A collaborative bus signal priority control method

Abstract

The present invention discloses a collaborative bus signal priority control method, including: a bus expected delay estimation method considering the randomness of arrival time; a social vehicle average delay estimation method based on a finite state machine; a dual-objective optimization model considering the interest game between buses and social vehicles; solving the optimization model based on a non-dominated genetic algorithm and obtaining a Pareto front solution set; a rule-based candidate solution generation method and priority control method. The present invention provides a bus signal priority control method for different implementation conditions, which can grant buses priority while giving full play to the road capacity, making it easier for traffic managers to optimize bus traffic in actual operations, and providing a new idea for solving the problem of road right competition at intersections.

Description

Technical Field

[0001] The present invention belongs to the field of transportation engineering, and in particular relates to a collaborative transit signal priority control method (Collaborative Transit Signal Priority Method, Co-TSP). Background Art

[0002] Traffic congestion has plagued many cities for many years. Buses are considered one of the effective ways to ease traffic congestion because of their large carrying capacity and are vigorously promoted. However, due to their low operating speed and poor punctuality, they are less competitive than other modes of transportation such as private vehicles and subways. If the operating speed and delay of buses can be optimized, traffic congestion can be alleviated to a certain extent, and bus signal priority is one of the most cost-effective methods.

[0003] Bus signal priority is a collective name for a series of technologies that achieve bus priority through intersections by statically or dynamically adjusting intersection signal timing plans, and is usually constructed as an optimization problem. Bus signal priority can be divided into absolute priority and conditional priority. Absolute priority achieves bus priority by adding specific constraints to the model, and bus priority is guaranteed by the feasibility of the optimization problem; conditional priority requires that priority be reflected in the objective function of the model. Generally speaking, the absolute priority method usually has other negative effects on intersection operation, such as greatly increasing the delay of social vehicles, so it is only used in special scenarios such as trams. To avoid this problem, some studies consider optimizing bus delays and social vehicle delays at the same time. Using weighted means to convert this multi-objective optimization problem into a single-objective problem is a common method for such studies. However, the weight determination of such methods is not very operational and has low transferability.

[0004] On the other hand, accurate estimation of the time when the bus arrives at the stop line is a key factor affecting the success of the bus signal priority method. The arrival time estimation method based on the uniform motion assumption is the most commonly used method in existing research. This is a typical estimation method based on the concept of determinism. When there is a bus stop between the bus detection section and the intersection stop line, the time when the bus arrives at the stop line is also random due to the randomness of the bus's stop time at the station. The bus signal priority method that does not take this randomness into consideration will find it difficult to achieve the expected effect in practical applications. Summary of the invention

[0005] The present invention provides a collaborative bus signal priority control method for different implementation conditions, which is applicable to application scenarios where the arrival time of buses is random due to the existence of bus stops. The present invention facilitates traffic managers to provide buses with priority rights that are adapted to actual operating conditions, so as to achieve the goal of granting buses priority rights while fully utilizing the road capacity, and provides a new idea for solving the problem of road right competition at intersections.

[0006] The present invention is achieved in this way, and the technical solution is:

[0007] A coordinated bus signal priority control method, characterized in that the coordinated bus signal priority control method comprises the following steps:

[0008] Step 1: Estimate the expected delay of the bus;

[0009] Step 2: Estimate the average delay of social vehicles;

[0010] Step 3: Based on the control window determined in advance, a dual-objective optimization model considering the competition between social vehicles and buses is established to simultaneously optimize the expected delay of buses and the average delay of social vehicles;

[0011] Step 4: Use the non-dominated genetic algorithm to solve the above dual-objective optimization model and generate candidate signal timing plans based on the preset bus priority division method.

[0012] Step 5: Consider the interest game between buses and social vehicles, and select the best signal timing plan based on bus priority requirements.

