, the authors propose to include a FIS technique to define if it is suitable to do a modification in the green light duration of a determined semaphore. This method will allow the system to validate a set of attributes to determine, prior to the start of a green light, if according to the conditions of the road, it will be necessary modify the duration of such light.
To consider a possible change of the green light duration in an isolated 4-lane traffic intersection using a FIS (Fuzzy Inference System), we propose a Mamdani model with five input variables such as:
・ Number of incoming cars in each line of this specific road.
・ Green light time assigned to the semaphore in its previous intervention in the junction phase.
・ Day time in real clock scheduling.
・ Type of road that semaphore should administrate.
・ Traffic condition at the moment of the FIS decision.
Each of these input variables are represented by a trapezoidal membership function. The response of the model (i.e., determine whether or not to change the duration of the green light) is then characterized by a triangular function as is illustrated in Figure 1. For sake of simplicity, the proposed approach defines a set of attributes for each input variable which are introduced in Table 1. These values were selected and calculated based on previous work presented in  using experience of human experts on traffic control.
In this way, the graphical representation of the membership functions of the linguistic attributes for each of the defined variables, by using the MatLab diffuse control is presented in Figure 2.
In order to ensure a proper application of green light times in a semaphore, the output variable called decision is represented by a dichotomous response (YES or NO) (Figure 3). To note, this new system procedure only is in-charge to decide if the semaphore should evaluate whether the green light interval must be modified. Only two answers are defined: “No”, which means that according to the FIS, the information provided for the road is not significant enough to indicate that a change in the duration of the green light should reflect a better vehicular
Figure 1. Scheme of the Mamdani model to evaluate semaphore decisions.
Figure 2. Membership representation of the attributes for each input variable and decision.
mobility. Contrary to this, the “Yes” response represents the membership of the road conditions in which is recommended to do a change in the time of the green light. To express the above, a set of 56 rules was generated, where each variable was combined with the rest, so that all possible combinations were considered, as illustrated in Figure 4 (only 30 rules are presented).
3. Experimental Results
All the experiments were developed on a Macbook Pro with the following
Figure 3. Surface view for number of cars and green light time.
Figure 4. Review of the behavior rules of the diffuse inference system based on the Mamdani model.
・ macOS Sierra OS10.12.6 version,
・ Intel Core i7 2.90 GHz Processor,
・ 8 GB 1600 MHz DDR3 memory,
・ 1 TB SSD storage.
To validate the efficiency of the generated FIS, a phase of 10,000 control experiments were performed each, taking as reference the representation of an infrastructure of four roads, one of the most used in Mexico (see Figure 5) with the following characteristics:
・ Each road has movements in both directions.
Figure 5. The representation of an infrastructure of four roads used in the test.
Table 1. Relation variable attributes for the fuzzy decision model.
・ It can turn left (according to the traffic laws that are regulated in Mexico).
・ Continuous right turn (i.e., not necessarily the semaphore should have green light, simply the driver must be cautious).
・ Each road has three lanes.
・ Average speed of the car 50 km/h.
・ Different types of cars (i.e., sizes and shapes).
The results are compared against the performance obtained from the system when it modifies the green light time at all turns of the semaphore cycle. In this sense, if the system uses a decision support technique, such as the FIS technique, its performance increases by almost 18% as shown in Figure 6.
Another interesting point of view to be noted is the number of experiments each one of the proposed approaches needed to reach stability in the overall system performance. In other words, this data reflects the number of situations that system requires to get sufficient information into their data base in order to reach trustworthy and reliable decisions. For instance, in Figure 7 the computed curve using a sliding window up to the current trial with a smooth order 3 method for the performance of the system under different solution perspectives is presented. As can be noted, the system requires almost 1000 cases to reach a more stable behavior in order to ensure a suitable and constant mobility level.
Figure 6. Performance obtained when the system uses a FIS to decide whether or not to modify the green light time.
Figure 7. Comparison of the computed curve of trial experiments to reach system stability.
4. Conclusions and Future Work
Road traffic congestion is one of the main causes in low productivity and the decrease in modern city standards. In this sense, some recent trends in artificial intelligence suggest that in the near future, intelligent agents will improve some road challenges. In this light, the present paper introduces the use of a fuzzy inference system to define when it will be opportune to change the length of the green light in a determine traffic light signal looking for improving the level of service offered in a particular junction.
The results show that using a decision support technique, such as a fuzzy logic rules, the system performance increases in almost 18%. Therefore, it is possible to identify that the use of this technique allows the system to modify the duration of the green light, improving its decision-making process which is reflected in an improvement of its operative capacity, its reliability and certainty. It is important to remark that for experimental tests, the human factor had a vital role because an expert in traffic control recommends the variables and the rules consider in the FIS. For future approaches, it is necessary considered to expand the study about which data should be taken into account in order to reach a suitable and trustworthy set of real variables.
From the obtained results, it is possible to argue that the proposed approach achieves significant benefits in vehicular mobility, in terms of congestions by increasing the traffic capacity of any intersections. However, future investigation is suggested including the following aspects: “Issues such as acceleration and des-acceleration, collision avoidance and vehicles with different velocities, must be included in the simulator by offering a set of more realistic situations in the virtual instrument proposed here”.
Indeed, people are different and react modifying their behavior pattern, considering variables that have not impact on the situation. Drivers are the most important source of data. At the moment, the literature has not reported a system robust enough to satisfy the road constraints of the cities. Intelligent transport systems must be closely designed according to the human beings. In this light, it is necessary to develop inference models based on humans where emotions, beliefs, politics, manners, etc., can be considered. In this light, it is necessary to develop inference models based on human must consider emotions, beliefs, politics, manners, etc.