Optimization Methods for Lane Layout and Signal Timing Combination at T-Intersections

Abstract

This invention discloses an optimization method for lane layout and signal timing combination at T-junctions. First, it defines index variables related to the model, including intersection branch index, flow direction index, lane index, and saturation flow reduction coefficient index. Second, by introducing a double-ring standard phase, and considering the saturation flow reduction effect as well as the configuration of shared lanes and right-turn phases, a mixed-integer linear programming model is constructed with the signal cycle minimization as the objective function and lane layout, phase duration, saturation flow, traffic flow, flow ratio, and saturation degree as constraints. Finally, the branch-and-bound method is used to solve the model, obtaining the optimal lane layout and signal timing scheme for the T-junction, thereby improving vehicle throughput and reducing vehicle delays at the intersection.

Description

Technical Field

[0001] This invention relates to the field of traffic channelization design and signal control technology in traffic management and control, specifically a method for optimizing lane layout and signal timing combination at T-shaped intersections. Background Technology

[0002] With the continuous increase in car ownership, many cities have experienced severe traffic congestion. Intersections are bottlenecks in urban road traffic systems, and the rational allocation of their spatial and temporal resources and the level of traffic management directly affect the overall efficiency of the road system. The spatial and temporal resources of intersections are mainly reflected in lane layout and signal timing schemes. Lane layout plays a crucial role in the maximum capacity that an intersection can achieve, while signal timing schemes determine the passage time and sequence of conflicting traffic flows.

[0003] Traditional intersection signal timing methods often assume a fixed lane layout, which fails to adapt well to the spatial distribution of traffic demand. The resulting signal timing schemes also depend on peak-hour traffic conditions and may not be applicable to other times, potentially leading to wasted resources. When intersection traffic demand is high, only by incorporating lane layout and signal timing schemes into a combined optimization model, and fully utilizing the intersection's spatiotemporal resources, can the intersection's traffic efficiency be effectively improved. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method for optimizing lane layout and signal timing combination at T-junctions, addressing the shortcomings of the prior art. This method introduces a double-ring standard phase, considers the reduction effect of saturation flow with the increase of lane number, and the configuration of shared lanes and right-turn phases. It takes minimizing the signal cycle as the objective function and uses lane layout, phase duration, saturation flow, traffic flow, flow ratio, and saturation as constraints to construct a mixed-integer linear programming model for optimizing lane layout and signal timing combination at T-junctions. This improves the traffic efficiency of vehicles at T-junctions and reduces vehicle delays at the intersection.

[0005] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for optimizing lane layout and signal timing at a T-shaped intersection includes:

[0007] Step 1: Define index variables: global index for intersection approach direction, local index for intersection flow direction, local index variable for intersection approach lanes, and saturation flow reduction coefficient index variable;

[0008] Step 2: Phase design: The intersection phase adopts the double-ring standard phase, and the double-ring standard phase is applied to the T-shaped intersection;

[0009] Step 3: Construct the objective function: Set the objective function to minimize the signal period duration;

[0010] Step 4: Set lane layout constraints;

[0011] Step 5: Set phase duration constraints;

[0012] Step 6: Set saturation flow constraints;

[0013] Step 7: Set traffic flow constraints;

[0014] Step 8: Set flow ratio constraints;

[0015] Step 9: Set saturation constraints;

[0016] Step 10: Using Step 3 as the objective function and Steps 4-9 as constraints, construct a mixed integer linear programming model for optimizing lane layout and signal timing; use the branch and bound method to solve the constructed mixed integer linear programming model to obtain the optimal lane layout and signal timing for the T-shaped intersection.

[0017] As a further improvement to the present invention, step 1 specifically comprises:

[0018] Step 1.1

[0019] Let A be the set of intersection entrance directions, and A = {1, 2, 3}; i is the global index of the intersection entrance direction, and i ∈ A; where i = 1 represents the east entrance, i = 2 represents the south entrance, and i = 3 represents the west entrance;

[0020] Let D be the set of intersection flow directions, and D = {1, 2}; j is the local index of the intersection flow direction, and j ∈ D; for the east entrance i = 1: j = 1 indicates a left turn at the east entrance, and j = 2 indicates a straight turn at the east entrance; for the south entrance i = 2: j = 1 indicates a left turn at the south entrance, and j = 2 indicates a right turn at the south entrance; for the west entrance i = 3: j = 1 indicates a straight turn at the west entrance, and j = 2 indicates a right turn at the west entrance; therefore, the flow direction or phase of the intersection can be represented by a pair (i, j);

[0021] Step 1.2: Define the formula for converting a local index into a global index:

[0022]

[0023] Where Γ(i,j) represents the global index value of the direction of flow into (i,j);

[0024] Step 1.3: Let K iLet K be the set of lanes in the direction i of the intersection entrance, and k be a local index variable of the lanes at the intersection entrance, where k ∈ K. i k=1 represents the innermost lane, k=n i Represents the outermost lane, where n i This represents the total number of lanes in the direction of entry i, with the remaining lanes numbered sequentially from the inside out.