[0013] Compared with the prior art, the present invention has the following advantages:

[0014] 1. The present invention provides an intuitive and highly operable bus priority control method;

[0015] 2. The present invention can ensure that bus delays will not be higher than before the implementation of the present invention;

[0016] 3. The present invention is applicable to the situation where there is a bus stop between the detection section and the stop line. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of the four states and state transition relationship in the finite state machine used in step 2 of the method of the present invention

[0018] Figure 2 Scenario 1 in step 2 of the method of the present invention: the queue has been cleared state is transferred to the queue has been cleared state, and the schematic diagram of the delay triangle ABC

[0019] Figure 3Scenario 2 in step 2 of the method of the present invention: the queue is transferred from the cleared state to the not cleared state, and the schematic diagram of the delay quadrilateral ABCD

[0020] Figure 4 Scenario 3 in step 2 of the method of the present invention: the queue is not cleared and transferred to the queue is cleared, and the schematic diagram of the delay quadrilateral ABCD

[0021] Figure 5 Scenario 4 in step 2 of the method of the present invention: the queue is not cleared state is transferred to the queue is not cleared state, and the schematic diagram of the delay quadrilateral ABCD

[0022] Figure 6 Schematic diagram of bus priority division area in step 4 of the method of the present invention

[0023] Figure 7 It is a step diagram of a collaborative bus signal priority control method according to an embodiment of the present invention.

[0024] Figure 8 It is a flow chart of a coordinated bus signal priority control method according to an embodiment of the present invention.

[0025] Fig. 9 It is a schematic diagram of the intersection and its associated road sections.

[0026] Fig.10 It is the background traffic survey data of the intersection.

[0027] Fig.11 This is the example optimization result diagram. Note: In the figure, "ConflictAvgDelays" represents the average delay of vehicles in the conflicting direction; "CarAvgDelays" represents the average delay of private cars; and "BusAvgDelays" represents the average delay of buses.

[0028] Fig.12 2 is a diagram comparing the benefits of the method under different congestion levels.

[0029] Fig.13 It is the parameter symbol explanation of the present invention. DETAILED DESCRIPTION

[0030] The collaborative bus signal priority control method of the present invention comprises the following steps:

[0031] Step 1: Estimate the expected delay of the bus;

[0032] Step 2: Estimate the average delay of social vehicles;

[0033] Step 3: Based on the control window determined in advance, a dual-objective optimization model considering the competition between social vehicles and buses is established to simultaneously optimize the expected delay of buses and the average delay of social vehicles;

[0034] Step 4: Use the non-dominated genetic algorithm to solve the above optimization model and generate candidate scheduling plans based on the preset bus priority division method.

[0035] Step 5: Consider the interest game between buses and social vehicles, and select the best signal timing plan based on bus priority requirements.

[0036] When estimating bus delays, consider the randomness of the bus stop time at the bus station. (Corresponding to step 1)

[0037] A method for estimating the average delay of social vehicles based on a finite state machine is established. According to whether the intersections before and after each phase are cleared, the arrival of social vehicles is divided into four scenarios, and then the average delay of social vehicles is estimated. The scenario classification is complete and can be applied to the estimation of the average delay of social vehicles under multi-phase conditions. The estimation method is based on fewer assumptions and has good transferability. (Corresponding to step 2)

[0038] Establish a dual-objective optimization model that minimizes both the expected delay of buses and the average delay of social vehicles, and maximize the traffic capacity of the intersection. (Corresponding to step 3)

[0039] The Pareto frontier solution set is obtained by using a non-dominated genetic algorithm. Considering the interest game between buses and social vehicles, the signal timing schemes representing different priorities are generated according to the preset bus priority division method, and the final executable signal timing scheme is selected according to actual needs. (Corresponding to step 4 and step 5)

[0040] Furthermore, the present invention assumes that the historical station time distribution information of buses at stations is known (through traffic surveys or GPS data, etc.) and has been discretized by methods such as histogram method or Monte Carlo method. Since the present invention aims to reduce both bus delays and social vehicle delays, the expected delay of buses in step 1 is calculated using the following three formulas:

[0041]

[0042]

[0043]

[0044] In the formula,

[0045] ——The detected station time of the mth bus in the jth signal cycle of the i-th import, s;

[0046] ——Station time is , the time when the bus arrives at the stop line, s;

[0047] t DETECTED ——The time when the bus detector detects the bus starting from the control window, s;

[0048] ——i entrance, the distance between the bus stop (the bus detector is located at the bus stop) and the stop line, m;

[0049] v i ——i import, design operating speed of the bus, m / s;

[0050] ——the start time of the most recent unfinished green phase of the j-th signal cycle of the i-th import, s;

[0051] ——Station time is When, the bus delay, s;

[0052] p i，j，m ——Station time is The probability of,the present invention considers the random time when the bus arrives at the bus station;

[0053] D PB ——expected delay of the bus, s;

[0054] ——i import, the possible station time of the bus after discretization.

[0055] Furthermore, consider the special case in step 1, that is, when there is no bus stop between the bus detector and the stop line, set the position of the bus stop to 0, and assume that the bus will stay at the bus stop for 0s, which can be expressed in mathematical language as follows:

[0056]

[0057]

[0058] Furthermore, in step 2, a finite state machine algorithm is used to estimate the average delay of social vehicles. The finite state machine includes four states: start state, queue cleared state, queue not cleared state, and end state. Figure 1 shown.

[0059] Among them, in addition to the end state, the queue cleared state and the queue not cleared state both include two result states in the state transition diagram. The following describes these four scenarios respectively.

[0060] Scenario 1: The queue is cleared from the previous cycle to the queue is cleared. That is, the queue is cleared in the previous cycle and will be cleared in this cycle. In this scenario, the total delay of social vehicles can be calculated by Figure 2 The area of ​​triangle ABC is expressed as follows. The formula for calculating the delay of social vehicles in this scenario is as follows.

[0061]

[0062]

[0063]

[0064] In the formula,

[0065] ——the jth signal cycle of the i-th import, the queue clearing time under scenario 1, s;

[0066] C j ——The length of the jth signal cycle after optimization, s;

[0067] ——After optimization, the green light duration for vehicles to pass in the jth signal cycle of the i-th entrance, s;

[0068] s i ——saturation flow rate at inlet i, car / s;

[0069] λ i ——i Imported vehicle arrival rate, car / s;

[0070] ——Scenario 1, the total delay of social vehicles in the jth signal cycle of the i-th import, s;

[0071] ——Scenario 1, the number of unemptied vehicles in the jth signal cycle of the i-th import, car.

[0072] Scenario 2: The queue is transferred from the cleared state to the not cleared state, that is, the queue was cleared in the previous cycle, but not in this cycle. In this case, the total delay of social vehicles can be calculated by Figure 3 The area of ​​quadrilateral ABCD is expressed as follows. The formula for calculating the delay of social vehicles in this scenario is as follows.

[0073]

[0074]

[0075] In the formula,

[0076] ——Scenario 2, the total delay of social vehicles in the jth signal cycle of the i-th import, s;

[0077] ——Scenario 2, the number of unemptied vehicles in the jth signal cycle of the i-th import, car;

[0078] The rest is the same as above.

[0079] Scenario 3: The queue is not cleared and then transferred to the cleared state. That is, the queue was not cleared in the previous cycle, but it is cleared in this cycle. In this case, the total delay of social vehicles can be calculated by Figure 4 The area of ​​quadrilateral ABCD is expressed as follows. The formula for calculating the delay of social vehicles in this scenario is as follows.

[0080]

[0081]

[0082]

[0083] In the formula,

[0084] ——the j-th signal cycle of the i-th import, the queue clearing time under scenario 3, s;

[0085] ——The number of unemptied vehicles in the j-1th signal cycle of the i import, car;

[0086] ——Scenario 3, the total delay of the social car in the jth signal cycle of the i-th import, s;

[0087] ——Scenario 3, the number of uncleared vehicles in the jth signal cycle of the i-th import, car;

[0088] The rest is the same as above.

