A method for intersection signal control considering truck start-up and car-following delay

Abstract

The application provides an intersection signal control method considering truck starting and following delay, comprising the following steps: establishing a truck starting delay model by respectively analyzing the under-saturated state and the over-saturated state truck starting delay; establishing a truck following delay model according to the mobile bottleneck theory and the definition of the truck following delay; based on the truck starting delay model and the truck following delay model, considering the truck starting delay and the truck following delay factors on the basis of the traditional delay minimum signal cycle calculation model, re-establishing the delay minimum signal cycle calculation model; and controlling the intersection signal according to the delay minimum signal cycle calculation model. The application utilizes the delay minimum signal cycle calculation method to reduce the vehicle delay of the intersection and improve the intersection service level.

Description

Technical Field

[0001] This invention relates to the field of traffic delay technology, and in particular to an intersection signal control method that takes into account the delays in truck start-up and following. Background Technology

[0002] Truck start-up delay refers to the delay caused by the dispersal of queuing vehicles. Due to signal control, when traffic arrives at an intersection during a red light, it must stop and queue at the approach lane, waiting for the red light to end before proceeding. When trucks are present in the queue, their large size and poor power performance cause subsequent queuing vehicles to be restricted from starting and dispersing when the trucks begin to move, resulting in a slower dispersal rate and additional dispersal time.

[0003] Truck following delay refers to the delay caused when ordinary cars follow behind trucks. When traffic arrives at and leaves the intersection during the green light period, trucks generally travel at lower speeds, causing cars following behind them to slow down when crossing the intersection, resulting in additional travel time.

[0004] In the study of truck driving characteristics, domestic and foreign scholars mainly employ two approaches when investigating the impact of trucks on traffic flow: one is to use vehicle conversion factors (PCEs) to convert trucks and other special vehicles on the road into standard vehicles for modeling and analysis; the other is to use moving bottleneck theory to study the impact of trucks traveling at low speeds on following vehicles. However, both approaches currently have certain shortcomings. The commonly used methods for PCEs primarily involve qualitative analysis of measurement data on road segments, without considering the impact of truck starts on the dissipation rate of following vehicles when trucks are present in the queue at intersections. Regarding moving bottleneck theory, current research is limited to the interference of trucks on traffic flow while traveling on road segments, lacking studies on the interference of trucks on traffic flow at intersections.

[0005] In the research on vehicle delays and traffic signal control strategies at intersections, most current studies convert trucks at intersections into standard vehicles using vehicle conversion factors for modeling and analysis, ignoring the impact of trucks on subsequent vehicles when they travel at intersections. As a result, existing delay calculation models and signal control models do not perform well in practical applications at some intersections where trucks arrive frequently. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides an intersection signal control method that considers truck start-up and following delays. By calculating the delays generated at intersections where trucks and regular vehicles share the same lanes, and utilizing a method for calculating the minimum delay signal cycle, the average vehicle delay at such intersections is reduced, thereby improving the level of service at these intersections. A calculation model for the average vehicle delay at intersections where trucks and regular vehicles share the same lanes is established, allowing for the optimization and adjustment of control strategies for these intersections.

[0007] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0008] A method for intersection signal control considering truck start-up and following delay includes the following steps: establishing a truck start-up delay model by analyzing truck start-up delays under undersaturated and oversaturated states respectively; establishing a truck following delay model based on the moving bottleneck theory and the definition of truck following delay; based on the truck start-up delay model and the truck following delay model, and considering the truck start-up delay and truck following delay factors, re-establishing the minimum delay signal cycle calculation model on the basis of the traditional minimum delay signal cycle calculation model; and controlling the intersection signal lights according to the minimum delay signal cycle calculation model.

[0009] Furthermore, based on the impact of truck mixing on undersaturated intersections, the truck start-up delay under undersaturation conditions is divided into two scenarios: truck start-up delay under undersaturation conditions and truck start-up delay under oversaturation conditions. A truck start-up delay calculation model is established, specifically as follows:

[0010] Analysis of the revised formulas for calculating total vehicle delay and average vehicle delay per traffic signal cycle under undersaturated conditions, assuming no trucks are in the queue:

[0011] Total vehicle delay d within a traffic signal cycle t(n) The calculation formula is revised as follows:

[0012]

[0013] Average vehicle delay per traffic signal cycle The calculation formula is revised as follows:

[0014]

[0015] Where: C represents the nth cycle time; r represents the red light duration within the nth cycle; q (n) S represents the arrival rate of vehicles arriving in the nth period, in vehicles / hour; S represents the vehicle dissipation saturation flow rate when there are no trucks arriving in the nth period, in vehicles / hour. This represents the number of vehicles that have not completely dissipated within the (n-1)th period;

[0016] When the first constraint condition is met, the queuing vehicles affected by trucks at the intersection under the undersaturated state will all dissipate when the green light ends; the first constraint condition is:

[0017]

[0018] in: This represents the number of vehicles in the queue following the starting time of the first truck in the queue during the nth period. The number of vehicles that have not completely dissipated within the nth cycle is represented by g; the green light time within the nth cycle is represented by g; and the dissipation rate is S'.

[0019] The calculation formula is:

[0020]

[0021] In the formula:

[0022] x represents the position of the first truck in the queue during the nth period; based on the assumption of truck start-up delay, the probability function for the value of x is:

[0023]

[0024] Where: n' represents the value of x; τ″ (n) The time it takes for all vehicles in the queue to dissipate before the first truck in the convoy during the nth period is calculated using the following formula:

[0025]

[0026] in: This represents the maximum number of vehicles queuing at the entrance lane during the nth period;

[0027] In the coordinate system, the departure line affected by the truck, the original departure line, and the arrival line of the traffic flow form a triangle. The area of ​​this triangle represents the additional delay time caused by the truck's influence on the traffic flow at the intersection. The calculation formula is as follows:

[0028]

[0029]

[0030] in: This represents the truck start-up delay value when the trucks remain undersaturated after being mixed in;

[0031] This indicates the average vehicle delay when the vehicle remains undersaturated even after trucks have joined the mix;

[0032] When the first constraint is not met, but the second constraint is met, the queuing vehicles affected by trucks at the intersection under the undersaturated state cannot all dissipate by the end of the green light, and some vehicles will need to queue again to pass through the intersection; the second constraint is:

[0033]

[0034] In the coordinate system, the departure line affected by trucks, the original departure line, the arrival line of the traffic flow, and the green light termination line form a closed area. This closed area represents the truck start-up delay time when the queue of vehicles affected by trucks at the intersection cannot completely dissipate by the end of the green light. The calculation formula is as follows:

[0035]

[0036] This represents the truck start-up delay value when the intersection is in an oversaturated state after trucks have entered the intersection from an undersaturated state.

[0037] Based on the first and second constraints, establish the critical value x. cr Calculation formula:

[0038]

[0039] If x cr If x < 0, it indicates that there are trucks at any point in the queue of vehicles at the intersection, and all queued vehicles can be cleared during the green light period, meaning the intersection remains undersaturated; if x cr If ≥ q(r+τ), it indicates that a truck exists at any point in the queue of vehicles at the intersection, and all queued vehicles cannot clear completely during the green light period, meaning the intersection is oversaturated; if 0 < x cr If ≤ q(r+τ), then the formula for calculating the average expected value of truck start-up delay in a single cycle under undersaturated conditions is:

[0040]

[0041] in: This represents the truck start delay value when the first truck is positioned at n' in the queue of vehicles under undersaturated conditions, and the queue of vehicles affected by the truck can still completely dissipate by the end of the green light. This represents the truck start delay value when the first truck is positioned n' in the queue of vehicles under undersaturation conditions, and the queue of vehicles affected by the truck cannot completely dissipate by the end of the green light.

