Keywords: traffic flow, real-time optimal control, road weighting, Dijkstra method
With the sustained and rapid development of the national economy, the number of all kinds of motor vehicles, especially private cars, has increased rapidly, which has brought unprecedented prosperity to the transportation industry. The traffic in most cities has developed from local congestion in the past to comprehensive tension on a large scale today. For example, in a big city in China, during the morning and evening rush hours, the length of traffic jams at intersections exceeds 1000 meters, and some traffic jams extend from one intersection to another. At this time, it often takes more than half an hour for a car to pass an intersection, so it is better to go quickly, which brings unbearable load to urban traffic. Crowding not only wastes time, but also leads to irregularities in the public transport system. For example, buses can't arrive at the station on time, which makes people unable to estimate their travel time and delays their work and plans. This kind of tension is becoming more and more serious, which has become one of the prominent social problems in big cities and a "bottleneck" problem for the further development of the national economy. Therefore, we must face the reality and solve the traffic congestion and congestion problems in cities.
So what are the reasons for urban traffic congestion and congestion? The analysis is as follows:
(1) The current traffic signal control method is not suitable for traffic flow. At present, the single-point fixed-period control mode is the most widely used in urban intersections. The problems existing in this control mode are as follows:
1. has no adaptability to the random change of traffic flow. Because it is a fixed cycle method, once the cycle time and green signal ratio are selected, they generally do not change frequently. However, the changes of traffic flow and people flow in the traffic network are random and frequent, and the traffic flow passing through the intersection in the same direction may be very different in each cycle. Different flows have different requirements for green light time. Therefore, the signal given by this control method often can't adapt to the random change of objective actual traffic flow. We often encounter such a situation: the traffic signal waiting for traffic is a red light, while the signal without traffic direction is also a green light, which wastes the existing intersection capacity in vain. In order to overcome this shortcoming, people consider using the method of probability statistics to optimize the cycle time and green signal ratio off-line on the basis of collecting a large number of traffic data, which greatly improves the rationality of the selected cycle time and green signal ratio in probability sense. However, this brings the following problems.
2. The control law needs to be adjusted frequently. First of all, because the urban land structure changes rapidly, the traffic volume changes rapidly. The previous data soon lost its practical value. Therefore, the optimization scheme is not optimal or even unreasonable, and data collection and optimal scheme selection need to be carried out again. This is more obvious for developing cities. Secondly, the traffic flow at the same intersection and on the same side is different every day in a week, and the traffic flow at the middle peak, the flat peak and the low peak is also different every day. These all need to change the cycle time and green signal ratio according to the pre-calculated timetable and date table, which has great limitations. The greater the randomness of traffic flow, the more obvious its shortcomings.
3. Do not consider the connection between intersections. "Single point" means that each intersection is controlled independently, regardless of the turnover law of traffic lights at adjacent intersections. This uncoordinated and uncoordinated control mode at intersections artificially sets a lot of resistance to the flow of traffic.
(2) The information circulation conditions are extremely poor, and it is impossible to induce and manage passengers and vehicles. This problem is not obvious when the traffic network runs smoothly, but it is very prominent when traffic jams, traffic accidents and other emergencies occur. However, these emergencies often occur. At this time, the bus dispatching station can't know the situation on the road, so it can't adjust the bus lines and departure frequency properly; Drivers of other vehicles can't get information and can't choose a smoother route; Passengers waiting at bus stops can't decide whether to wait for the bus, transfer to other trains or walk. In fact, many times, as long as proper guidance is given, road congestion will be greatly alleviated or guaranteed to be smooth. For example, during the Los Angeles 1984 Olympic Games, a large number of dynamic signboards were used to guide vehicles to choose suitable routes. Therefore, although the number of vehicles has increased a lot, the traffic flow in the network is better than usual.
(3) The parking lot has insufficient capacity and inappropriate location. This is an old disease that has lasted for many years. Only build roads and not parking lots. For example, there are many wholesale markets in the East and West Second Ring Road of Chengdu Railway Station, but there are no reasonable parking lots. Most drivers park their cars directly on the street, which seriously affects the road capacity. The parking lot should be dedicated and underground. Setting up socialized parking lots under hotels, shopping malls, government buildings and residential buildings is an effective way to solve urban traffic congestion and congestion.
Transportation is a complex large-scale system, which must be operated under strict and scientific rules. It is not an adaptive system, and any violation of rules and regulations may lead to partial or even "whole" paralysis of large-scale systems.