[0089] Scenario 4: In the second case of the queue not being emptied, the queue was not emptied in the previous cycle, and it is not emptied in this cycle. In this case, the total delay of social vehicles can be calculated by Figure 5 The area of ​​quadrilateral ABCD is expressed as follows. The formula for calculating the delay of social vehicles in this scenario is as follows.

[0090]

[0091]

[0092] In the formula,

[0093] ——Scenario 4, the total delay of the social car in the jth signal cycle of the i-th import, s;

[0094] ——Scenario 4, the number of uncleared vehicles in the jth signal cycle of the i-th import, car;

[0095] The rest is the same as above.

[0096] The average delay of social vehicles can be calculated by the following formula.

[0097]

[0098] In the formula,

[0099] D PC ——average delay of social vehicles, s;

[0100] N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s;

[0101] N leg ——The number of entrance directions in the intersection;

[0102] ——The total delay of social vehicles in the jth signal cycle of the i-th import, s; Decide.

[0103] The rest is the same as above.

[0104] Furthermore, in step three, a dual-objective optimization model considering the competition between social vehicles and buses is established to simultaneously optimize the expected delay of buses and the average delay of social vehicles.

[0105] The model objective function is as follows.

[0106] min D PB

[0107] min D PC

[0108] In the formula,

[0109] D PB - Buses are expected to be delayed;

[0110] D PC ——Average delay of social vehicles.

[0111] The model has five types of constraints, as follows.

[0112] Constraint 1: Green light duration constraint. A green light duration that is too short is not conducive to the comfort and safety of pedestrians crossing the street. The formula for constraint 1 is as follows.

[0113]

[0114] In the formula,

[0115] g j，k ——After optimization, the green light duration of the kth phase of the jth signal cycle, s;

[0116] ——The minimum green light duration required for the kth phase, s;

[0117] N phase ——The number of phases at the intersection.

[0118] Constraint 2: Period length constraint. The period should not be too long or too short. The formula for constraint 2 is as follows.

[0119] C min ≤C j ≤C max , 1≤j≤N cycle

[0120] In the formula,

[0121] C min ——required minimum cycle length, s;

[0122] C j ——The length of the jth cycle after optimization, s;

[0123] C max ——required maximum cycle length, s;

[0124] N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s;

[0125] Constraint 3. Saturation constraint.

[0126]

[0127]

[0128] In the formula,

[0129] s i ——saturation flow rate at inlet i, car / s;

[0130] λ i ——i Imported vehicle arrival rate, car / s;

[0131] ——The maximum flow rate allowed at inlet channel i, car / s;

[0132] N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s;

[0133] N leg ——The number of entrance directions in the intersection;

[0134] C j——The length of the jth signal cycle after optimization, s;

[0135] ——After optimization, the green light duration for vehicles to pass in the jth signal cycle of the i-th entrance is,

[0136] T——Control window duration, s.

[0137] Constraint 4. Passing time constraint. If the green light phase of a phase has ended, the start and end time of the green light phase of this phase cannot be modified. If the green light phase of a phase has started, the start and end time of the green light phase of this phase and the phase before it cannot be modified.

