

[0227] Table 1 Conversion factors for different turning flows

[0228]

[0229] The total control time is 1 hour, which is divided into 4 periods, each of which is 15 minutes long (this period can be shortened or lengthened according to actual conditions). The flow data required for each calculation is required to be automatically collected and input into the model according to the road conditions. The input flow data for the 4-stage solution is shown in Tables 2 to 5. Table 2 data is the initial flow input in stage 1, which is used to generate the initial signal timing scheme, the initial lane channeling scheme, and the initial channeling restriction constraints. The data in Table 3 is the flow input in stage 2, which is used to generate the updated signal timing scheme, the lane channeling scheme, and the updated channeling restriction constraints. Tables 4 and 5 follow the same pattern.

[0230] Table 2 Traffic demand in stage 1

[0231]

[0232]

[0233] Table 3 Traffic demand in stage 2

[0234]

[0235] Table 4 Traffic demand in stage 3

[0236]

[0237] Table 5 Traffic demand in stage 4

[0238]

[0239] The Python platform is used to call the CPLEX solver to directly solve each mixed integer linear programming model involved in the rolling optimization process. Figures 12 to 15 The intersection lane channeling schemes generated for stages 1 to 4 are Figures 8 to 11 The signal timing schemes generated for stages 1 to 4 are

[0240] From Figures 12-15 It can be seen that:

[0241] For 1 import (west import), the left-turn lane is initially distributed in 4 lanes, then distributed in 3 and 4 lanes, and finally distributed in 4 lanes; the right-turn lane is initially distributed in 1 lane, then distributed in 1 and 2 lanes, and finally distributed in 1 lane; the straight lane is initially distributed in 2 and 3 lanes, then distributed in 3 lanes, and finally distributed in 2, 3 and 4 lanes.

[0242] For 2 import (north import), the left-turn lane is initially distributed in 4 lanes, then distributed in 3 and 4 lanes; the right-turn lane is always distributed in 1 lane; the straight lane is initially distributed in 2 and 3 lanes, then distributed in 2 lanes, then distributed in 2 and 3 lanes, and finally distributed in 2 lanes.

[0243] For 3 import (east import), the left-turn lane is initially distributed in 4 lanes, then distributed in 3 and 4 lanes; the right-turn lane is always distributed in 1 lane; the straight lane is always distributed in 2 and 3 lanes.

[0244] For 4 import (south import), the left-turn lane is initially distributed in 3 and 4 lanes, then distributed in 4 lanes, and then always distributed in 3 and 4 lanes; the right-turn lane is always distributed in 1 lane; the straight lane is always distributed in 2 and 3 lanes.

[0245] It can be seen that the changes of the lanes of different directions of each import meet the condition that the driver needs to change lanes at most once to complete the driving task, i.e. there is no "too large difference" in the channelization scheme.

[0246] Tables 6 and 7 further give the signal timing parameters and the corresponding objective function values obtained by the four-stage optimization. ​ The signal timing scheme obtained by the four-stage optimization is shown in the figure.

[0247] Table 6 Green start time and green duration obtained by optimization in different stages

[0248]

[0249] Table 7 Traffic capacity coefficient and signal cycle value obtained by optimization in different stages

[0250]

[0251] The remaining matters of the present application are known technologies.

[0252] The above examples are only for illustrating the technical concept and characteristics of the present application, and the purpose is to enable those skilled in the art to understand the content of the present application and implement it, and cannot limit the protection scope of the present application. Any equivalent changes or modifications made according to the spirit and essence of the present application should be covered within the protection scope of the present application.

