# Efficient Intersection Management Based on an Adaptive Fuzzy-Logic Traffic Signal
## 5 Evaluation and Discussion
### Comparison against Other Approaches  
The calibrated microsimulation model was used as a test bench to compare the proposed adaptive FL controller against five approaches: (1) the existing Pre-Timed controller (see Figure 6), (2) a Time-Gap controller [78; 79], (3) the Time-Delay controller proposed by [PERSON] and [PERSON] [43; 44], (4) an FL Green-Extension controller based on the works of [PERSON] et al. [23] and [PERSON] and [PERSON] [58], and (5) the adaptive FL-based method with  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{5}{c}{**Destination**} \\ \hline  & \(r_{1}\) & \(r_{2}\) & \(r_{3}\) & \(r_{4}\) & \(r_{5}\) \\ \hline \multirow{4}{*}{**Origin**} & \(r_{1}\) & — & 3.64\% & 6.16\% & 16.81\% & 73.38\% \\ \cline{2-6}  & \(  
modified [PERSON]'s formula proposed by [PERSON] et al. [34], which is hereinafter referred to as the FL Phase-Adjustment controller. From the in situ retrieved traffic volumes, eleven levels of arrival flow rate were simulated to mimic the observed variations from free-flow to congested traffic conditions. For each level of arrival flow rate, a ten-hour simulation period was carried out comprising at least 300 traffic signal cycles. The simulation outputs (e.g., performance metrics) were fine-grained configured using 5-min intervals, excluding the first and the last simulated hours to ensure steady-state conditions. Finally, all the collected registers were averaged to reduce the stochastic fluctuation. Traffic density and waiting time were selected as performance metrics. Figure 7a-c depict the performance of the six signal controllers tested with respect to the traffic density as a function of the averaged system's arrival flow rate. Similarly, Figure 8a-c show the waiting time as a function of the averaged system's arrival flow rate. Figure 6: Configuration of the current pre-timed control at the case study. Figure 7: Traffic density as a function of the averaged system’s arrival flow rate: (**a**) stream A, (**b**) stream B, and (**c**) stream C.  
Plots of Figures 7 and 8 depict the efficiency boundaries, which were established from the performance achieved by the studied traffic signal controllers. By considering the three incoming streams in the worst-case scenario, which is an arrival flow of 447 veh/h/ln for stream \(A\), 573 veh/h/ln for stream \(B\), and 249 veh/h/ln for stream \(C\), the highest efficiency level is reached by the Time-Gap approach. So, Time-Gap achieves a density of 12.7 veh/km/ln and waiting time of 431.69 s for stream \(A\), 27.3 veh/km/ln density and waiting time of 147.02 s for stream \(B\), and 10.2 veh/km/ln density and waiting time of 593.91 s for stream \(C\). Here, is important to note that the proposed adaptive FL controller shows a performance close enough to the highest, achieving 15.6 veh/km/ln density and waiting time of 715.73 s for stream \(A\), 27.7 veh/km/ln density and waiting time of 168.48 s for stream \(B\), and 11.1 veh/km/ln density and waiting time of 791.54 s for stream \(C\). Another interesting result is that the fuzzy green-extension system, as well as the FL Phase-Adjustment controller, achieved a sound performance level only for some scenarios. On the one hand, by considering the resultant conditions with respect to stream \(B\), it is noticed that the fuzzy green-extension system also matches the performance of Time-Gap and Time-Delay. On the other hand, by considering the waiting time for stream \(A\), the FL Phase-Adjustment controller has a similar performance to Time-Gap and Time-Delay, and it even overcomes both the proposed mechanism and the fuzzy green-extension system. Nevertheless, behind such relative achievements exists an unbalanced phases distribution, which is highlighted when the waiting times for stream \(C\) are analyzed.