[0138] I j，k ·e j，k ≤E j，k ≤I j，k ·e j，k +(1-I j，k )·M, 1≤j≤N cycle , 1≤k≤N phase

[0139] C0=0

[0140]

[0141]

[0142]

[0143]

[0144] I j，k =I{e j，k <t DETECTED +t buffer}, 1≤j≤N cycle , 1≤k≤N phase

[0145] In the formula,

[0146] I j，k ——Binary variable, reflecting whether the end time of the kth phase of the jth cycle has changed;

[0147] e j，k ——The end time of the kth phase of the jth cycle before optimization, s;

[0148] E j，k ——After optimization, the end time of the kth phase of the jth cycle, s;

[0149] M – a very large positive number;

[0150] N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s;

[0151] N phase ——The number of phases at the intersection;

[0152] C j ——The length of the jth signal cycle after optimization, s;

[0153] g j，k ——After optimization, the green light duration of the kth phase of the jth signal cycle, s;

[0154] C′ j ——The length of the jth signal cycle before optimization, s;

[0155] g′ j，k ——The green light duration of the kth phase of the jth signal cycle before optimization, s;

[0156] t DETECTED ——The time when the bus detector detects the bus starting from the control window, s;

[0157] t buffer ——Buffer time. During the buffer period, the signal phase cannot be changed due to the arrival of the bus. It is usually the sum of the green light duration and the yellow light duration, s.

[0158] Constraint 5. Control window constraint. The length of the control window, i.e. the sum of the lengths of all cycles within the optimization range, should remain fixed.

[0159]

[0160] In the formula,

[0161] ——Control window duration before optimization, s;

[0162] ——Optimized control window duration, s;

[0163] N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s;

[0164] N phase ——The number of phases at the intersection.

[0165] Furthermore, in step 4, the non-dominated sorting genetic algorithm is first used to solve the optimization model established in step 3 to obtain the Pareto front solution set consisting of candidate scheduling schemes. The candidate scheduling schemes are generated according to the preset bus priority division method. The generation method is mainly divided into three steps, as follows.

[0166] Step 4-1, delete the solutions where the expected bus delay after optimization is higher than that before optimization (this step ensures that the bus delay is not higher than that before optimization);

[0167] Step 4-2, the reference bus priority division method provided by the present invention is to sort the Pareto front solution set according to the expected delay of the bus, and divide the Pareto front solution into three areas of low, medium and high priority with 30% and 70% quantiles as critical points ( Figure 6 ). The priority is relative to the bus, that is, the higher the priority means the less delay the bus will experience.

[0168] Step 4-3, according to the preset rules, select the appropriate solution from the three areas obtained in step 4-2 as the final solution representing the corresponding priority. The reference selection rule provided by the present invention is the average delay of social vehicles (D PC )minimum.

[0169] Furthermore, step five considers the interest game between buses and social vehicles and selects the best signal timing plan based on the actual demand for bus priority.

[0170] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0171] Embodiment 1

[0172] The embodiment of the present invention takes the Hongde Road intersection of Shanghai-Yixing Highway as an example to demonstrate the changes in delays of buses and private vehicles before and after the implementation of the present invention through simulation experiments.

[0173] The Hongde Road intersection of Huyi Highway adopts a three-phase control mode. The intersection and its related sections are as follows: Fig. 9 As shown in the figure, the phase that gives the bus the right of way is the first phase, and the other phases are arranged in sequence. The green light time of the four phases is 60 seconds, 19 seconds and 25 seconds respectively. There is a 3-second yellow light time between each two adjacent phases, no full red time, and the cycle length is 113 seconds. In the simulation experiment, the two bus stops are preset to be about 100m away from the intersection stop line.

[0174] The control window is set to 3 cycles, and the background traffic survey data of the intersection is as follows: Fig.10 The saturation is about 0.44, the average headway of buses is set to 6 minutes, and the station time follows a random discrete distribution of 20s, 30s, 40s and 50s.

[0175] All experiments were performed on PTV VISSIM 7. Fig.11As shown, compared with the case without bus priority, the method of the present invention reduces the expected bus delay by 27.7%, 33.3%, and 41.0% respectively in the cases of low bus priority, medium bus priority, and high bus priority. Although it may cause an increase in the average delay of vehicles in the conflicting direction, the method of the present invention reduces the average delay of social vehicles by 13.4%. This further illustrates that the method described in this aspect has the potential to simultaneously optimize the expected bus delay and the average delay of social vehicles. In contrast, the traditional bus signal priority method performs relatively poorly because the randomness of bus arrival time is not taken into account, which further illustrates that the method of the present invention can effectively deal with the situation of random bus arrival time.