Claims

1. A method for dynamic regulation of intersection space-time resources based on mixed integer linear programming, characterized in that: Comprising: Co, collect the relevant information of a signalized intersection, including the number of import directions and export directions R, the number of import lanes included in each import U a and the number of export lanes L a ; wherein the import direction, the export direction and the import lane are numbered in clockwise order from small to large, wherein: a∈A={1,2,...,R} is the import number, c∈C a ={1,2,...,U a} is the import lane number, and correspondingly, the export direction number b∈B={1,2,...,R}. C1, investigate the actual situation and select various model parameters, the maximum and minimum values of the signal light cycle p max , p min , the maximum and minimum values of the green light time g max , g min , the maximum acceptable saturation of each lane υ a,c , the emptying time of all conflict traffic flows α a,b,d,f , the green light compensation time Θ, the conversion coefficient of different flow directions ε a,b , the conversion coefficient increased by the influence of left and right traffic on the shared lane The flow of each import in each period Q a,b ; C2, the flow data Q a,b The lane channelization scheme, the traffic flow distribution scheme and the signal timing scheme of each intersection in each time period are obtained by constructing a set of mixed integer linear programming models aiming at minimizing a common multiplier and cooperating with channelization constraints, so as to realize the rolling and collaborative optimization of the space-time resources of the intersection; the mixed integer linear programming model specifically comprises a lane channelization constraint, a traffic flow distribution constraint, a signal timing constraint and an objective function. The constraint is to ensure that the vehicle only needs to change lane once to complete the normal driving task under the channeling scheme calculated twice, and the constraint is as follows: Definition Ξ n,a,b,c is a binary variable, which takes the value 1 if at the n-th iteration the lane c is allowed to be used by the traffic flow (a, b) and 0 otherwise. n,a,b,c is a binary variable, which takes the value 1 if at the n-th iteration the lane c is allowed to be used by the traffic flow (a, b) and 0 otherwise. n,a,b,c is a binary variable, which takes the value 1 if at the n-th iteration the lane c is allowed to be used by the traffic flow (a, b) and 0 otherwise. a,b,min , c a,b,max are the minimum and maximum values of the lane numbers allowed to be used by the traffic flow (a, b) at the previous iteration, respectively. If c a,b,max + 2 < U a , then make so that The constraint means that only the lane numbered c a,b,max +1 can be added as a drivable lane for traffic flow (a, b), and no further lanes can be allowed for traffic flow (a, b). When c a,b,max +2>U a then no additional constraints are needed; If c a,b,min -2≥1, then make such that This constraint means that only the lane numbered c a,b,nin -1 can be added as a drivable lane for traffic flow (a, b), and no further lanes can be allowed for traffic flow (a, b). When c a,b,min -2 < 1, no additional constraints are needed; Constraints (23) and (24) control the tendency of different turning lanes to increase outward, and for the same traffic flow (a, b), the number of lanes that can be increased in the next calculation is limited to the adjacent lanes of the channeling lane in the last calculation; If (a, b) is a left-turn flow, and c a,b,min ≠ c a,b,max , then make such that The constraint means that if there are at least two lanes in the previous stage optimization result allowing the left-turn traffic flow (a, b) to pass, then the next stage optimization needs to ensure that the first c a,b,min +1 lane is allowed to pass the traffic flow (a, b). If (a, b) is a right-turn flow, and c a,b,min ≠ c a,b,max then make such that The constraint means that at least two lanes in the optimization result of the last stage allow the right-turn traffic flow (a, b) to pass, so the next stage optimization needs to ensure that the c a,b,max -1 lane is allowed to pass the traffic flow (a, b); If (a, b) is a straight flow, and there are two lanes allowing straight, i.e. c a,b,max - c a,b,min = 1, then make sure that The constraint means that at least one lane of the two lanes allowed to go straight in the last stage still allows straight driving when optimizing in the next stage; If (a, b) is a straight flow, and there are three or more lanes allowing straight, i.e. c a,b,max - c a,b,min >1, then make sure that The constraint means that among the lanes allowed to go straight in the last stage, except for the two outermost lanes, the other lanes still allow straight driving when optimizing in the next stage.

2. The method of claim 1, wherein: The west import is numbered 1, and the other imports are numbered clockwise as 2, 3, …, R; at the same time, the west export is numbered 1, and the other exports are numbered clockwise as 2, 3, …, R.