[0042] Calculate the truck start-up delay time under oversaturation conditions: Under oversaturation conditions, all queued vehicles at the intersection cannot completely dissipate without the influence of trucks, thus failing to meet the first and second constraints; establish the third constraint for truck start-up delay under oversaturation conditions: q (n) C-Sg > 0;

[0043] Under oversaturation conditions, the formula for calculating the average vehicle delay at an intersection is:

[0044]

[0045] Under oversaturation conditions, the formula for calculating the total vehicle delay at an intersection is:

[0046]

[0047] In the coordinate system, the area of ​​the triangle formed by the original driving line, the driving line affected by trucks, and the green light termination line is the truck start delay value under oversaturation conditions; the formula for calculating the truck start delay value under oversaturation conditions is:

[0048]

[0049] in: This represents the truck start-up delay value when there are trucks among the vehicles queuing at an oversaturated intersection.

[0050] In an oversaturated state, the formula for calculating the number of vehicles in the queue following the first truck's departure time is:

[0051]

[0052] The formula for calculating the average expected value of truck start-up delay in a single cycle under oversaturation conditions is as follows:

[0053]

[0054] Where: E(d) tr ) represents the average expected value of truck start-up delay; This represents the truck start delay value when the first truck is positioned n' in the queue under oversaturation conditions.

[0055] Analyze the state of intersections over multiple consecutive cycles and establish a state judgment model for intersections in each cycle:

[0056]

[0057] Where: sign represents the sign function, and the value in parentheses is negative, 0, and positive, respectively, taking the values ​​-1, 0, and 1; U (n)This indicates the state of the intersection in the nth cycle. A value of -1 indicates that the intersection is undersaturated; a value of 0 indicates that the intersection is critically saturated; and a value of 1 indicates that the intersection is oversaturated. al (n) This is used to determine the impact of truck startup on the intersection under undersaturated conditions. A value of 1 indicates that the intersection becomes oversaturated after trucks enter; otherwise, the intersection remains undersaturated after trucks enter.

[0058] Analyze the delay status of intersections over multiple cycles, and establish a model for calculating total vehicle delay over n cycles assuming no trucks:

[0059]

[0060] in: This represents the total vehicle delay at the intersection under undersaturated conditions when there is no truck interference in the nth period. This represents the total vehicle delay at the intersection under oversaturated conditions when there is no truck interference in the nth period.

[0061] Analyze the delay status of intersections in multiple cycles, and establish a model for the total truck start delay in n cycles, assuming the presence of trucks:

[0062]

[0063] in: This represents the truck start delay value when the intersection is undersaturated in the nth cycle, and the queue of vehicles affected by trucks after they enter the intersection can still completely dissipate by the end of the green light. This represents the truck start delay value when the intersection is undersaturated in the nth cycle, and the queue of vehicles affected by trucks cannot be completely cleared by the end of the green light after the trucks enter the intersection. This represents the truck start-up delay value at the intersection when the intersection is in an oversaturated state during the nth period.

[0064] Furthermore, based on the mobility bottleneck theory and the definition of truck following delay, a truck following delay model is established, specifically as follows:

[0065] Analyze the distance a car needs to travel during the reaction phase, deceleration phase, and following phase to determine the minimum safe headway under the moving bottleneck effect.

[0066] Analyze the following scenarios of a single car following a truck in the absence of signal interference, and establish a calculation model for the truck following delay under the single car following scenario:

[0067]

[0068] Where: T1 represents the delay time incurred by the vehicle during the deceleration phase; T2 represents the delay time incurred by the vehicle during the following phase; d fo This indicates the following delay of a single vehicle while the truck is traveling on the road segment; α max Indicates the maximum deceleration of the car; k' represents the rate of change of deceleration; v f Indicates the speed of a car while it is in free-moving mode; v tr S indicates the speed of the truck; fo This indicates the distance traveled while the car is affected by the mobility bottleneck effect;

[0069] Analyze the scenario of multiple vehicles following each other and a truck following each other in the absence of signal interference, and establish a calculation model for truck following delay in the scenario of multiple vehicles following each other:

[0070] n”=q(t e -t s )

[0071]

[0072] Where: t s Indicates the moment when the bottleneck effect begins; t e Indicates the end time of the mobility bottleneck effect; n" represents the number of vehicles affected by trucks; q represents t. s To t e Average number of arriving vehicles within the time period; D fo This indicates the total delay of all following trucks; This indicates the delay caused by the single affected truck (the nth vehicle).

[0073] Under signal control conditions, analyze the conditions that cause truck following delays and establish a fourth constraint:

[0074]

[0075] Where: τ' (n) Let this represent the time required for all queued vehicles to dissipate within the nth period;

[0076] Analyzing the undersaturated state, under the remaining green light time after the queue of vehicles has completely dispersed and when all following vehicles cannot pass through the intersection during the remaining green light time, the time required for the affected n”' car to pass through the intersection is as follows:

[0077] g re =g-τ' (n)

[0078]

[0079] Wherein: g reThe remaining green light after all the vehicles in the queue have left; T (n”') L represents the time required for the affected nth car to pass through the intersection; c Indicates the length of the car; This indicates the delay caused by the single affected truck (the nth vehicle).

[0080] Establish the number of vehicles n passing through the intersection despite being affected by the mobility bottleneck effect. a Computational model:

[0081]

[0082] in:

[0083] Indicates the nth affected a The delay caused by a single truck; Indicates the nth affected a -1 vehicle caused single-vehicle truck and delay;

[0084] Establish the maximum number of vehicles n allowed to pass through during the remaining green light time, assuming no mobile bottleneck effect. max Computational model:

[0085]

[0086] When a mobility bottleneck effect exists, there exists n max -n a Vehicles cannot pass through the intersection in this cycle and need to stop and queue until the next signal cycle when the queued vehicles dissipate. A model for calculating truck following delay under the mobility bottleneck effect is established:

[0087]

[0088] in: This indicates the single-vehicle truck delay caused by the i-th affected vehicle;

[0089] Assume the truck arrival rate α at the target intersection tr It remains constant, and τ' (n) The value is related to the number of vehicles queuing at the intersection and the position of the first truck in the queue. The time τ' required for all vehicles in the queue to dissipate within the nth period is established. (n) Computational model:

[0090]

[0091] Establish the expected value of the remaining green light time E(g) re The expected total delay of trucks following at intersections, E(D) foComputational model:

[0092]

[0093]

[0094] Where: E(n) max E(n) represents the expected maximum number of vehicles allowed to pass through the intersection during the remaining green light time; a This represents the expected number of vehicles that can still pass through the intersection despite the traffic bottleneck effect.

[0095] Furthermore, the analysis of the distances required for the vehicle to travel during the reaction phase, deceleration phase, and following phase confirms the minimum safe headway under the moving bottleneck effect, specifically:

[0096] Reaction phase:

[0097] S1 = v f τ r =v f (t2-t1)

[0098] Where: S1 represents the vehicle's travel distance during the reaction phase; v f τ represents the speed of a car in free-moving conditions. r t1 represents the driver's reaction time; t2 represents the moment the driver notices the truck ahead while driving; t2 represents the moment the car begins to decelerate.

[0099] Deceleration phase:

[0100] Where: S2 represents the total distance the car travels during the deceleration phase; This represents the distance traveled by the car during the first sub-stage of the deceleration phase, as the deceleration gradually reaches its maximum value; α max This indicates the maximum deceleration of the car; k' represents the rate of change of deceleration. This represents the second sub-stage of the deceleration phase, where the car's deceleration reaches its maximum value and remains constant. The distance the car travels until its speed matches that of the truck in front is reached; v tr Indicates the speed of the truck;

[0101] Follow-up phase:

[0102] Wherein: S tr This indicates the distance the truck traveled during the following phase;

[0103] Establish a calculation model for the minimum safe vehicle spacing and the distance traveled while following another vehicle under the mobile bottleneck effect:

[0104] l = S1 + S2 + Ltr -S tr

[0105] S fo =L-(S f +S1+S2)-l

[0106] Where: l represents the minimum safe vehicle spacing under the moving bottleneck effect; S fo L represents the distance traveled by the car during the phase affected by the moving bottleneck effect; S represents the length of the road segment affected by the moving bottleneck effect. f This indicates the length of the distance a car can travel freely.