[0025] Step 1.4: Let R be the set of saturation flow reduction coefficients, and R = {1, 2, 3, 4}; r is the index variable of the saturation flow reduction coefficient, and r ∈ R;

[0026] If the flow direction (i,j) is a left turn or a right turn, then r=1 indicates that there is no dedicated lane for the flow direction (i,j), r=2 indicates that there is 1 dedicated lane for the flow direction (i,j), r=3 indicates that there are 2 dedicated lanes for the flow direction (i,j), and r=4 indicates that there are 3 or more dedicated lanes for the flow direction (i,j).

[0027] If the flow direction (i,j) is straight, then r=1 indicates that there is no dedicated lane or shared lane for the flow direction (i,j); r=2 indicates that there is 1 dedicated lane or shared lane for the flow direction (i,j); r=3 indicates that there are 2 dedicated lanes or 1 dedicated lane and 1 shared lane for the flow direction (i,j); and r=4 indicates that there are 3 or more lanes for the flow direction (i,j), and all 3 or more lanes are dedicated lanes or 1 shared lane, with the rest being dedicated lanes.

[0028] As a further improvement to the present invention, step 2 specifically comprises:

[0029] The intersection phase adopts the double-ring standard phase, which is applied to the T-shaped intersection;

[0030] With Φ i,j Φ represents the ratio of the duration of phase (i,j) to the duration of the signal period. i,j ∈(0,1); the duration of phase (i,j) includes the sum of the green light, yellow light and all-red light times.

[0031] As a further improvement to the present invention, step 3 specifically comprises:

[0032] The objective function is set as minimizing the signal period duration:

[0033] max = ξ;

[0034] In the formula, ξ is the reciprocal of the signal period duration C, i.e., ξ = 1 / C, where C must be located at the minimum allowable signal period C at the intersection. min and the maximum signal period C max Between them, as shown in the following formula:

[0035] Cmin ≤C≤C max .

[0036] As a further improvement to the present invention, step 4 specifically comprises:

[0037] Step 4.1: Set lane sequence constraints;

[0038] Introduce 0-1 variables x i,j,k Indicates whether the k-th lane in the import direction i is configured with flow direction j; if x i,j,k =1, then set the flow direction j; if x = 1, then set the flow direction j; i,j,k =0, then the opposite is true;

[0039] Since the flow direction j=1 needs to be to the left of the flow direction j=2 in each inlet direction, the following constraint applies:

[0040]

[0041]

[0042] Step 4.2: Set lane sharing constraints:

[0043] Introducing 0-1 variable δ i,k,s Indicates whether the k-th lane in the direction of entry i is set as a shared lane; if δ i,k,s =1, then it is set as a shared lane; if δ i,k,s =0, then the opposite is true;

[0044] For a T-junction, each entrance can have a maximum of one shared lane, therefore:

[0045]

[0046] If the k-th lane in the direction of entry i is a shared lane, then that lane has two flow directions; otherwise, it has only one flow direction. Therefore:

[0047]

[0048]

[0049] Where M is an arbitrarily large positive number;

[0050] Step 4.3: Set exit lane constraints;

[0051] Since the total number of inlet channels flowing to (i,j) cannot exceed the total number of corresponding outlet channels, the following constraint applies:

[0052]

[0053] In the formula E Γ(i,j)Let Γ(i,j) be the number of exit lanes in the import direction.

[0054] As a further improvement to the present invention, step 5 specifically comprises:

[0055] Step 5.1: Set loop and barrier constraints;

[0056] The T-shaped intersection features a double-loop phase structure with a phase duration Φ. i,j The following constraints should apply:

[0057] Φ 3,1 +Φ 2,1 +Φ 1,1 =1;

[0058] Step 5.2: Set the minimum green light constraint;

[0059] To ensure drivers have sufficient reaction time to changes in traffic lights and that vehicles can safely pass through intersections, Φ i,j There should be a minimum phase duration T i,j,min Constraints:

[0060]

[0061] Step 5.3: Set pedestrian crossing time constraints;

[0062] To meet the needs of pedestrians crossing the street and ensure that pedestrians crossing at the same phase (i,j) can smoothly cross the crosswalk, the following constraints are required, taking into account the phase relationship of the double-ring phase structure of the T-shaped intersection:

[0063]

[0064] Φ 1,2 +p 1,1 ·ξ=Φ 1,1 +Φ 3,1 ;

[0065]

[0066] Where p i,j L represents the time required for a pedestrian to cross the street in phase (i,j); i,j This represents the length of the pedestrian crossing corresponding to phase (i,j); v p This indicates the 15th percentile pedestrian crossing speed;

[0067] Step 5.4: Set the right turn phase duration constraint;

[0068] When all right-turn traffic flows are allocated dedicated lanes and do not share lanes with other traffic flows, the right-turn phase overlaps with two phases simultaneously. For example, when all right-turn traffic flows at the south entrance are allocated dedicated lanes, the right-turn phase can overlap with both the left-turn phase at the south entrance and the left-turn phase at the east entrance. Therefore:

[0069]

[0070] When right-turn traffic shares a lane with other traffic flows, the right-turn phase can only overlap with one phase; for example, when there is a shared lane at the south entrance, the right-turn phase can only be released synchronously with the left-turn phase at the south entrance, therefore:

[0071]

[0072] As a further improvement to the present invention, step 6 specifically comprises:

[0073] As the number of lanes in the same direction of flow increases, the saturation flow rate in that direction will be reduced.