3. The dynamic control method of intersection space-time resources based on mixed integer linear programming according to claim 1, characterized in that: The lane channeling constraint comprises: In the formula: B is a set of export numbers, b∈B, b1∈B, b2∈B; C a is a set of numbers for import lanes, c e C a ; U a is the maximum value of the number of import lanes; λ a,b,c is a binary variable, indicating whether the lane c allows the traffic flow (a, b) to use, and when it takes the value 1, it indicates that it allows to use, and when it takes the value 0, it does not allow to use; (a, b) indicates the flow direction of the traffic flow; E Γ(a,b) is the number of exit lanes for the traffic flow (a, b); is a binary variable that indicates whether lane c allows traffic flow or not (a, b1) and (a, b2) are common traffic flows, and when the value is 1, it means that both traffic flows can travel on lane c, that is, lane c is a shared lane of the two traffic flows, and when the value is 0, it is the opposite; M is a large number; Constraint (1) ensures that at least one traffic flow passes through lane c to leave; Constraint (2) limits the distribution of different lanes, that is, the left-turn lane must be on the left side of the straight lane, and the right-turn lane must be on the right side of the straight lane; Constraint (3) means that for each traffic flow (a, b), the number of import lanes should be less than the number of export lanes, Γ(a, b) = b, indicating the number of export lanes; Constraint (4) is used to determine whether traffic flows (a, b1) and (a, b2) can travel on the same lane, that is, to determine whether lane c is a shared lane of the two traffic flows.

4. The dynamic control method of intersection space-time resources based on mixed integer linear programming according to claim 1, characterized in that: The traffic distribution constraint comprises: q a,b,c ≤Mλ a,b,c a∈A,b∈B,c∈C a (5) In the formula: q a,b,c is the traffic flow on the lane c, (a, b) indicates the flow direction of the traffic flow; Q a,b Q is the total traffic demand for the traffic flow (a, b); Ω is a common multiplier and also a target function; ε a,b The conversion factor, ε, needed to convert a turning traffic flow into a straight-ahead traffic flow equivalent a,b = 1 + 1.5 / d a,b ,d a,b is the turning radius; The meaning is the additional conversion factor for the traffic flow (a, b1) influenced by the traffic flow (a, b2) in the same lane. ζ a,c represents the capacity of the import a lane c; Constraint (5) ensures that traffic flow (a, b) can only leave the intersection through the allowed lane c; Constraint (6) ensures that the sum of the flows of traffic flows (a, b) distributed on different import lanes is equal to the total demand of the flow direction; The constraint (7) guarantees that the traffic flow distribution of each permitted lane obeys the queuing theory, i.e. the saturation degree is equal, where represents the equivalent of straight traffic flow to a certain flow direction turning traffic flow, represents the equivalent flow of traffic flow (a, b1) on lane c which is increased by the influence of traffic flow (a, b2).

5. The dynamic control method of intersection space-time resources based on mixed integer linear programming according to claim 1, characterized in that: The signal timing constraint comprises: In the formula: σ is the reciprocal of the cycle length; p max is the maximum period duration; p min is the minimum period duration; Ψ a,b The green light duration corresponding to the traffic flow (a, b) is in units of cycle duration 1 / σ, (a, b) represents the flow direction of the traffic flow; g max is the maximum green light duration; g min is the minimum green light duration; delta a,b is the green start time for traffic flow (a, b) in units of cycle length 1 / sigma; Δ a,c The green light start time corresponding to the lane c of the import a, in the period length 1 / σ units; Ψ a,c is the green light duration corresponding to the import a lane c, in units of cycle duration 1 / σ; Y a,b,d,f is a binary variable, indicating the precedence of the conflicting traffic flow; if Y a,b,d,f = 0, it means that the green signal of traffic flow (a, b) precedes the green signal of the conflicting traffic flow (d, f), otherwise, the traffic flow (d, f) precedes. a a,b,d,f clear time, including yellow light time and all red time; υ a,c max accepted saturation for ingress a lane c; Θ is the effective green compensation time; Λ is a set of all conflicting traffic flows; The constraint (8) limits the range of values of the reciprocal of the period length to The constraint (9) limits the range of green light time values to [g min σ, g max σ]; Constraint (10) means that the start time of the green light is greater than 0; Constraint (11) limits the end time of the green light to be less than 1; Constraint (12) means that different traffic flows traveling on the same lane have the same green start time; Constraint (13) means that different traffic flows traveling on the same lane have the same green duration. Constraints (14) and (15) separate the conflicting traffic flows by signal phase sequence; Constraint (16) limits the saturation of all lanes to be less than a maximum acceptable saturation.

6. The method of claim 4 or 5, wherein: Let Rewrite constraints (7) and (16) into two constraints (17), (18) respectively; and Linearize constraints (19)-(22) as follows:

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