[0107] Furthermore, based on the truck start-up delay model and the truck following delay model, and building upon the traditional minimum delay signal period calculation model, a new minimum delay signal period calculation model is established, taking into account the truck start-up delay and truck following delay factors. Specifically:

[0108] Assuming the research object is a signal-controlled intersection, the impact of upstream and downstream intersections and traffic merging on the target intersection is not considered; the green light time is allocated according to the principle of equal saturation to formulate signal control, the intersection is not set to full red time, and the yellow light time is 3 seconds by default;

[0109] In signal timing, each phase should meet the minimum green light time requirement. A fifth constraint is established, including:

[0110] The shortest green light time for straight-ahead traffic must meet the needs of pedestrians crossing the street:

[0111]

[0112] Wherein: g i'(min) Indicates the shortest green light time; l i' This indicates the pedestrian crossing distance for that phase; v p Indicates pedestrian crossing speed; I represents green light interval time; i'=2 indicates eastbound traffic at the intersection entrance; i'=4 indicates southbound traffic at the intersection entrance; i'=6 indicates westbound traffic at the intersection entrance; i'=8 indicates northbound traffic at the intersection entrance.

[0113] The minimum green light time for left turns must ensure that vehicles at the stop line of the intersection approach lane have sufficient time to pass through the intersection:

[0114] g i'(min) =L i' +t i' -I,i'=1,3,5,7

[0115] Where: t i' Indicates the travel time required for a truck to turn left through the intersection; L i'This indicates the vehicle start-up time loss for this phase; i' = 1 indicates the intersection approach lane is east left turn; i' = 3 indicates the intersection approach lane is south left turn; i' = 5 indicates the intersection approach lane is west left turn; i' = 7 indicates the intersection approach lane is north left turn;

[0116] The shortest green light time for each phase is equal to the maximum of the shortest green light times for each flow direction within that phase.

[0117] In the intersection signal control model, both the signal period and the green light time for each phase have shortest time constraints. A sixth constraint is established: Where: C min The shortest signal period time;

[0118] Based on basic traffic flow theory, the green light time for each phase is allocated according to the principle of equal saturation, as specified in the formula:

[0119]

[0120] Wherein: g i' Indicates the green light time for phase i'; L represents the vehicle start delay; y i' This represents the maximum value among all traffic flow ratios in the i' phase.

[0121] Without considering trucks entering the intersection, establish an overall average vehicle delay calculation model for the intersection:

[0122]

[0123] Where: d i' The average vehicle delay represents the main flow direction in phase i'; q i' This indicates that the i'th phase mainly flows towards traffic flow; This indicates that there is no traffic delay at the intersection even without truck interference.

[0124] By comparing the changes in average vehicle delays for each direction at an intersection with and without considering truck entry delays, it is found that as the cycle length increases, the average vehicle delay for each direction first decreases rapidly and then increases slowly. There exists a cycle value that minimizes the total vehicle delay at the intersection. This cycle value is the minimum delay signal cycle value for an intersection considering truck entry delays.

[0125] Establish the objective function of the minimum average vehicle delay signal period calculation model:

[0126]

[0127] Where: dr represents the main flow direction of each phase; This indicates that there are delays caused by trucks entering the intersection where trucks and cars share the road. in: This indicates that the presence of trucks causing delays is a concern for all vehicles. This indicates that the truck start-up is delayed; This indicates that both the truck and the following vehicle are delayed.

[0128] The beneficial effects of this invention are as follows:

[0129] The intersection signal control method of this invention, which considers the starting and following delays of trucks, reduces the average vehicle delay at such intersections by calculating the delays caused by mixed truck and regular vehicle traffic and using a method for calculating the minimum delay signal cycle, thereby improving the level of service at these intersections. A calculation model for the average vehicle delay at mixed truck and regular vehicle intersections is established, which allows for the optimization and adjustment of control strategies for these intersections. Attached Figure Description

[0130] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. The drawings described below are some embodiments of the present invention. For those skilled in the art, it is obvious that other drawings can be obtained from these drawings without creative effort.

[0131] Figure 1 This diagram illustrates the delay in truck startup under under-saturation conditions.

[0132] Figure 2 This diagram illustrates the delay in truck start-up caused by trucks mixing in under oversaturated conditions.

[0133] Figure 3 This diagram illustrates the delay in truck startup under oversaturation conditions.

[0134] Figure 4 The graph shows the changes in the average delay of trucks starting at each entrance lane over the period and the number of vehicles affected by trucks. In the graph, a represents eastward straight; b represents eastward left turn; c represents westward straight; d represents westward left turn; e represents southward straight; f represents southward left turn; g represents northward straight; and h represents northward left turn.

[0135] Figure 5 The graph shows the expected average delay per truck starting over a period of time. In the graph, a represents the straight-ahead flow and b represents the left-turn flow.

[0136] Figure 6 The graph shows the expected delay of each direction of freight trucks following other vehicles under signal interference as a function of the signal cycle. In the graph, a represents the straight-ahead flow and b represents the left-turn flow.

[0137] Figure 7 The graph shows the change in average vehicle delay at intersections over a period of time when trucks are mixed in with the delays. In the graph, a represents the traditional solution; b represents the solution of this invention.

[0138] Figure 8This is a schematic diagram of the intersection signal control method that takes into account truck start-up and following delays as described in this invention. Detailed Implementation

[0139] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0140] like Figure 8 As shown, the intersection signal control method of the present invention, which takes into account the starting and following delays of trucks, includes the following steps:

[0141] S01: By analyzing the truck start-up delay under undersaturated and oversaturated states respectively, a truck start-up delay model is established; the calculation formula for truck start-up delay under undersaturated and oversaturated states is derived; and then, based on the principle of probability and statistics, a calculation model for the expected value of truck start-up delay is constructed.

[0142] S1.1: Based on the general definition of delay, analyze the delay caused by truck entry. Specifically: When there are no trucks in the queue during a given period, the truck entry delay is 0; when a truck is at the head of the queue, all queued vehicles are affected, the dissipation rate decreases, and the truck entry delay reaches its maximum; when a truck is at the tail of the queue, only that truck is affected, and the truck entry delay equals the difference between the truck's actual time to pass through the intersection and the time it would take to pass through the intersection after being converted to a standard vehicle size. Furthermore, based on fundamental principles of probability and statistics, establish basic assumptions about truck start-up delay for the intersection's signal timing scheme, traffic flow conditions, and truck arrival rate:

[0143] (1) The cycle of the signal control scheme at the intersection remains unchanged during the study period.

[0144] (2) During the nth signal cycle in the study period, the number of vehicles arriving at the intersection approach lane is q. n Its value follows a Poisson distribution, i.e., q n ~P(λ'), its calculation formula is:

[0145]

[0146]

[0147] Where: λ' represents the average number of vehicles arriving at the intersection approach lane in each cycle during the study period.

[0148] For ease of calculation, we take the confidence level α = 95%, that is:

[0149]

[0150] (3) Truck arrival rate α during each signal cycle within the study period tr To keep it constant, the calculation formula is:

[0151]

[0152] in: This represents the number of trucks arriving at the intersection's approach lane during the nth signal cycle within the study period.

[0153] (4) The green light time for each phase is allocated according to the principle of equal saturation.

[0154] S1.2: Based on the impact of truck mixing on undersaturated intersections, the truck start-up delay under undersaturation conditions is divided into two scenarios: truck start-up delay under undersaturation conditions and truck start-up delay under oversaturation conditions. A truck start-up delay calculation model is established, specifically as follows:

[0155] S1.2.1: Analysis of the correction of the calculation formulas for total vehicle delay and average vehicle delay in the cycle when there are no trucks in the queue under undersaturated conditions:

[0156] Total vehicle delay d within a traffic signal cycle t(n) The calculation formula is revised as follows:

[0157]

[0158] Average vehicle delay per traffic signal cycle The calculation formula is revised as follows:

[0159]

[0160] in:

[0161] C represents the time of the nth cycle; r represents the red light duration within the nth cycle; q (n) S represents the arrival rate of vehicles arriving in the nth period, in vehicles / hour; S represents the vehicle dissipation saturation flow rate when there are no trucks arriving in the nth period, in vehicles / hour. This represents the number of vehicles that have not completely dissipated within the (n-1)th period;

[0162] S1.2.2: Vehicles arriving at an intersection during a red light are affected by signal control, resulting in a queue that dissipates during the green light. This causes an additional delay for all queued vehicles as they pass through the intersection. The difference between the dissipation time and arrival time of each queued vehicle is its delay time. Assuming the arrival rate at the intersection in a given cycle is q, if no trucks arrive during that cycle, the queue dissipates at a saturation rate S. If trucks are present in the dissipating queue, the dissipation rate of all subsequent queued vehicles decreases to S' when the truck starts moving. Due to the reduced dissipation rate, all subsequent queued vehicles experience an additional delay, which is the truck start delay time.