[0074] Introducing 0-1 variable δ i,j,r Whether the r-th saturation flow reduction factor is set for the flow direction j in the inlet direction i, the constraint condition for the saturation flow reduction effect is as follows:

[0075]

[0076]

[0077] Furthermore, for any flow direction (i,j), there exists only one saturation flow reduction factor, thus the following constraints apply:

[0078]

[0079] As a further improvement to the present invention, step 7 specifically comprises:

[0080] Let the traffic flow to (i,j) be q. i,j The traffic flow direction (i,j) distributed along lane k is q. i,j,k , then q i,j With q i,j,k The following relationship should exist:

[0081]

[0082] If x i,j,k =0, meaning that the k-th lane in the import direction i does not have a flow direction j, then the corresponding q i,j,k It is also 0, therefore we have:

[0083]

[0084] The saturation flow reduction in step 6 is equivalent to an increase in traffic flow, and q is then adjusted accordingly. i,j,k ;

[0085] Let q i,j,k,f Let q be the traffic flow after adjustment to the k-th lane (i,j). i,j,k,f The following constraints must be met:

[0086]

[0087] Where f i,j,r This represents the reduction factor for the r-th saturated flow rate towards (i,j).

[0088] As a further improvement to the present invention, step 8 specifically comprises:

[0089] Step 8.1: Traffic flow allocation;

[0090] When there is no shared lane for the incoming direction i, the traffic flow to (i,j) is evenly distributed across each lane with the flow direction j. Therefore:

[0091]

[0092] When a shared lane is provided in the inbound direction i, the traffic flow distribution in each direction is equal in terms of the flow ratio of each lane. Therefore:

[0093]

[0094] Where s i,j The saturation flow rate of a single lane flowing towards (i,j);

[0095] Step 8.2: Flow ratio calculation;

[0096] When there is no shared lane in the inbound direction i, the flow rate in the direction (i,j) is evenly distributed across each lane, therefore its flow rate is higher than that in the direction y. i,j The following constraints should be met:

[0097]

[0098] When a shared lane is provided in the direction of entry i, the flow ratio of each lane is equal, therefore y i,j This can be taken as the flow ratio on lane k=1:

[0099]

[0100] As a further improvement to the present invention, step 9 specifically comprises:

[0101] To ensure efficient traffic flow for motor vehicles, maximum saturation limits are set for each phase, namely:

[0102]

[0103] Among them l i,j x represents the time loss for phase (i,j); m This represents the maximum saturation that each phase can accept.

[0104] Compared with existing technologies, the beneficial effects of this method are:

[0105] By introducing dual-ring standard phases into the lane layout and signal timing combination optimization model, the conflict relationship between phases at T-junctions is accurately reflected. A saturation flow reduction coefficient constraint is introduced to reflect the reduction effect of saturation flow with increasing lane number. The model also effectively handles the configuration of right-turn phases and shared lanes at intersections. Furthermore, the constructed model is a mixed-integer linear programming model, which can quickly obtain relatively ideal lane layout and signal timing optimization schemes. This improves the traffic efficiency of vehicles at T-junctions and reduces vehicle delays at intersections. Attached Figure Description

[0106] Figure 1 This is a schematic diagram of the intersection branch in the T-shaped intersection lane layout and signal timing combination optimization method of the present invention.

[0107] Figure 2 This is a schematic diagram of the intersection flow direction in the T-shaped intersection lane layout and signal timing combination optimization method of the present invention.

[0108] Figure 3 This is a schematic diagram of the standard phase of a cross-shaped intersection for the optimization method of lane layout and signal timing combination at a T-shaped intersection according to the present invention.

[0109] Figure 4 This is a schematic diagram of the standard phase of a double-ring T-shaped intersection in the T-shaped intersection lane layout and signal timing combination optimization method of the present invention.

[0110] Figure 5 These are schematic diagrams of the geometric shape of a T-shaped intersection in Embodiments 1 and 2 of the present invention, which are examples of the optimization method for lane layout and signal timing combination at T-shaped intersections.

[0111] Figure 6 This is a schematic diagram of the T-shaped intersection lane layout scheme of Embodiment 1 of the T-shaped intersection lane layout and signal timing combination optimization method of the present invention.