[0176] The experimental results at different congestion levels are as follows Fig.12 As shown, the method of the present invention can reduce bus delays by 35% to 45% when congestion is low, and by 33% to 47% when congestion is high, and at the same time reduce the average delay of social vehicles.

Claims

1. A collaborative bus signal priority control method, characterized in that: The following steps are involved: Step 1: Estimate the expected delay of the bus; Step 2: Estimate the average delay of social vehicles; Step 3: Based on the control window determined in advance, a dual-objective optimization model considering the competition between social vehicles and buses is established to simultaneously optimize the expected delay of buses and the average delay of social vehicles; Step 4: Use the non-dominated genetic algorithm to solve the above dual-objective optimization model and generate candidate signal timing schemes according to the preset bus priority division method; Step 5: Consider the interest game between buses and social vehicles, and select the best signal timing scheme based on bus priority requirements; The expected delay of the bus in step 1 is calculated using the following three formulas: In the formula, ——The detected station time of the mth bus in the jth signal cycle of the i-th import, s; ——Station time is , the time when the bus arrives at the stop line, s; t DETECTED ——The time when the bus detector detects the bus starting from the control window, s; ——i entrance, distance between bus stop and stop line, m; v i ——i import, design operating speed of the bus, m / s; ——the start time of the most recent unfinished green phase of the j-th signal cycle of the i-th import, s; ——Station time is When, the bus delay, s; p i，j，m ——Station time is The probability of,the present invention considers the random time when the bus arrives at the bus station; D PB ——expected delay of the bus, s; ——i import, the possible station time of the bus after discretization; In step 2, the finite state machine algorithm is used to estimate the average delay of social vehicles. The finite state machine includes four states: start state, queue cleared state, queue not cleared state, and end state. Among them, in addition to the end state, the queue cleared state and the queue not cleared state both include two result states in the state transition diagram, namely, scenario 1, scenario 2, scenario 3, and scenario 4; Scenario 1: The queue is cleared from the state to the state, that is, the queue was cleared in the previous cycle and will be cleared in this cycle. The calculation formula for the delay of social vehicles in this scenario is as follows; In the formula, ——the jth signal cycle of the i-th import, the queue clearing time under scenario 1, s; C j ——The length of the jth signal cycle after optimization, s; ——After optimization, the green light duration for vehicles to pass in the jth signal cycle of the i-th entrance, s; s i ——saturation flow rate at inlet i, car / s; λ i ——i Imported vehicle arrival rate, car / s; ——Scenario 1, total delay of social vehicles in the jth signal cycle of the i-th import, s; ——Scenario 1, the number of uncleared vehicles in the jth signal cycle of the i-th import, car; Scenario 2: The queue is cleared and then transferred to the queue is not cleared, that is, the queue was cleared in the previous cycle, but not in this cycle. The calculation formula for the delay of social vehicles in this scenario is as follows; In the formula, ——Scenario 2, total delay of social vehicles in the jth signal cycle of the i-th import, s; ——Scenario 2, the number of unemptied vehicles in the jth signal cycle of the i-th import, car; The rest is the same as scenario 1; Scenario 3: The queue is not cleared and is transferred to the cleared state. That is, the queue was not cleared in the previous cycle, but it is cleared in this cycle. The calculation formula for the delay of social vehicles in this scenario is as follows: In the formula, ——the j-th signal cycle of the i-th import, the queue clearing time under scenario 3, s; ——The number of unemptied vehicles in the j-1th signal cycle of the i import, car; ——Scenario 3, the total delay of the social car in the jth signal cycle of the i-th import, s; ——Scenario 3, the number of uncleared vehicles in the jth signal cycle of the i-th import, car; The rest is the same as scenario 1; Scenario 4: The second case of the queue not being emptied, the queue was not emptied in the previous cycle, and it is not