[0163] S1.2.3: To calculate the truck start-up delay time at the intersection, it is necessary to analyze the intersection under both undersaturated and oversaturated states.

[0164] S1.2.3.1: Calculate the truck start-up delay time under undersaturated conditions. When the first constraint condition is met, all queuing vehicles affected by trucks at the intersection under undersaturated conditions will dissipate when the green light ends; the first constraint condition is:

[0165]

[0166] in: This represents the number of vehicles in the queue following the starting time of the first truck in the queue during the nth period. The number of vehicles that have not completely dissipated within the nth cycle is represented by g; the green light time within the nth cycle is represented by g; and the dissipation rate is S'.

[0167] The calculation formula is:

[0168]

[0169] In the formula: x represents the position of the first truck in the queue within the nth period; based on the assumption of truck start-up delay, the probability function of x is:

[0170]

[0171] Where: n' represents the value of x; τ″ (n) The time it takes for all vehicles in the queue to dissipate before the first truck in the convoy during the nth period is calculated using the following formula:

[0172]

[0173] in: This represents the maximum number of vehicles queuing at the entrance lane during the nth period;

[0174] According to basic traffic flow theory, the arrival and departure of traffic at an intersection exhibit a linear relationship with time. Therefore, the arrival line, departure line, and time of the traffic flow can form a triangle, and the area of ​​this triangle represents the delay time at the intersection. When a truck is present at the intersection, its movement slows down the dispersal rate of subsequent vehicles leaving the intersection. Therefore, the departure lines of all vehicles queuing after the first truck will change. At this point, the departure line affected by the truck, the original departure line, and the arrival line can form a triangle, and the area of ​​this triangle represents the additional delay time caused by the truck's influence on the traffic flow at the intersection—that is, the truck's departure delay time. Figure 1 As shown. Figure 1 In the diagram, the horizontal axis represents time; the vertical axis represents the number of arriving vehicles; Q m This represents the maximum number of vehicles queuing at the entrance lane during this period; r is the red light duration (including the yellow light duration); OD is the arrival line of the traffic flow, with an arrival rate of q; AC is the departure line of the traffic flow, where the traffic flow dissipates at a saturation rate S; BD is the departure line affected by trucks, where the traffic flow dissipates at S'. At this time... Figure 1 The area enclosed by the center lines OD, AC, and BD represents the truck start-up delay when the intersection remains undersaturated after trucks have entered. The formula for calculating the truck start-up delay under this condition is as follows:

[0175]

[0176]

[0177] in: This represents the truck start-up delay value when the trucks remain undersaturated after being mixed in;

[0178] This indicates the average vehicle delay when the vehicle remains undersaturated even after trucks have joined the mix;

[0179] S1.2.3.2: In an undersaturated state, if the queuing vehicles affected by trucks at the intersection cannot all dissipate by the end of the green light, i.e., the first constraint condition is not met, some vehicles need to queue again to pass through the intersection. This situation requires the second constraint condition to be met, namely:

[0180]

[0181] In this scenario, some vehicles affected by trucks cannot completely dissipate during the green light period. That is, the truck-affected driving line cannot intersect with the arrival line at the end of the green light. At this point, the arrival line, the original driving line, the truck-affected driving line, and the green light termination line will form a closed area. The area of ​​this area is the truck start-up delay value in this situation. For example... Figure 2 As shown, DD' is the green light termination line. At this time... Figure 2 The shaded area represents the truck start-up delay under undersaturated conditions, where the queue of vehicles affected by trucks at the intersection cannot completely dissipate by the end of the green light. The formula for calculating the truck start-up delay under this condition is:

[0182]

[0183] This represents the truck start-up delay value when the intersection is in an oversaturated state after trucks have entered the intersection from an undersaturated state.

[0184] S1.2.3.3: Based on the first and second constraints, establish the critical value x. cr Calculation formula:

[0185]

[0186] If x cr If x < 0, it indicates that there are trucks at any point in the queue of vehicles at the intersection, and all queued vehicles can be cleared during the green light period, meaning the intersection remains undersaturated; if x cr If ≥ q(r+τ), it indicates that a truck exists at any point in the queue of vehicles at the intersection, and all queued vehicles cannot clear completely during the green light period, meaning the intersection is oversaturated; if 0 < x cr If ≤ q(r+τ), then the formula for calculating the average expected value of truck start-up delay in a single cycle under undersaturated conditions is:

[0187]

[0188] in: This represents the truck start delay value when the first truck is positioned at n' in the queue of vehicles under undersaturated conditions, and the queue of vehicles affected by the truck can still completely dissipate by the end of the green light. This represents the truck start delay value when the first truck is positioned n' in the queue of vehicles under undersaturation conditions, and the queue of vehicles affected by the truck cannot completely dissipate by the end of the green light.

[0189] S1.2.3.4: Calculate the truck start-up delay time under oversaturation conditions: Under oversaturation conditions, all queued vehicles at the intersection cannot completely dissipate without the influence of trucks, i.e., the first and second constraints are not satisfied; establish the third constraint for truck start-up delay under oversaturation conditions:

[0190] q (n) C-Sg>0; (1-17)

[0191] Under oversaturation conditions, the formula for calculating the average vehicle delay at an intersection is:

[0192]

[0193] Under oversaturation conditions, the formula for calculating the total vehicle delay at an intersection is:

[0194]

[0195] In an oversaturated state, if there are no trucks in the queue, all queued vehicles will be unable to pass through the intersection by the time they dissipate at a rate S. If there are trucks in the queue, the dissipation rate of some queued vehicles decreases to S', resulting in an increase in the number of vehicles unable to pass through the intersection. This means that the original departure line and the arrival line no longer intersect before the green light ends. In this case, the area of ​​the triangle formed by the original departure line, the departure line affected by trucks, and the green light termination line is the truck start delay value in this situation. Figure 3 As shown. At this time Figure 3 The shaded area represents the truck start-up delay value under oversaturated conditions, and its calculation formula is as follows:

[0196]

[0197] in: This represents the truck start-up delay value when there are trucks among the vehicles queuing at an oversaturated intersection.

[0198] In an oversaturated state, the formula for calculating the number of vehicles in the queue following the first truck's departure time is:

[0199]

[0200] The formula for calculating the average expected value of truck start-up delay in a single cycle under oversaturation conditions is as follows:

[0201]

[0202] Where: E(d) tr ) represents the average expected value of truck start-up delay;

[0203] This represents the truck start delay value when the first truck is positioned n' in the queue under oversaturation conditions.

[0204] S1.2.4: Analyze the state of the intersection within multiple consecutive cycles and establish a state judgment model for the intersection in each cycle:

[0205]

[0206] in:

[0207] The sign function is indicated by the sign function. When the value in parentheses is negative, 0, or positive, the corresponding values ​​are -1, 0, and 1, respectively.

[0208] U (n) This indicates the state of the intersection in the nth cycle. A value of -1 indicates that the intersection is undersaturated; a value of 0 indicates that the intersection is critically saturated; and a value of 1 indicates that the intersection is oversaturated.

[0209] V al (n) This is used to determine the impact of truck startup on the intersection under undersaturated conditions. A value of 1 indicates that the intersection becomes oversaturated after trucks enter; otherwise, the intersection remains undersaturated after trucks enter.

