# Efficient Intersection Management Based on an Adaptive Fuzzy-Logic Traffic Signal
## 5 Evaluation and Discussion
### Prospective Strengths of Proposal  
As discussed above, the proposed adaptive FL controller is competitive when compared to Time-Gap and Time-Delay approaches, which are still two of the best and most used approaches today; they are successfully implemented in different cities and included in global projects and initiatives such as VITAL and MAVEN [81; 82; 83]. This achievement is remarkable, since the proposed design only considers data retrieved from simple vehicle counters, such as widely used piezoelectric, avoiding the use of more sophisticated sensors such as those required by Time-Gap or Time-Delay controllers, which assume data-harvesting from video processing and even from vehicle probes through a V2X communication.  
Regarding technical requirements for setup and maintenance, since the proposed controller is defined through a type-1 fuzzy logic, it only requires operators to know the minimum and maximum expected values for arrival flows and cycle lengths to establish if-then mappings. This advantage severely contrasts against the technical requirements involved with the definition of scalar states, actions, and rewards, besides the specifications for data collection, aggregation, formatting, and storage, as required for approaches based on NN or DRL. In addition, since fuzzy sets for input mappings consider a single input domain, the proposed adaptive FL controller effortlessly can include larger values than those usually retrieved from traffic surveys, overcoming the major drawback attributed to FL-based controllers [37].  
In terms of computational efficiency, since the proposed adaptive controller is based on sequential and conditional instructions, such as basic arithmetic and if-then statements, the execution time is directly proportional to the number of fuzzy sets and incoming traffic streams (converging roads), which are constant values. For example, by considering an intersection with three incoming traffic streams and five linguistic terms for fuzzification, such as the case study depicted in Section 5.1, in the most demanding conditions (i.e., without rule trimming), the controller executes 90 arithmetic operations and 30 comparisons to fuzzify the input values, 125 comparisons for the FIS, and 625 arithmetic operations for defuzzification. This means the controller executes up to 870 \(O(1)\) operations every \(\tau\) traffic-light cycles. Exploring even a more complex scenario, for instance, a six-way intersection and five fuzzy sets without rule trimming, the controller executes up to 78,365 \(O(1)\) operations. These low complexity bounds significantly contrast against the computational costs involved in most machine-learning-based controllers (e.g., NN, DRL, etc.) whose complexity bounds are above \(O(n^{2})\), in addition to the storage requirements [37]. In summary, due to its design principles, the proposed adaptive FL controller can be implementedover simple microcontrollers (e.g., a US$2 SAM D21 chip), which makes the proposal an affordable option for many cities, especially in developing countries.