Traffic congestion and congestion countermeasures can generally be divided into three categories:
(1) Strengthen road construction and improve the traffic capacity of the traffic network;
(2) Strengthen the use and management of traffic, give full play to the role of existing road facilities, and maximize the efficiency of traffic network;
(3) Fully implement the traffic demand management, so that the traffic demand will be homogenized in time and space and the traffic structure will be rationalized. Due to the long construction period and high cost of transportation infrastructure, it is necessary to analyze the effect of countermeasures in advance when solving specific urban traffic problems under the current limited funds.
As mentioned above, in order to effectively solve the traffic congestion in cities, the congestion problem cannot simply rely on increasing the road area and length, but should constantly improve the road network system, adjust the road network structure, strengthen the modernization of traffic management, and control and guide individual vehicles. First of all, the static state of traffic flow is an ideal state, assuming that the speed of traffic flow is constant in a city block, the control and guidance of single vehicle are studied and analyzed, and the regulation standards are given.
The topological properties of traffic network can be analyzed by the basic principles of graph theory. The graph consists of "arcs" and "vertices", and the topological model of traffic network can be abstracted as a directed graph consisting of nodes (intersections) and arcs (roads). The direction of the edge is the direction of traffic. Because roads and intersections have many attributes, the regional traffic network between origin and destination can be abstracted as a multi-attribute weighted directed graph.
Suppose:
1. All roads are the same width;
2. Every road does not need to stop and wait;
3. The traffic speed is constant;
4. The road length is known.
The time taken from one point to another is only related to the length of the road.
Regardless of the impact of the accident on traffic. The location of the car is set to point and the destination is set to point. So the route to be taken by the car can be represented by p.
The distance between two points
V: speed of traffic flow
T: the time from the start to the end.
: sum of all arc lengths in p
Represents the weight of road conditions.
Represents the weight given to the road due to the change of traffic speed.
express
Model structure
Since the speed is assumed to be constant, it can be seen that the shortest time from the origin to the destination can be converted into the shortest road. At this point, this problem can be described by the following mathematical model:
( * )
We describe the urban road network as a weighted directed graph D=(V, u). For every directed edge ∈U, there is an L corresponding to it, and L represents the distance between two nodes of the road, which is called the weight of the directed edge.
=
Solution of the model
In the weighted directed graph, we choose a starting point and an ending point, and adopt the E.W.Dijkstra algorithm. The basic idea of Dijkstra method is to find the shortest path step by step from the beginning. In the process of execution, a number corresponding to each point (called the point label) is recorded, which either represents the shortest path weight from this point (called the P label) or represents the upper bound of the shortest path weight from this point (called the T label). Every step of this method is to modify the T label, change a point with T label into a point with P label, and increase the number of vertices with P label in D by 1.
The mathematical model of the static traffic weighted shortest path problem is established, but there are still many factors that affect the traffic running time, such as different road widths, which will make the traffic flow different (the traffic flow is expressed by the traffic flow, which is the number of vehicles arriving or leaving at a certain point on the road, for short); Rush hours will cause traffic congestion or even a certain section of a certain period of time, thus reducing the speed of traffic, that is to say, only static consideration is given to practical problems. Without considering these factors, if analyzed according to the ideal model, the estimated results will be rough and distorted, and it is impossible to effectively guide and control a single vehicle. Therefore, we modified the model on the basis of the previous assumption: when the flow is in dynamic change, we consider the factors such as road width and traffic congestion. In this way, the problem of the shortest time for vehicles to stay on fixed-point sections is much more complicated than the static situation. We use factor transformation method to transform multi-factor variables into single-factor variables to establish an optimization model.
First of all, we can use automatic traffic detection equipment to measure the traffic flow status of different parts of the traffic network, and then send these detected information to the control center or radio station through some telecommunications equipment, so that we can know the traffic conditions of each road section at a certain time, thus providing information for us to guide drivers.
Due to the addition of influencing factors, the speed of traffic flow changes with the congestion during peak hours for a period of time. As we all know, the scheme with the shortest time is bound to change. But we can change the speed change into the road length change, that is, change the road weight into a function that changes with time. For example, if the speed increases, the road weight will be a positive decimal, and if the speed decreases, the weight will be a positive integer, so the shortest time required can still be converted into the shortest road.
We have considered the change of traffic speed just now. Now, let's look at the changes in traffic conditions, such as road paralysis caused by traffic accidents or traffic congestion caused by rush hours. At this time, we can still weigh the roads in a period of time and turn the problem into a static model, that is, to find the shortest road model. The weight of the road can be given by experience. When the road is unclear, we set its weight as a positive integer greater than 1, and vice versa.
