# Efficient Intersection Management Based on an Adaptive Fuzzy-Logic Traffic Signal
## 5 Evaluation and Discussion
### Simulation Model  
Algorithms 1 and 2 were codified in python and embedded in the simulation environment through the Traffic Control Interface (TraCI) API provided by SUMO [73; 74].  
In SUMO, the microscopic simulation is based on the behavior of the driver-vehicle units. Because of this, vehicles are modeled by considering the length, maximum speed as well as acceleration/deceleration profiles.  
The calibration of the SUMO model was carried out by setting the parameters required by the lane change model LC2013 [75] and the Krauss car-following model [76]. These parameters were obtained through in situ measurements, which were retrieved from radar trackers and road tube counters that were deployed to count and classify the traffic volumes in the study site. In addition, the GEH statistic was used to ensure that the calibrated microsimulation model was representative of the observed traffic conditions [77]. A summary of the collected traffic data is shown on weekly average daily traffic metrics and average hourly flow rates in Tables 2 and 3, respectively. In Table 2, the average travel speed was estimated from the corresponding observations as the 85 th percentile of the entire sample. Table 4 displays the average directional movement distribution through an OD-Matrix.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Rule**} & \multicolumn{3}{c}{**Input**} & **Output** \\ \cline{2-5}  & **Flow A** & **Flow B** & **Flow C** & **Cycle Length** \\ \hline
1 & Very Low & Very Low & Low & Very Short \\ \hline
2 & Low & Very Low & Low & Very Short \\ \hline
3 & Medium & Very Low & Low & Short \\ \hline
4 & High & Very Low & Low & Average \\ \hline
5 & Very High & Very Low & Low & Average \\ \hline
6 & Very Low & Low & Low & Very Short \\ \hline
7 & Low & Low & Low & Very Short \\ \hline
8 & Medium & Low & Low & Short \\ \hline
9 & High & Low & Low & Average \\ \hline... &... &... &... &... \\ \hline
75 & Medium & Medium & Medium & Average \\ \hline \hline \end{tabular}
\end{table}
Table 1: Example of the if–then rules used for the fuzzy inference system.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Roads**} \\ \hline  & \(r_{1}\) & \(r_{2}\) & \(r_{3}\) & \(r_{4}\) & \(r_{5}\) \\ \hline Traffic volume (veh/day) & 4765 & 5393 & 8652 & 9450 & 4664 \\ \hline Avg. travel speed (km/h) & 32.20 & 28.30 & 42.30 & 57.90 & 26.40 \\ \hline Mean flow rate (veh/h) & 451 & 329 & 554 & 770 & 226 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Weekly average daily traffic metrics.  
For the traffic demand, three vehicle types were defined in the microsimulation model: _car_, _van_, and _bus_. The type _car_ represents private vehicles characterized by a length of 4.5 m, an acceleration of 2.6 m/s\({}^{2}\), a deceleration of 4.6 m/s\({}^{2}\), and a maximum speed of 80 km/h. Meanwhile, _van_ and _bus_ types were incorporated into the simulation, since they are the vehicles that provide public transport in the zone. The type _van_ is characterized by a length of 5 m, an acceleration of 1.5 m/s\({}^{2}\), a deceleration of 3.6 m/s\({}^{2}\), and a maximum speed of 60 km/h. The type _bus_ is characterized by a length of 7 m, an acceleration of 1.5 m/s\({}^{2}\), a deceleration of 3.6 m/s\({}^{2}\), and a maximum speed of 42 km/h. In addition, for all vehicles, a standard deviation of 10% up and down from the maximum speed was considered to reproduce real-world fluctuations as well as a sigma value of 0.5 mimicking drivers' stochasticity.