[0112] Figure 7 This is a schematic diagram of the signal timing scheme for a T-shaped intersection, which is an embodiment of the optimization method for lane layout and signal timing combination of the present invention.

[0113] Figure 8 This is a schematic diagram of the T-shaped intersection lane layout scheme of Embodiment 1 of the T-shaped intersection lane layout and signal timing combination optimization method of the present invention.

[0114] Figure 9 This is a schematic diagram of the signal timing scheme for a T-shaped intersection, which is an embodiment of the optimization method for lane layout and signal timing combination of the present invention. Detailed Implementation

[0115] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0116] A method for optimizing lane layout and signal timing at a T-shaped intersection includes the following steps 1-10.

[0117] Step 1: Define the index variable;

[0118] Step 1.1: Let A be the set of intersection entrance directions, and A = {1, 2, 3}; i is the global index of the intersection entrance direction, and i ∈ A, where i = 1 represents the east entrance, and the other entrances are numbered sequentially in a clockwise direction, as shown in the attached figure. Figure 1 As shown.

[0119] Let D be the set of intersection flow directions, and D = {1, 2}; j is a local index of the intersection flow direction, and j ∈ D. For the east entrance (i = 1), j = 1 and j = 2 represent left turns and straight-through traffic at the east entrance, respectively; for the south entrance (i = 2), j = 1 and j = 2 represent left turns and right turns at the south entrance, respectively; for the west entrance (i = 3), j = 1 and j = 2 represent straight-through traffic and right turns at the west entrance, respectively, as shown in the appendix. Figure 2 As shown. Therefore, the flow direction or phase at an intersection can be represented by a pair (i,j).

[0120] Step 1.2: Define the formula for converting local index j to global index i:

[0121]

[0122] Where Γ(i,j) represents the global index value of the direction of flow into (i,j).

[0123] Step 1.3: Let K i Let K be the set of lanes in the direction i of the intersection entrance, and k be a local index variable of the lanes at the intersection entrance, where k ∈ K. ik=1 represents the innermost lane, k=n i Indicates the outermost lane (where n) i (This represents the total number of lanes in the direction of entry i), and the remaining lanes are numbered in order from the inside out.

[0124] Step 1.4: Let R be the set of saturated flow reduction coefficients, and R = {1, 2, 3, 4}; r is the index variable of the saturated flow reduction coefficient, and r ∈ R.

[0125] If the flow direction (i,j) is a left turn or a right turn, then r=1 indicates that there is no dedicated lane for the flow direction (i,j), r=2 indicates that there is 1 dedicated lane for the flow direction (i,j), r=3 indicates that there are 2 dedicated lanes for the flow direction (i,j), and r=4 indicates that there are 3 or more dedicated lanes for the flow direction (i,j).

[0126] If the flow direction (i,j) is straight, then r=1 indicates that there is no dedicated lane or shared lane for the flow direction (i,j), r=2 indicates that there is 1 dedicated lane or shared lane for the flow direction (i,j), r=3 indicates that there are 2 dedicated lanes or 1 dedicated lane and 1 shared lane for the flow direction (i,j), and r=4 indicates that there are 3 or more lanes for the flow direction (i,j) (all of which are dedicated lanes or 1 shared lane and the rest are dedicated lanes).

[0127] Step 2: Phase design;

[0128] The intersection phase adopts the dual-loop standard phase specified by the National Electrical Manufacturers Association (NEMA) in TS-2, as shown in the attached document. Figure 3 As shown.

[0129] Based on the flow distribution at the T-junction, the double-loop phase is applied to the T-junction, as shown in the attached diagram. Figure 4 As shown. (Using Φ) i,j The ratio (Φ) of the duration of phase (i,j) (including the sum of the green, yellow, and all-red times) to the signal period duration. i,j ∈(0,1)).

[0130] Step 3: Construct the objective function;

[0131] The objective function of the model is set to minimize the signal period duration:

[0132] max = ξ;

[0133] In the formula, ξ is the reciprocal of the signal period duration C(s). -1 That is, ξ = 1 / C, where C must be located at the minimum allowable signal period C of the intersection. min (s) and maximum signal period Cmax Between (s), as shown in the following formula:

[0134] C min ≤C≤C max .

[0135] Step 4: Set lane layout constraints;

[0136] Step 4.1: Set lane sequence constraints;

[0137] Introduce 0-1 variables x i,j,k This indicates whether the k-th lane in the import direction i has a flow direction j setting. If x i,j,k =1, then set the flow direction j; if x = 1, then set the flow direction j; i,j,k =0, then the opposite is true.

[0138] Since for each inlet direction, the flow direction j=1 needs to be to the left of the flow direction j=2 (e.g., the left-turn lane of the east inlet should be to the left of the straight-ahead lane), the following constraint applies:

[0139]

[0140]

[0141] Step 4.2: Set lane sharing constraints;

[0142] Introducing 0-1 variable δ i,k,s This indicates whether the k-th lane in the direction of entry i is designated as a shared lane. If δ i,k,s =1, then it is set as a shared lane; if δ i,k,s =0, then the opposite is true. For a T-junction, each entrance can have at most one shared lane (two or more shared lanes will cause traffic flow trajectory conflicts), therefore:

[0143]

[0144] If the k-th lane in the direction of entry i is a shared lane, then that lane has two flow directions; otherwise, it has only one flow direction. Therefore:

[0145]

[0146]

[0147] Where M is an arbitrarily large positive number.