[0210] S1.2.5: Analyze the delay status of intersections in multiple cycles, and establish a model for calculating the total vehicle delay in n cycles assuming no trucks:

[0211]

[0212] in:

[0213] This represents the total vehicle delay at the intersection under undersaturated conditions when there is no truck interference in the nth period.

[0214] This represents the total vehicle delay at the intersection under oversaturated conditions when there is no truck interference in the nth period.

[0215] S1.2.6: Analyze the delay status of intersections in multiple cycles, and establish a model for the total truck start delay in n cycles, assuming the presence of trucks:

[0216]

[0217] in:

[0218] This represents the truck start delay value when the intersection is undersaturated in the nth cycle, and the queue of vehicles affected by trucks after they enter the intersection can still completely dissipate by the end of the green light.

[0219] This represents the truck start delay value when the intersection is undersaturated in the nth cycle, and the queue of vehicles affected by trucks cannot be completely cleared by the end of the green light after the trucks enter the intersection.

[0220] This represents the truck start-up delay value at the intersection when the intersection is in an oversaturated state during the nth period.

[0221] S02: Consider the situation where a vehicle is driving near the entrance lane of an intersection and cannot change lanes on the road, and can only follow behind a truck. Based on the moving bottleneck theory and the definition of truck following delay, establish a truck following delay calculation model based on the moving bottleneck theory.

[0222] S2.1: Based on the fundamental assumption of truck start-up delay, the following additional assumptions are added to establish the truck following delay assumption of the mobility bottleneck theory:

[0223] (1) Before the moving bottleneck effect occurs, both trucks and cars are in a state of free movement, always maintaining a constant speed, and the expected speeds all follow a normal distribution.

[0224] (2) The vehicles of the same model in the study have the same power performance; the driver reaction parameters of all vehicles are consistent.

[0225] (3) During the braking phase, the rate of deceleration of the car remains constant. When the maximum deceleration is reached, the car decelerates uniformly until its speed is the same as that of the vehicle in front. At the same time, during this phase, the car decelerates until its speed is the same as that of the vehicle in front, and then maintains the minimum safe distance between the two vehicles.

[0226] (4) The study section extends from the starting point of the lane-change prohibition line at the intersection entrance to the starting point of the channelization line at the intersection exit. Within the study section, no lane-changing behavior is observed in following vehicles. It is assumed that the vehicle will actively change lanes after passing through the study section and gradually resume free driving.

[0227] S2.2: Analyze the distance the car needs to travel during the reaction phase, deceleration phase, and following phase to determine the minimum safe headway under the moving bottleneck effect;

[0228] S2.2.1: Reaction Stage:

[0229] S1 = v f τ r =v f (t2-t1) (2-1)

[0230] Where: S1 represents the vehicle's travel distance during the reaction phase; v f τ represents the speed of a car in free-moving conditions. r t1 represents the driver's reaction time; t2 represents the moment the driver notices the truck ahead while driving; t2 represents the moment the car begins to decelerate.

[0231] S2.2.2: Deceleration Phase:

[0232]

[0233] Where: S2 represents the total distance the car travels during the deceleration phase; This represents the distance traveled by the car during the first sub-stage of the deceleration phase, as the deceleration gradually reaches its maximum value; α max This indicates the maximum deceleration of the car; k' represents the rate of change of deceleration. This represents the second sub-stage of the deceleration phase, where the car's deceleration reaches its maximum value and remains constant. The distance the car travels until its speed matches that of the truck in front is reached; v tr Indicates the speed of the truck;

[0234] S2.2.3: Follow-up Phase:

[0235]

[0236] Wherein: S tr This indicates the distance the truck traveled during the following phase;

[0237] S2.2.4: Establish a calculation model for the minimum safe vehicle spacing and following distance under the moving bottleneck effect:

[0238] l = S1 + S2 + L tr -S tr (2-4)

[0239] S fo =L-(S f +S1+S2)-l (2-5)

[0240] Where: l represents the minimum safe vehicle spacing under the moving bottleneck effect; S fo L represents the distance traveled by the car during the phase affected by the moving bottleneck effect; S represents the length of the road segment affected by the moving bottleneck effect. f This indicates the length of the distance a car can travel freely.

[0241] S2.3: Analyze the following scenario of a truck following a single vehicle under no signal interference, and establish a calculation model for the truck following delay under the following scenario of a single vehicle following a single vehicle:

[0242]

[0243] in:

[0244] T1 represents the delay time caused by the car during the deceleration phase;

[0245] T2 represents the delay time incurred by the car during the car-following phase;

[0246] d fo This indicates the following delay of a single vehicle while the truck is traveling on the road segment.

[0247] α max Indicates the maximum deceleration of the car; k' represents the rate of change of deceleration; v f Indicates the speed of a car while it is in free-moving mode; v tr S indicates the speed of the truck; fo This indicates the distance traveled while the car is affected by the mobility bottleneck effect;

[0248] S2.4: Analyze the scenario of multiple vehicles following each other and a truck following each other in the absence of signal interference, and establish a calculation model for the truck following delay in the scenario of multiple vehicles following each other:

[0249] n” = q(t) e -t s (2-7)

[0250]

[0251] Where: t s Indicates the moment when the bottleneck effect begins; t e Indicates the end time of the mobility bottleneck effect; n" represents the number of vehicles affected by trucks; q represents t. s To t e Average number of arriving vehicles within the time period; D fo This indicates the total delay of all following trucks; This indicates the delay caused by the single affected truck (the nth vehicle).

[0252] S2.5: Under signal control conditions, analyze the conditions that cause truck following delays and establish a fourth constraint:

[0253]

[0254] Where: τ' (n) Let this represent the time required for all queued vehicles to dissipate within the nth period;

[0255] S2.6: Analyze the time required for the affected n”' car to pass through the intersection under undersaturated conditions, when the remaining green light time after the queue of vehicles has completely dissipated and all following vehicles cannot pass through the intersection during the remaining green light time:

[0256] g re =g-τ' （n） (2-10)

[0257]

[0258] Wherein: g re The remaining green light after all the vehicles in the queue have left; T （n”')L represents the time required for the affected nth car to pass through the intersection; c Indicates the length of the car; This indicates the delay caused by the single affected truck (the nth vehicle).

[0259] S2.7: Establish the number n of vehicles passing through the intersection despite being affected by the traffic bottleneck effect. a Computational model:

[0260]

[0261] in:

[0262] Indicates the nth affected a The delay caused by a single truck;

[0263] Indicates the nth affected a -1 vehicle caused single-vehicle truck and delay;

[0264] S2.8: Determine the maximum number of vehicles n allowed to pass through during the remaining green light time, assuming no mobile bottleneck effect. max Computational model:

[0265]

[0266] In summary, when a mobility bottleneck effect exists, there exists n max -n a Vehicles cannot pass through the intersection in this cycle and need to stop and queue until the next signal cycle when the queued vehicles dissipate. A model for calculating truck following delay under the mobility bottleneck effect is established:

[0267]

[0268] in: This indicates the single-vehicle truck delay caused by the i-th affected vehicle;

[0269] S2.9: Based on the assumptions, assume the truck arrival rate α at the target intersection. tr It remains constant, and τ' (n) The value is related to the number of vehicles queuing at the intersection and the position of the first truck in the queue. The time τ' required for all vehicles in the queue to dissipate within the nth period is established. (n) Computational model:

[0270]

[0271] S2.10: Establish the expected value of the remaining green light time E(g) reThe expected total delay of trucks following at intersections, E(D) fo Computational model:

[0272]

[0273]

[0274] Where: E(n) max E(n) represents the expected maximum number of vehicles allowed to pass through the intersection during the remaining green light time; a This represents the expected number of vehicles that can still pass through the intersection despite the traffic bottleneck effect.

[0275] S03: Based on the truck start-up delay model and the truck following delay model, and on the basis of the traditional minimum delay signal period calculation model, a new minimum delay signal period calculation model is established considering the truck start-up delay and truck following delay factors.

[0276] S3.1: Add the following assumptions:

[0277] (1) The research object is a signal-controlled intersection, and the impact of upstream and downstream intersections and road segment traffic merging on the target intersection is not considered.