Just like the initial traffic weighted shortest path problem, the regional traffic network between the origin and destination can be abstracted as a multi-attribute weighted directed graph.
With the data information fed back by the automatic traffic detection device, we can give a certain weight to a road and determine the specific weight according to the degree of the situation.
When the speed of traffic on the road is affected for various reasons, we can set the weight range to [1, ∞], where =∞ means that the road is seriously blocked and vehicles cannot pass; = 1 indicates that the traffic speed is not affected and you can drive freely. When the vehicle speed changes, we can set the range of weights to (0, ∞), which means that the vehicle speed increases. When, it means that the speed of traffic decreases; = 1, indicating that there is no change compared with the initial velocity.
According to the above, we can establish the following model.
( ** )
Although the road conditions and speed are different at each moment, the above model is only a parameter change after conversion, so the initial shortest path problem model can still be used to solve the problem, which greatly simplifies the problem.
In the next concrete solution step of Dijkstra method, P and T are respectively used to represent the P label and T label of a point, indicating the point set with P label in the first step. In order to find the shortest path from to each point and the distance from to each point, give each point a value. When the algorithm terminates, if the previous point on the shortest path from to is; If yes, the path from to is not included in D; Representative = where m represents an infinite number.
Model checking and practical research
A general optimization model has been given above. Now give an example to calculate the model.
As the picture shows, this is a one-way traffic network. The vehicle is traveling at speed v, and the number next to each arc indicates the relative distance between two points. Now a taxi will start from here, cross this traffic network and find the shortest route.
Figure 5- 1
It can be seen that if the speed and other factors have not changed, according to the model (*), the Dijkstra algorithm is directly used to solve the problem, and the shortest path from to is.
Assuming that the vehicle speed or road conditions change at this time, according to the model (* *), we can get:
Let's assume that the car is driving at this time, the speed is 2v( =0.5), and the traffic on the way to it is not the main road because of the traffic jam during the rush hour (=5), and the unblocked rate is higher than before (=0.6), and other road conditions have not changed (= 1). At this time, the display mode (* *):
The shortest route from arrival to use can be obtained as follows.
Practical research
The optimized model has a good guiding and controlling effect on the actual traffic flow control. When using this model, data can be obtained through three devices, which is feasible. The first is vehicle-mounted equipment, the second is roadside equipment, and the third is control center.
Vehicle equipment includes:
(1) an operation keyboard for receiving data input by the driver;
(2) a receiving and sending part for receiving data from roadside communication equipment and sending data to the equipment;
(3) a real control panel capable of providing data received from roadside communication equipment;
(4) An interface for receiving information transmitted from roadside or central broadcasting equipment.
Roadside equipment includes:
(1) Roadside communication equipment, which records the data transmitted from the central processing equipment and performs bidirectional communication with a single vehicle through the annular coil embedded in the road surface and the vehicle antenna.
⑵ Connect the central control and roadside broadcasting equipment directly with cables, and then carry out vehicle-mounted communication. (3) Automatic traffic detection device, which can measure vehicle speed and detect road conditions.
In this way, the driver inputs the required terminal code into the keyboard installed on the car. Once the car approaches a certain position, the microcomputer on the car transmits the stored coded data to the microcomputer equipment on the roadside through the vehicle antenna and the annular coil embedded in the road surface, and the microcomputer feeds back the coded data to the control center. The control center uses the optimized model and the algorithm given in this paper to solve the problem and get a reasonable driving route, which is fed back to the microcomputer in the car through roadside equipment, and the driver can get the shortest route through the display.
Because the traffic is not a single vehicle, but multiple vehicles participate in the operation, the traffic situation may change at any time, thus affecting the change of the driving route of a single vehicle. Considering this situation, the guidance and control in this paper will be carried out in different time periods:
Table 5- 1
water channel
5:00-
7:30 rush hour
7:30-
9:00 in the middle.
9:00-
12:00 rush hour
12:00-
13:00 middle time
13:00-
17:30- rush hour
17:30-
19:00 trough
19:00-
Eleven p.m.
The feedback period is 30 minutes in the valley period, 0/5 minutes in the middle period/kloc, and every 5 minutes in the peak period. Because the road conditions change rapidly during the rush hour, the data interval fed back to the driver should not be too long. This makes the model in this paper more feasible.