Design and Simulation of a fuzzy Controller for a busy Intersection

A. Next green phase selector stage
This stage comprises three inputs and one output. The inputs are: ‘Length of Queue Num’, ‘Length of Link Num’ and ‘Waiting time’. The number of vehicles that remain on one lane behind the traffic light during a red light phase is indicated by the ‘Length of Queue Num’. The ‘Length of Link Num’ denotes the number of vehicles on a link between two intersections, and the number of vehicles on the front, left and right side links are all sent to the fuzzy controller. This input is important for the prevention of traffic congestion on links. Another important parameter that has been used in the design of fuzzy controller is the ‘waiting time’. This parameter calculates the length of time the vehicles spend behind the red light. This, in fact, is done by a timer installed at each intersection. In a more precise definition, this parameter indicates the time duration that the first vehicle arriving at the intersection spends behind the red light until it turns green. In many of the previous works on this subject, usually a parameter has been used to determine the number of vehicles behind the red light. While the aim of defining such an input is to reduce the waiting time of vehicles behind the red light and in this regard, the parameter defined in this article seems to be a more appropriate parameter. Each input parameter has three membership functions, and the output has five membership functions. The output indicates the worst traffic conditions for the selected phase. The worse the traffic of a chosen phase gets, the higher the value of output becomes. To obtain the urgent value of a phase, we should consider the urgency of every lane in that phase. The combination of urgency values of these lanes is considered as the value of that particular phase. The phase that has a higher value is selected as the next phase. As is shown in Table 1 (in Appendix A), at this stage, 28 rules have been developed to relate the three inputs to the output. The criteria considered in determining the output are:
1. If the number of vehicles on a link between the main intersection and other intersections reaches its maximum capacity, no vehicle will be allowed to enter that link through the target intersection. This prevents congestion.

2. 
   
   Figure 4. Membership functions
   If the waiting time becomes too long, the vehicles will have the right of way in passing through the intersection. This will certainly minimize the waiting time for each vehicle.
   

Rule 1 in Table 1 indicates that when the input parameter of ‘Length of Queue Num’ is zero, the output will also be zero regardless of the values of other two inputs. With the increase of the ‘Length of Queue Num’ and ‘Waiting time’, the output value relatively increases; while with the increase of the ‘Length of Link Num’, the output value relatively diminishes.

2. 
   Green light extender stage
   

This stage considers the traffic situation during the green light and includes three inputs of ‘Length of arrival’, ‘Length of Queue’ and ‘Length of Link’ and one output called the ‘Extend’. These input parameters are like the inputs of the next green phase stage, with the difference that the fuzzy output variable has 6 membership functions. The ‘Length of arrival’ represents the average number of vehicles entering an intersection during a green light phase; while the ‘Length of Queue’ indicates the average number of existing vehicles behind the red lights, and the ‘Length of Link’ shows the number of vehicles on the links. As is shown in Table 1 (middle frame), 28 rules have been used at this stage.

2. 
   Decision making stage
   

The decision stage comprises two inputs, and these inputs are in fact the outputs of the next green phase selector stage and the green phase extender stage, which are expressed as ‘Extend’ and ‘Urgency’. These two references (i.e., Extend and Urgency) are compared with each other at every moment and based on this comparison, it is decided whether to change the green phase or extend the green light. In this regard ‘T’ is used for ending the green light phase and ‘F’ is used for the prolongation of the active green phase. If the output of ‘Urgency’ is higher than ‘Extend’, it means that the traffic conditions are more suited to the establishment of the next green phase; and therefore, the output will go to the next green phase. The rules pertaining to the decision stage have been outlined in Table 1 (left side). The Max-Min reasoning method has been employed in these three stages of the fuzzy controller [11, 14].

4. 
   Simulation of Fuzzy Controller
   

In this section, we will simulate the designed fuzzy controller algorithm. For this purpose, first, each of the design steps will be modeled and then the final output will be implemented. As is observed in Fig. 1, for the modeling of the next green phase selection stage, two fuzzy controllers and a comparer have been used, where these two controllers specify the two phases that are supposed to be selected as the next green phase. Based on their inputs, each of these controllers displays a value between zero (0) and one (1) in its output. So, in the comparer block of Fig. 5, a program has been written that compares the outputs of the controllers with each other and after choosing the largest numerical value associated with the selected phase, displays it in the output. The closer the output value of a controller is to one (1) means that that phase will be in priority for being selected as the next green phase. The comparer block has been programmed in such a way that if number one (1) appears in the output, the next green phase will be phase B and if the output number is 2, it will indicate that phase C has been chosen as the next green phase.
In the green phase extender stage, we have only one fuzzy controller, where the three inputs of ‘Length of arrival’, ‘Length of queue’ and ‘Length of link’ have been connected to the green phase extender block by a Mux. With regards to the membership functions considered for the inputs, the output of this fuzzy controller can have a value between 0 and 1. The closer the controller’s output value is to one (1), the longer the active green phase should remain green.
At the end, the outputs of previous stages act as inputs of this stage. In fact, the deciding is done by the decision block, which compares the values of its inputs (i.e., ‘u’ and ‘ex’) and displays the largest chosen value in the final output. If the value of ‘ex’ is larger, the number zero (0) will appear in the output, which means that the green light is to be extended. And if the output of ‘u’ is larger, ‘y’ will appear in the output, which can have a value of 1 or, 2.
To evaluate the fuzzy model, we randomly apply some data to the inputs of controllers. For example, the following results have been obtained in the output of the green phase extender stage. These results (shown in Fig. 6) have been obtained in the course of 100 seconds by using the considered random data. At every moment, this implemented model compares the outputs of the green phase extender stage and the next green phaseselector stage with each other and makes a decision based on their values. The final output can display values of 0, 1 or 2 at any instance. With respect to the input data, the number zero (0) in the output indicates that the green light should be extended, and if the output displayed a one (1), it would mean that the current green phase should be terminated and phase B should be the next green phase. And finally, if the output showed number 2, the green phase should be terminated and the next green phase should be activated; and therefore, considering the number 2 in the output, the next green phase that should be activated is phase C.

5. 
   Simulation Results
   

In order to show the more effective performance of the designed fuzzy controller relative to that of common controllers, a comparison has been made between the presented fuzzy controller and the preset cycle time controller. As has been demonstrated in Fig. 7, in the presented controller, the average number of vehicles entering the intersection diminishes significantly compared to the preset cycle time controller.

6. 
   Conclusion
   

Since in the future, the intelligent control of traffic in busy areas will be inevitable, the fuzzy control method, which is one of the most effective control techniques, was used in this article. The goal of this article was to design a new fuzzy control system for the control of a traffic intersection with two­way streets and left and right turn options. This controller functions on the basis of fuzzy rules and instantaneous traffic information. The fuzzy control system includes a selector phase and a green light extender phase. The outputs of these stages were considered as inputs for the decision making phase. The decision to go to the next green phase or to extendthe green light duration was made according to the value of each input. When these three phases were employed in high volume traffic conditions, a better performance was achieved. Finally, by simulating the controller, the accuracy of fuzzy rules was validated.

Figure 6. Output of the green phase extender stage



Figure 7. Simulation results of the presented fuzzy controller with preset cycle time

7. 
   Appendix A
   

TABLE I. Fuzzy rules related to the next green phase stage;
Letters VL, L, M, S and Z are abbreviations for Very Large, Large,
Medium, Small and Zero, respectively.