[0278] (2) When formulating the signal control scheme, the green light time of each phase is allocated according to the principle of equal saturation. The red light time is not set at the intersection, and the yellow light time is 3 seconds by default.

[0279] S3.2: Each phase in the signal timing should meet the minimum green light time requirement. A fifth constraint is established, including:

[0280] S3.2.1: The shortest green light time for the straight-ahead phase must meet the pedestrian crossing requirements:

[0281]

[0282] Wherein: g i'(min) Indicates the shortest green light time; l i' This indicates the pedestrian crossing distance for that phase; v p Indicates pedestrian crossing speed; I represents green light interval time; i'=2 indicates eastbound traffic at the intersection entrance; i'=4 indicates southbound traffic at the intersection entrance; i'=6 indicates westbound traffic at the intersection entrance; i'=8 indicates northbound traffic at the intersection entrance.

[0283] S3.2.2: The shortest green light time for left turns must ensure that vehicles at the stop line of the intersection approach lane have sufficient time to pass through the intersection.

[0284] g i'(min) =L i'+t i' -I,i'=1,3,5,7 (3-2)

[0285] in:

[0286] t i' Indicates the travel time required for a truck to turn left through the intersection; L i' This indicates the vehicle start-up time loss for this phase; i' = 1 indicates the intersection approach lane is east left turn; i' = 3 indicates the intersection approach lane is south left turn; i' = 5 indicates the intersection approach lane is west left turn; i' = 7 indicates the intersection approach lane is north left turn;

[0287] S3.2.3: The shortest green light time for each phase is equal to the maximum value of the shortest green light time for each flow direction within that phase;

[0288] S3.3: In the intersection signal control model, both the signal period and the green light time for each phase have shortest time constraints. A sixth constraint is established:

[0289]

[0290] Where: C min The shortest signal period time;

[0291] S3.4: Based on traffic flow theory, the green light time for each phase is allocated according to the principle of equal saturation, and the specific formula is as follows:

[0292]

[0293] Wherein: g i' Indicates the green light time for phase i'; L represents the vehicle start delay; y i' This represents the maximum value among all traffic flow ratios in the i' phase.

[0294] S3.5: Establish an overall average vehicle delay calculation model for the intersection without considering trucks entering the intersection:

[0295]

[0296] Where: d i' The average vehicle delay represents the main flow direction in phase i'; q i' This indicates that the i'th phase mainly flows towards the traffic flow direction; d t This indicates that there is an average delay at the intersection even without interference from trucks.

[0297] S3.6: Comparing the changes in average vehicle delay for each direction at the intersection with the signal cycle before and after considering truck entry delays, it is found that as the cycle increases, the average vehicle delay for each direction first decreases rapidly and then increases slowly; there exists a certain cycle value that minimizes the total vehicle delay at the intersection; this cycle value is the minimum delay signal cycle value for the intersection considering truck entry delays; the objective function of the traditional minimum average vehicle delay signal cycle calculation model is:

[0298]

[0299] Where: dr represents the main flow direction of each phase, that is, the direction with the largest traffic volume among all the traffic flow directions that are allowed to pass in each phase.

[0300] S3.6: Based on the theories in steps 1 and 2, at intersections where trucks and cars share the same traffic, there is also a truck entry delay factor, the value of which is the sum of truck start delay and truck following delay:

[0301]

[0302] S3.7: In summary, the objective function of the minimum average vehicle delay signal period calculation model is established as follows:

[0303]

[0304] in: This indicates that there are delays caused by trucks entering the intersection where trucks and cars share the road. in: This indicates that the presence of trucks causing delays is a concern for all vehicles. This indicates that the truck start-up is delayed; This indicates that both the truck and the following vehicle are delayed.

[0305] S04: Control the traffic lights at the intersection based on the calculation model of the minimum delay signal cycle.

[0306] Example 1

[0307] Example 1 selects the intersection of the old Provincial Highway 07 and Miaofeng Road in Jiaxing City as the data collection scenario. The following data is mainly collected:

[0308] (1) Traffic flow data and signal timing data of the target intersection during the evening peak period (16:30-17:30). See Table 2 and Table 3 for details.

[0309] Table 2. Evening Peak Traffic Statistics at the Intersection of Provincial Highway 07 and Miaofeng Road

[0310]

[0311] Table 3. Current Evening Peak Hour Timing Plan for the Intersection of Old Provincial Highway 07 (Hsinchu North Road - Miaofeng Road)

[0312] period / s East-west straight Turn left (east or west) North-South Straight Turn left from north or south 135 38 27 34 24

[0313] (2) Free-flow vehicle speed data. A total of 70 sets of truck speed samples and 100 sets of car speed samples were collected. The measured speed data were fitted and analyzed using SPSS software to obtain a statistical table of vehicle speed characteristic values ​​for the measured road sections, as shown in Table 4:

[0314] Table 4. Statistics of vehicle speed characteristics on the old Provincial Highway 07 (Hsinchu North Road - Miaofeng Road)

[0315]

[0316]

[0317] (3) Actual road channelization data for the target intersection. The lengths of the prohibited lane change lines and the distances between each approach lane and its corresponding exit lane were measured on-site. The measurement results are shown in Table 5.

[0318] Table 5. Statistics on Road Channelization at the Intersection of Old Provincial Highway 07 and Miaofeng Road

[0319]

[0320] Considering that vehicles are not in an emergency braking state when braking due to the bottleneck effect, the average driver reaction time τ is taken as 0.6s; the maximum deceleration of the vehicle is taken as 3.5m / s², and the rate of change of deceleration k' is taken as 5.83, meaning that the vehicle deceleration reaches its maximum value about 0.6s after the start of braking; the average vehicle length is taken as 5m; and the average length of trucks is taken as 12m. Simultaneously, the measurement data are substituted into the relevant formulas in steps 1 and 3 to obtain the relationship between the average delay of truck starting, the average delay of truck following, the signal cycle, and the number of vehicles affected by trucks in each direction.

[0321] The relationship between the average delay of truck start-up and the signal cycle and the number of vehicles affected by trucks was obtained through equations (1-11), (1-14), and (1-20). The specific results are shown in Figure (4). The results show that when the number of vehicles affected by trucks remains constant, the average delay of truck start-up in each direction decreases as the signal cycle increases, but the rate of decrease gradually decreases; when the cycle remains constant, as the number of vehicles affected by trucks increases, the average delay of truck start-up in each direction also increases, and the rate of increase gradually increases.

[0322] Equations (1-16) and (1-22) provide curves illustrating the variation of the expected average delay of trucks starting at the intersection of Provincial Highway 07 and Miaofeng Road with the time period, under the current truck arrival rate. Specific results are shown in Figure (5). The results show that under the same time period, the higher the truck arrival rate, the higher the expected average delay of trucks starting. As the time period increases, the expected average delay of trucks starting gradually decreases, but the rate of decrease gradually diminishes.

[0323] Equations (2-16) and (2-17) describe the relationship between the expected value of truck following delay and the signal cycle at each approach lane of the intersection under the current truck arrival rate. The specific results are shown in Figure (6). The results show that as the signal cycle increases, the expected value of the average truck following delay gradually increases, but the rate of increase gradually decreases. Moreover, the higher the truck arrival rate, the higher the expected value of the average truck following delay.

[0324] The pedestrian crossing speed is set at 1.2 m / s. Substituting the measured data into the constraints in step 5, the calculation results are rounded up to obtain the shortest green light time constraints for each flow direction at the intersection, as shown in Table 6.

[0325] Table 6. Statistics on flow ratios and shortest green light time constraints at intersections.

[0326] Flow direction Turn left to the east East Straight Turn left to the south Go straight south Turn left to the west Go straight west Turn left to the north Go straight north Flow ratio 0.1816 0.2544 0.1668 0.2262 0.1168 0.0767 0.0552 0.1751 Shortest green light time 13 31 13 30 13 31 14 30

[0327] According to the data in Table 6, when the four-phase symmetrical release is adopted, that is, the release pattern is (2, 6)-(1, 5)-(4, 8)-(3, 7), the main flow directions of each phase are: east straight, east left turn, south straight, and south left turn.