[0148] Step 4.3: Set exit lane constraints;

[0149] Since the total number of inlet channels flowing to (i,j) cannot exceed the total number of corresponding outlet channels, the following constraint applies:

[0150]

[0151] In the formula E Γ(i,j) Let Γ(i,j) be the number of exit lanes in the import direction.

[0152] Step 5: Set phase duration constraints;

[0153] Step 5.1: Set the loop-barrier constraint conditions;

[0154] From the appendix Figure 4 The T-shaped intersection double-loop phase structure shown has a phase duration Φ i,j The following constraints should apply:

[0155] Φ 3,1 +Φ 2,1 +Φ 1,1 =1.

[0156] Step 5.2: Set the minimum green light constraint;

[0157] To ensure drivers have sufficient reaction time to changes in traffic lights and that vehicles can safely pass through intersections, Φ i,j There should be a minimum phase duration T i,j,min Constraints of (s):

[0158]

[0159] Step 5.3: Set pedestrian crossing time constraints;

[0160] To meet the needs of pedestrians crossing the street and ensure that pedestrians with synchronized phases (i,j) can smoothly cross the crosswalk, combined with the attached... Figure 4 The phase relationship shown requires the following constraints:

[0161]

[0162] Φ 1,2 +p 1,1 ·ξ=Φ 1,1 +Φ 3,1 ;

[0163]

[0164] Where p i,j L represents the time (in seconds) required for a pedestrian to cross the street in phase (i,j); i,j This represents the length (m) of the pedestrian crossing corresponding to phase (i,j); v p This indicates the 15th percentile pedestrian crossing speed (m / s).

[0165] Step 5.4: Set the right turn phase duration constraint;

[0166] When all right-turn traffic flows are allocated dedicated lanes and do not share lanes with other traffic flows, the right-turn phase can overlap with two phases simultaneously. For example, when all right-turn traffic flows at the south entrance are allocated dedicated lanes, the right-turn phase can overlap with both the left-turn phase at the south entrance and the left-turn phase at the east entrance. Therefore:

[0167]

[0168] When a right-turn flow shares a lane with other flows, the right-turn phase can only overlap with one phase. For example, when there is a shared lane at the south entrance, the right-turn phase can only be released simultaneously with the left-turn phase at the south entrance. Therefore:

[0169]

[0170] Step 6: Set saturation flow constraints;

[0171] As the number of lanes in the same direction of traffic increases, the saturation flow rate in that direction will be reduced. The provisions regarding this in the Highway Capacity Manual 2010 (HCM2010) are shown in Table 1:

[0172] Table 1. Reduction factor of saturation flow rate as the number of lanes increases

[0173]

[0174] Table 1 is converted into a constraint condition based on the saturation flow reduction effect. A 0-1 variable δ is introduced. i,j,r Whether the r-th saturation flow reduction factor is set for the flow direction j in the inlet direction i, the constraint condition for the saturation flow reduction effect is as follows:

[0175]

[0176]

[0177] Furthermore, for any flow direction (i,j), there exists only one saturation flow reduction factor, thus the following constraints apply:

[0178]

[0179] Step 7: Set traffic flow constraints;

[0180] Let the traffic flow to (i,j) be q. i,j (veh / h), the traffic flow direction (i,j) distributed on lane k is q. i,j,k (veh / h), then q i,j With q i,j,k The following relationship should exist:

[0181]

[0182] If x i,j,k =0 (i.e., the k-th lane in the import direction i does not have a flow direction j), then the corresponding q i,j,k It is also 0, therefore we have:

[0183]

[0184] The saturation flow reduction in step 6 is equivalent to an increase in traffic flow, and q is then adjusted accordingly. i,j,k Let q i,j,k,f Let q be the traffic flow (veh / h) after adjustment to the k-th lane (i,j). i,j,k,f The following constraints must be met:

[0185]

[0186] Where f i,j,r Let be the reduction factor value for the r-th saturated flow rate towards (i,j). According to Table 1, its specific values ​​are as follows: f 1,1,3 =f 1,1,4 =f 2,1,3 =f 2,1,4 =0.971, f 2,2,3 =f 2,2,4 =f 3,2,3 =f 3,2,4 =0.885, f 1,2,3 =f 3,1,3 =0.952, f 1,2,4 =f 3,1,4 =0.908.