emptied in this cycle either; the delay calculation formula for social vehicles in this scenario is as follows; In the formula, ——Scenario 4, the total delay of the social car in the jth signal cycle of the i-th import, s; ——Scenario 4, the number of uncleared vehicles in the jth signal cycle of the i-th import, car; The rest is the same as scenario 1; The average delay of social vehicles can be calculated by the following formula; In the formula, D PC ——average delay of social vehicles, s; N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s; N leg ——The number of entrance directions in the intersection; ——The total delay of social vehicles in the jth signal cycle of the i-th import, s; Decide; The rest is the same as scenario 1; In step 3, a dual-objective optimization model considering the competition between social vehicles and buses is established to simultaneously optimize the expected delay of buses and the average delay of social vehicles; The model objective function is as follows; my D PB my D PC In the formula, D PB - Buses are expected to be delayed; D PC ——Average delay of social vehicles; The model has five types of constraints, as follows; Constraint 1: Green light duration constraint; too short a green light duration is not conducive to the comfort and safety of pedestrians crossing the street; the formula for constraint 1 is as follows; In the formula, g j，k ——After optimization, the green light duration of the kth phase of the jth signal cycle, s; ——The minimum green light duration required for the kth phase, s; N phase ——Number of phases at the intersection; Constraint 2: Cycle length constraint; the cycle should not be too long or too short; the constraint 2 formula is as follows; C min ≤C j ≤C max , 1≤j≤N cycle In the formula, C min ——required minimum cycle length, s; C j ——The length of the jth cycle after optimization, s; C max ——required maximum cycle length, s; N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s; Constraint 3: saturation constraint; In the formula, s i ——saturation flow rate at inlet i, car / s; λ i ——i Imported vehicle arrival rate, car / s; ——The maximum flow rate allowed at inlet channel i, car / s; N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s; N leg ——The number of entrance directions in the intersection; C j ——The length of the jth signal cycle after optimization, s; ——After optimization, the green light duration for vehicles to pass in the jth signal cycle of the i-th entrance is, T——control window duration, s; Constraint 4: Passing time constraint: If the green light phase of a phase has ended, the start and end time of the green light phase of this phase cannot be modified; if the green light phase of a phase has started, the start and end time of the green light phase of this phase and the phase before it cannot be modified; I j,k ·e j,k ≤E j，k ≤I j，k ·e j,k +(1-I j,k )·M,1≤j≤N cycle ,1≤k≤N phase C0＝0 I j，k =I{e j，k <t DETECTED +t buffer },1≤j≤N cycle ,1≤k≤N phase In the formula, I j，k ——Binary variable, reflecting whether the end time of the kth phase of the jth cycle has changed; e j，k ——The end time of the kth phase of the jth cycle before optimization, s; E j，k ——After optimization, the end time of the kth phase of the jth cycle, s; M – a very large positive number; N cycle ——Control window length, i.e. the number of signal cycles within an optimization range, s; N phase ——Number of phases at the intersection; C j ——The length of the jth signal cycle after optimization, s; g k，k ——After optimization, the green light duration of the kth phase of the jth signal cycle, s; C′ j ——The length of the jth signal cycle before optimization, s; g′ j，k ——The green light duration of the kth phase of the jth signal cycle before optimization, s; t DETECTED ——The time when the bus detector detects the bus starting from the control window, s; t buffer ——Buffer time: during the buffer period, the signal phase cannot be changed due to the arrival of a bus. It is usually the sum of the green light duration and the yellow light duration, s; Constraint 5: Control window constraint: The length of the control window, that is, the sum of the lengths of all cycles within the optimization range, should remain fixed; In the formula, ——Control window duration before optimization, s; ——Optimized control window duration, s; N cycle ——Control window length, that is, the number of signal cycles within an optimization range, s; N phase ——The number of phases at the intersection.

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