[0328] Substituting the expected values ​​of average vehicle delay for truck start-up and average vehicle delay for truck following in Figures (5) and (6) into equations (3-7), we obtain the relationship between the average vehicle delay and signal cycle of each approach lane at the target intersection under the traditional scheme and the scheme presented in this paper. See details in [link to relevant documentation]. Figure 7 .Will Figure 7 Substituting the results into equation (3-8), we obtain the intersection signal cycle scheme with the minimum average vehicle delay at the intersection.

[0329] After determining the signal cycle scheme, by combining equations (3-1) to (3-4), the green light time for each phase of the intersection is obtained. The calculation results are shown below:

[0330] Table 7 Intersection Signal Control Scheme

[0331]

[0332] Based on the signal control scheme obtained in Table 7, the intersection of the old Provincial Highway 07 and Miaofeng Road was simulated using VISSIM software version 4.30 to obtain the simulated values ​​of vehicle delays for each direction at the intersection. The specific results are shown in Table 8.

[0333] Table 8. Statistical Table of Simulation Results for Vehicle Delay in Each Direction at the Intersection

[0334]

[0335] Compared to the traditional signal model that minimizes delay, the signal control scheme calculated by this patented model, while increasing the average vehicle delay for some traffic flows, reduces the overall average vehicle delay at the intersection. Compared to the existing signal scheme, the overall average vehicle delay at the intersection is reduced from 78.8s to 57.4s under this patented scheme, a reduction of 27.2%.

[0336] The detailed descriptions listed above are merely specific illustrations of feasible embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for intersection signal control considering truck start-up and following delays, characterized in that, Includes the following steps: By analyzing the truck start-up delay under under-saturated and over-saturated conditions respectively, a truck start-up delay model is established. Based on the mobility bottleneck theory and the definition of truck following delay, a truck following delay model is established. Based on the truck start-up delay model and the truck following delay model, and on the basis of the traditional minimum delay signal period calculation model, a new minimum delay signal period calculation model is established considering the truck start-up delay and truck following delay factors. Control the traffic lights at the intersection based on the calculation model of the minimum delay signal cycle; Specifically, based on the impact of truck mixing on undersaturated intersections, truck start-up delays under undersaturation conditions are divided into two scenarios: truck start-up delays under undersaturation conditions and truck start-up delays under oversaturation conditions. A truck start-up delay calculation model is established, as follows: Analysis of the revised formulas for calculating total vehicle delay and average vehicle delay per traffic signal cycle under undersaturated conditions, assuming no trucks are in the queue: Total vehicle delay within a traffic signal cycle The calculation formula is revised as follows: ， Average vehicle delay per traffic signal cycle The calculation formula is revised as follows: ， in: C represents the nth cycle time; r represents the red light duration within the nth cycle; S represents the arrival rate of vehicles arriving in the nth period, in vehicles / hour; S represents the vehicle dissipation saturation flow rate when there are no trucks arriving in the nth period, in vehicles / hour. This represents the number of vehicles that have not completely dissipated within the (n-1)th period; When the first constraint condition is met, the queuing vehicles affected by trucks at the intersection under the undersaturated state will all dissipate when the green light ends; the first constraint condition is: ， in: This represents the number of vehicles in the queue following the starting time of the first truck in the queue during the nth period. The number of vehicles that have not completely dissipated within the nth cycle is represented by g; the green light duration within the nth cycle is represented by g; the dissipation rate is 1. ; express to Average number of arriving vehicles within a time period; The calculation formula is: ， In the formula: x represents the position of the first truck in the queue during the nth period; based on the assumption of truck start-up delay, the probability function for the value of x is: ， in: This represents the possible values ​​of x; The truck arrival rate within the period; The time it takes for all vehicles in the queue to dissipate before the first truck in the convoy during the nth period is calculated using the following formula: ， in: Indicates the first Maximum number of vehicles queuing at the import lane within a cycle; In the coordinate system, the departure line affected by the truck, the original departure line, and the arrival line of the traffic flow form a triangle. The area of ​​this triangle represents the additional delay time caused by the truck's influence on the traffic flow at the intersection. The calculation formula is as follows: ， ， in: This represents the truck start-up delay value when the trucks remain undersaturated after being mixed in; This indicates the average vehicle delay when the vehicle remains undersaturated even after trucks have joined the mix; When the first constraint is not met, but the second constraint is met, the queuing vehicles affected by trucks at the intersection under the undersaturated state cannot all dissipate by the end of the green light, and some vehicles will need to queue again to pass through the intersection; the second constraint is: ， In the coordinate system, the departure line affected by trucks, the original departure line, the arrival line of the traffic flow, and the green light termination line form a closed area. This closed area represents the truck start-up delay time when the queue of vehicles affected by trucks at the intersection cannot completely dissipate by the end of the green light. The calculation formula is as follows: ， This represents the truck start-up delay value when the intersection is in an oversaturated state after trucks have entered the intersection from an undersaturated state. Based on the first and second constraints, establish the critical value of x. Calculation formula: ， like This indicates that there are trucks at any point in the queue of vehicles at the intersection, and all queued vehicles can be cleared completely during the green light period, meaning the intersection remains undersaturated; if This indicates that trucks are present at any point in the queue of vehicles at the intersection, and the queue cannot be completely cleared during the green light period, meaning the intersection is oversaturated; if Under under saturated conditions, the formula for calculating the average expected value of single-cycle truck start-up delay is: ； in: This indicates the position of the first truck in the queue under undersaturated conditions. The truck start delay value when the queue of vehicles affected by the trucks still completely disperses by the end of the green light; This indicates the position of the first truck in the queue under undersaturated conditions. The truck start delay value when the queue of vehicles affected by the trucks cannot completely disperse by the end of the green light. Calculate the truck start-up delay time under oversaturation conditions: Under oversaturation conditions, all queued vehicles at the intersection cannot completely dissipate without the influence of trucks, thus failing to meet the first and second constraints; establish a third constraint for truck start-up delay under oversaturation conditions: ； Under oversaturation conditions, the formula for calculating the average vehicle delay at an intersection is: ， Under oversaturation conditions, the formula for calculating the total vehicle delay at an intersection is: ， In the coordinate system, the area of ​​the triangle formed by the original driving line, the driving line affected by trucks, and the green light termination line is the truck start delay value under oversaturation conditions; the formula for calculating the truck start delay value under oversaturation conditions is: ， in: This represents the truck start-up delay value when there are trucks among the vehicles queuing at an oversaturated intersection. In an oversaturated state, the formula for calculating the number of vehicles in the queue following the first truck's departure time is: ， The formula for calculating the average expected value of truck start-up delay in a single cycle under oversaturation conditions is as follows: ， in: This represents the average expected value of truck start-up delay; This indicates that under oversaturated conditions, the position of the first truck in the queue is... Truck start-up delay value at that time; Analyze the state of intersections over multiple consecutive cycles and establish a state judgment model for intersections in each cycle: ， in: This indicates a sign function. When the value inside the parentheses is negative, 0, or positive, the corresponding values ​​are -1, 0, and 1, respectively. This indicates the state of the intersection in the nth cycle. A value of -1 indicates that the intersection is undersaturated; a value of 0 indicates that the intersection is critically saturated; and a value of 1 indicates that the intersection is oversaturated. This is used to determine the impact of truck startup on the intersection under undersaturated conditions. A value of 1 indicates that the intersection becomes oversaturated after trucks enter; otherwise, the intersection remains undersaturated after trucks enter. Analyze the delay status of intersections over multiple cycles, and establish a model for calculating total vehicle delay over n cycles assuming no trucks: ， in: Indicates the first The total vehicle delay value at the intersection under undersaturated state when there is no truck interference within a cycle; Indicates the first The total vehicle delay at the intersection under oversaturated conditions when there is no truck interference within a cycle; Analyze the delay status of intersections in multiple cycles, and establish a model for the total truck start delay in n cycles, assuming the presence of trucks: ， in: Indicates the first The truck start delay value when the intersection is undersaturated within a cycle, and the queue of vehicles affected by trucks can still be completely cleared by the end of the green light after the green light ends. Indicates the first The truck start delay value when the intersection is undersaturated within a cycle, and the queue of vehicles affected by trucks cannot be completely cleared by the end of the green light. Indicates the first The truck start-up delay value at the intersection when the intersection is in an oversaturated state within a cycle; Based on the mobility bottleneck theory and the definition of truck following delay, a truck following delay model is established, specifically as follows: Analyze the distance a car needs to travel during the reaction phase, deceleration phase, and following phase to determine the minimum safe headway under the moving bottleneck effect. Analyze the following scenarios of a single car following a truck in the absence of signal interference, and establish a calculation model for the truck following delay under the single car following scenario: ， in: T1 represents the delay time caused by the car during the deceleration phase; T2 represents the delay time incurred by the car during the car-following phase; This indicates the following delay of a single vehicle while the truck is traveling on the road segment. Indicates the maximum deceleration of the car; Indicates the rate of change of deceleration; v f Indicates the vehicle's speed while it is in free-roaming mode; Indicates the speed of the truck; This indicates the distance traveled by the car while it is in a state of motion bottleneck effect; Analyze the scenario of multiple vehicles following each other and a truck following each other in the absence of signal interference, and establish a calculation model for truck following delay in the scenario of multiple vehicles following each other: ， ， in: Indicates the moment when the mobile bottleneck effect begins; Indicates the moment when the mobile bottleneck effect ends; Indicates the number of vehicles affected by the truck; express to Average number of arriving vehicles within a time period; This indicates the total delay of all trucks following the vehicle. Indicates the affected number The delay caused by a single truck; Under signal control conditions, analyze the conditions that cause truck following delays and establish a fourth constraint: ， in: To indicate the first The time required for all queued vehicles to clear within a cycle. Analysis of undersaturated conditions: After the queue of vehicles has completely cleared, the remaining green light time, and the inability of all following vehicles to pass through the intersection within the remaining green light time, will affect the [number of vehicles affected]. Time required for a car to pass through the intersection: ， ， in: The remaining green light after all the vehicles in the queue have left; Indicates the affected number The time required for a car to pass through the intersection; Indicates the length of the car; Indicates the affected number The delay caused by a single truck; Establish the number of vehicles passing through intersections despite being affected by the mobility bottleneck effect. Computational model: ； in: Indicates the affected number The delay caused by a single truck; Indicates the affected number The delay caused by a single truck; Establish the maximum number of vehicles allowed to pass through during the remaining green light time, assuming no mobile bottleneck effect. Computational model: ； When a mobility bottleneck effect exists, there is Vehicles cannot pass through the intersection in this cycle and need to stop and queue until the next signal cycle when the queued vehicles dissipate. A model for calculating truck following delay under the mobility bottleneck effect is established: ； in: This indicates the single-vehicle truck delay caused by the i-th affected vehicle; Assuming the truck arrival rate at the target intersection Always remain constant, and The value is related to the number of vehicles queuing at the intersection and the position of the first truck in the queue. The first... Time required for all queued vehicles to clear within a cycle Computational model: ； Establish the expected value of remaining green light time Expected total delay of trucks following at intersections Computational model: ； ； in: This represents the expected maximum number of vehicles allowed to pass through the intersection during the remaining green light time. This represents the expected number of vehicles that can still pass through the intersection despite the traffic bottleneck effect.