[0187] Step 8: Set flow ratio constraints;

[0188] Step 8.1: Traffic flow allocation;

[0189] When there is no shared lane for the incoming direction i, the traffic flow to (i,j) is evenly distributed across each lane with the flow direction j. Therefore:

[0190]

[0191] When a shared lane is provided in the inbound direction i, the traffic flow distribution in each direction is equal in terms of the flow ratio of each lane. Therefore:

[0192]

[0193] Where s i,jThe single-lane saturation flow rate (veh / h) is the flow direction (i,j).

[0194] Step 8.2: Flow ratio calculation;

[0195] When there is no shared lane in the inbound direction i, the flow rate in the direction (i,j) is evenly distributed across each lane, therefore its flow rate is higher than that in the direction y. i,j The following constraints should be met:

[0196]

[0197] When a shared lane is provided in the direction of entry i, the flow ratio of each lane is equal, therefore y i,j This can be taken as the flow ratio on lane k=1:

[0198]

[0199] Step 9: Set saturation constraints;

[0200] To ensure efficient traffic flow for motor vehicles, maximum saturation limits are set for each phase, namely:

[0201]

[0202] Among them l i,j x represents the time loss (s) for phase (i,j); m This represents the maximum acceptable saturation level for each phase.

[0203] Step 10: Use the branch and bound method to solve the constructed mixed integer linear programming model to obtain the optimal lane layout and signal timing scheme for the T-shaped intersection.

[0204] like Figures 5-9 As shown, the present invention provides two embodiments:

[0205] Example 1:

[0206] As attached Figure 5 As shown, the geometric design parameters of a certain T-shaped intersection are: the east and west entrances include 4 approach lanes and 4 exit lanes, the south entrance includes 3 approach lanes and 2 exit lanes, and the length L of the pedestrian crossing in each direction is... i,j =20.4m (of which the south direction is the full width and the east and west directions are half width), the width of each entrance and exit lane is 3m, and the turning radius for right turns at the west entrance and the south entrance is 15m and 25m respectively.

[0207] The intersection signal control parameters are: the minimum allowable signal period C of the intersection. min The maximum signal period is 60 seconds. maxThe time is 150 seconds. The basic saturation flow rate for straight driving is taken as 1650 veh / h, and the basic saturation flow rate for left and right turns is taken as 1550 veh / h. The minimum duration T for each phase is... i,j,min All are 10s, and the maximum acceptable saturation x for each phase. m =0.7.

[0208] Other parameters for the intersection are: the intersection is not located in a CBD area, and the 15th percentile pedestrian crossing speed v. p =1.2m / s.

[0209] Input the various parameters of the intersection into Synchro software to obtain the single-lane saturation flow rate s for each direction of traffic. i,j Table 2 shows the traffic flow and single-lane saturation flow for each direction in Example 1.

[0210] Table 2. Traffic flow and single-lane saturation flow in each direction, Example 1

[0211] Flow direction (1,1) (1,2) (2,1) (2,2) (3,1) (3,2) Traffic flow (veh / h) 320 600 580 410 530 590 Single-lane saturation flow rate (veh / h) 1374 1540 1374 1230 1540 1230

[0212] Using the method provided by this invention, an optimization model for lane layout and signal timing combination is established for the intersection in Example 1. The model is solved using the branch and bound method to obtain the lane layout and signal timing schemes, as shown in the appendix. Figure 6 and attached Figure 7 As shown. From the appendix Figure 6 As can be seen, the lane layout scheme of Example 1 only includes dedicated lanes, with the east entrance having 2 dedicated left-turn lanes and 2 dedicated straight-ahead lanes, the south entrance having 2 dedicated left-turn lanes and 1 dedicated right-turn lane, and the west entrance having 2 dedicated straight-ahead lanes and 2 dedicated right-turn lanes.

[0213] The lane layout scheme in Example 1 includes only dedicated lanes because the traffic flow distribution in each direction is relatively balanced, thus dedicated lanes are sufficient to meet the needs. Correspondingly, in the appendix... Figure 7 In the middle, the right turn phase can overlap with two phases simultaneously.

[0214] Example 2:

[0215] The intersection used in Example 2 is identical to that in Example 1 in terms of geometric design, signal control, and other parameters, but the traffic flow in each direction is changed. Table 3 shows the traffic flow and single-lane saturation flow for each direction in Example 2.

[0216] Table 3. Traffic flow and single-lane saturation flow in each direction, Example 1

[0217] Flow direction (1,1) (1,2) (2,1) (2,2) (3,1) (3,2) Traffic flow (veh / h) 60 1330 780 140 900 90 Single-lane saturation flow rate (veh / h) 1374 1540 1374 1230 1540 1230

[0218] Using the method provided by this invention, an optimization model for lane layout and signal timing combination is established for the intersection in Example 2. The model is solved using the branch and bound method to obtain the lane layout and signal timing schemes, as shown in the attached figures. Figure 8 and attached Figure 9 As shown. From the appendix Figure 8 As can be seen, each entrance direction in Example 2 includes a shared lane. The east entrance has one straight-left shared lane and three straight-only lanes, the south entrance has two left-turn dedicated lanes and one left-right-turn shared lane, and the west entrance has three straight-only lanes and one straight-right shared lane.