2. The intersection signal control method considering truck start-up and following delays according to claim 1, characterized in that, Analyze the distance a car needs to travel during the reaction phase, deceleration phase, and following phase to determine the minimum safe headway under the moving bottleneck effect, specifically: Reaction phase: ， in: Indicates the distance traveled by the vehicle during the reaction phase; Indicates the vehicle's speed while it is in free-roaming mode; Indicates the driver's reaction time; This indicates the moment when a driver notices the truck ahead while driving; Indicates the moment when the car begins to decelerate; Deceleration phase: ， in: This indicates the total distance the car travels during the deceleration phase. This indicates the distance the car travels during the first sub-stage of the deceleration phase, as the deceleration gradually reaches its maximum value. Indicates the maximum deceleration of the car; Indicates the rate of change of deceleration; This indicates the second sub-stage of the deceleration phase, where the car's deceleration reaches its maximum value and remains constant, and the distance the car travels when it decelerates uniformly until its speed matches that of the truck in front. Indicates the speed of the truck; Follow-up phase: ， in: This indicates the distance the truck traveled during the following phase; Establish a calculation model for the minimum safe vehicle spacing and the distance traveled while following another vehicle under the mobile bottleneck effect: ， ， in: This represents the minimum safe vehicle spacing under the mobile bottleneck effect. This indicates the distance traveled by the car while it is in a state of motion bottleneck effect; This indicates that the moving bottleneck effect affects the length of the road segment; This indicates the length of the distance a car can travel freely.

3. The intersection signal control method considering truck start-up and following delays according to claim 1, characterized in that, Based on the truck start-up delay model and the truck following delay model, and building upon the traditional minimum delay signal period calculation model, a new minimum delay signal period calculation model is established, taking into account both truck start-up delay and truck following delay factors. Specifically: Assuming the research object is a signal-controlled intersection, the impact of upstream and downstream intersections and traffic merging on the target intersection is not considered; the green light time is allocated according to the principle of equal saturation to formulate signal control, the intersection is not set to full red time, and the yellow light time is 3 seconds by default; In signal timing, each phase should meet the minimum green light time requirement. A fifth constraint is established, including: The shortest green light time for straight-ahead traffic must meet the needs of pedestrians crossing the street: ； in: Indicates the shortest green light time; This indicates the pedestrian crossing distance for that phase; Indicates the speed at which pedestrians cross the street; Indicates the green light interval; =2 indicates that the flow direction at the intersection entrance is eastbound straight; =4 indicates that the flow direction at the intersection entrance is southbound straight; =6 indicates that the flow direction at the intersection entrance is westbound straight; =8 indicates that the flow direction at the intersection entrance is northbound straight; The minimum green light time for left turns must ensure that vehicles at the stop line of the intersection approach lane have sufficient time to pass through the intersection: ； in: This indicates the travel time required for a truck to turn left through the intersection; This indicates the vehicle startup time lost in this phase; =1 indicates that the flow direction at the intersection entrance is east-left turn; =3 indicates that the flow direction at the intersection entrance is south-turning left; =5 indicates that the flow direction at the intersection entrance is a west-to-left turn; =7 indicates that the flow direction at the intersection entrance is north-turning left; The shortest green light time for each phase is equal to the maximum of the shortest green light times for each flow direction within that phase. In the intersection signal control model, both the signal period and the green light time for each phase have shortest time constraints. A sixth constraint is established: ； Where: C min The shortest signal period time; Based on basic traffic flow theory, the green light time for each phase is allocated according to the principle of equal saturation, as specified in the formula: ， in: Indicates the first Phase green light time; This indicates a delay in vehicle startup; Indicates the first The maximum value among the traffic flow ratios of all directions in a given phase; Without considering trucks entering the intersection, establish an overall average vehicle delay calculation model for the intersection: ， in: Indicates the first Average vehicle delay in the main flow direction of the phase; Indicates the first The phase primarily flows towards traffic flow; This indicates that there is no traffic delay at the intersection even without truck interference. By comparing the changes in average vehicle delays for each direction at an intersection with and without considering truck entry delays, it is found that as the cycle length increases, the average vehicle delay for each direction first decreases rapidly and then increases slowly. There exists a cycle value that minimizes the total vehicle delay at the intersection. This cycle value is the minimum delay signal cycle value for an intersection considering truck entry delays. Establish the objective function of the minimum average vehicle delay signal period calculation model: ， in: Indicates the main flow direction of each phase; This indicates that there are delays caused by trucks entering the intersection where trucks and cars share the road. ;in: This indicates that the presence of trucks causing delays is a concern for all vehicles. This indicates that the truck start-up is delayed; This indicates that both the truck and the following vehicle are delayed.

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