[0219] The reason why each approach direction in Example 2 includes a shared lane is that the traffic flow distribution in each direction is uneven (for example, the through traffic flow at the east approach is much greater than the left-turn flow), so using shared lanes can better utilize the space resources of the approach lanes. Correspondingly, in the appendix Figure 9 In this case, a right turn phase can only overlap with one phase.

[0220] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is limited by the appended claims and their equivalents.

Claims

1. A method for optimizing lane layout and signal timing at a T-shaped intersection, characterized in that, include: Step 1: Define index variables: global index for intersection approach direction, local index for intersection flow direction, local index variable for intersection approach lanes, and saturation flow reduction coefficient index variable; Step 1 specifically includes: Step 1.1 Let A be the set of intersection entrance directions, and A = {1, 2, 3}; i is the global index of the intersection entrance direction, and i ∈ A; where i = 1 represents the east entrance, i = 2 represents the south entrance, and i = 3 represents the west entrance. Let D be the set of intersection flow directions, and D = {1, 2}; j is the local index of the intersection flow direction, and j ∈ D; for the east entrance i = 1: j = 1 indicates a left turn at the east entrance, and j = 2 indicates a straight turn at the east entrance; for the south entrance i = 2: j = 1 indicates a left turn at the south entrance, and j = 2 indicates a right turn at the south entrance; for the west entrance i = 3: j = 1 indicates a straight turn at the west entrance, and j = 2 indicates a right turn at the west entrance; therefore, the flow direction or phase of the intersection can be represented by a pair (i, j); Step 1.2: Define the formula for converting a local index into a global index: ； Where Γ(i, j) represents the global index value of the flow direction (i, j) into the merging direction; Step 1.3: Let K i Let K be the set of lanes in the direction i of the intersection entrance, and k be a local index variable of the lanes at the intersection entrance, where k ∈ K. i k=1 represents the innermost lane, k=n i Represents the outermost lane, where n i This represents the total number of lanes in the direction of entry i, with the remaining lanes numbered sequentially from the inside out. Step 1.4: Let R be the set of saturated flow reduction coefficients, and R = {1, 2, 3, 4}; r is the index variable of the saturated flow reduction coefficient, and r ∈ R; If the flow direction (i, j) is a left turn or a right turn, then r=1 indicates that there is no dedicated lane for the flow direction (i, j), r=2 indicates that there is 1 dedicated lane for the flow direction (i, j), r=3 indicates that there are 2 dedicated lanes for the flow direction (i, j), and r=4 indicates that there are 3 or more dedicated lanes for the flow direction (i, j). If the flow direction (i, j) is straight, then r=1 indicates that there is no dedicated lane or shared lane for the flow direction (i, j), r=2 indicates that there is 1 dedicated lane or shared lane for the flow direction (i, j), r=3 indicates that there are 2 dedicated lanes or 1 dedicated lane and 1 shared lane for the flow direction (i, j), and r=4 indicates that there are 3 or more lanes for the flow direction (i, j), and all 3 or more lanes are dedicated lanes or 1 shared lane, with the rest being dedicated lanes; Step 2: Phase design: The intersection phase adopts the double-ring standard phase, and the double-ring standard phase is applied to the T-shaped intersection; Step 3: Construct the objective function: Set the objective function to minimize the signal period duration; Step 4: Set lane layout constraints; Step 4 specifically includes: Step 4.1: Set lane sequence constraints; Introduce 0-1 variables x i,j,k Indicates whether the k-th lane in the import direction i is configured with flow direction j; if x i,j,k =1, then set the flow direction to j; if x i,j,k If =0, then the opposite is true; Since the flow direction j=1 needs to be to the left of the flow direction j=2 in each inlet direction, the following constraint applies: ； ； Step 4.2: Set lane sharing constraints: Introducing 0-1 variable δ i,k,s Indicates whether the k-th lane in the direction of entry i is set as a shared lane; if δ i,k,s =1, then it is set as a shared lane; if δ i,k,s If =0, then the opposite is true; For a T-junction, each entrance can have a maximum of one shared lane, therefore: ； If the k-th lane in the direction of entry i is a shared lane, then that lane has two flow directions; otherwise, it has only one flow direction. Therefore: ； ； Where M is an arbitrarily large positive number; Step 4.3: Set exit lane constraints; Since the total number of inlet channels flowing to (i, j) cannot exceed the total number of corresponding outlet channels, the following constraint applies: ； In the formula E Γ(i, j) Let Γ(i, j) be the number of exit lanes in the import direction; Step 5: Set phase duration constraints; Step 6: Set saturation flow constraints; Step 7: Set traffic flow constraints; Step 8: Set flow ratio constraints; Step 9: Set saturation constraints; Step 10: Using Step 3 as the objective function and Steps 4-9 as constraints, construct a mixed integer linear programming model for optimizing lane layout and signal timing; use the branch and bound method to solve the constructed mixed integer linear programming model to obtain the optimal lane layout and signal timing for the T-shaped intersection.

2. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 1, characterized in that, Step 2 specifically refers to: The intersection phase adopts the double-ring standard phase, which is applied to the T-shaped intersection; With Φ i,j Φ represents the ratio of the duration of phase (i, j) to the duration of the signal period. i,j ∈(0, 1); the duration of phase (i, j) includes the sum of the green light, yellow light and all-red light times.

3. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 2, characterized in that, Step 3 specifically includes: The objective function is set as minimizing the signal period duration: ； In the formula, ξ is the reciprocal of the signal period duration C, i.e., ξ = 1 / C, where C must be located at the minimum allowable signal period C at the intersection. min and the maximum signal period C max Between them, as shown in the following formula: 。 4. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 3, characterized in that, Step 5 specifically includes: Step 5.1: Set loop and barrier constraints; The T-shaped intersection features a double-loop phase structure with a phase duration Φ. i,j The following constraints should apply: ； Step 5.2: Set the minimum green light constraint; To ensure drivers have sufficient reaction time to changes in traffic lights and that vehicles can safely pass through intersections, Φ i,j There should be a minimum phase duration T i,j,min Constraints: ； Step 5.3: Set pedestrian crossing time constraints; To meet the needs of pedestrians crossing the street and ensure that pedestrians crossing at the same phase (i, j) can smoothly cross the crosswalk, the following constraints are required, considering the phase relationship of the double-ring phase structure of the T-shaped intersection: ； ； ； Where p i,j This represents the time required for a pedestrian to cross the street in phase (i, j); L i,j This represents the length of the pedestrian crossing corresponding to phase (i, j); v p This indicates the 15th percentile pedestrian crossing speed; Step 5.4: Set the right turn phase duration constraint; When all right-turn traffic flows are allocated dedicated lanes and do not share lanes with other traffic flows, the right-turn phase overlaps with two phases simultaneously. For example, when all right-turn traffic flows at the south entrance are allocated dedicated lanes, the right-turn phase can overlap with both the left-turn phase at the south entrance and the left-turn phase at the east entrance. Therefore: ； When right-turn traffic shares a lane with other traffic flows, the right-turn phase can only overlap with one phase; for example, when there is a shared lane at the south entrance, the right-turn phase can only be released synchronously with the left-turn phase at the south entrance, therefore: 。 5. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 4, characterized in that, Step 6 specifically includes: As the number of lanes in the same direction of flow increases, the saturation flow rate in that direction will be reduced. Introducing 0-1 variable δ i,j,r Whether the r-th saturation flow reduction factor is set for the flow direction j in the inlet direction i, the constraint condition for the saturation flow reduction effect is as follows: ； ； Furthermore, for any flow direction (i, j), there exists only one saturation flow reduction factor, thus the following constraints apply: 。 6. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 5, characterized in that, Step 7 specifically includes: Let the traffic flow direction (i, j) be q. i,j The traffic flow direction (i, j) distributed along lane k is q. i,j,k , then q i,j With q i,j,k The following relationship should exist: ； If x i,j,k =0, meaning that the k-th lane in the import direction i does not have a flow direction j, then the corresponding q i,j,k It is also 0, therefore we have: ； The saturation flow reduction in step 6 is equivalent to an increase in traffic flow, and q is then adjusted accordingly. i,j,k ; Let q i,j,k,f Let q be the traffic flow after adjustment to the k-th lane (i, j). i,j,k,f The following constraints must be met: ； Where f i,j,r is the reduction factor value for the r-th saturated flow rate in the direction of (i, j).

7. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 6, characterized in that, Step 8 specifically refers to: Step 8.1: Traffic flow allocation; When there is no shared lane for the incoming direction i, the traffic flow to (i, j) is evenly distributed across each lane with the flow direction j. Therefore: ； When a shared lane is provided in the inbound direction i, the traffic flow distribution in each direction is equal in terms of the flow ratio of each lane. Therefore: ； Where s i,j The saturation flow rate of a single lane flowing towards (i, j); Step 8.2: Flow ratio calculation; When there is no shared lane in the inbound direction i, the flow rate in the direction (i, j) is evenly distributed across each lane, therefore its flow rate is higher than that in the direction y. i,j The following constraints should be met: ； Among them, s i,j,k Let be the saturation flow rate of the k-th lane flowing towards (i, j); When a shared lane is provided in the direction of entry i, the flow ratio of each lane is equal, therefore y i,j This can be taken as the flow ratio on lane k=1: 。 8. The method for optimizing lane layout and signal timing at a T-shaped intersection according to claim 7, characterized in that, Step 9 specifically includes: To ensure efficient traffic flow for motor vehicles, maximum saturation limits are set for each phase, namely: ； Among them l i,j x represents the time loss for phase (i, j); m This represents the maximum saturation that each phase can accept.

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