## 3 Methodology  
The research work followed a quantitative approach tested by computational simulation to study a typical small-city intersection, using representative traffic profiles. A simulation framework has been proposed and developed specifically for this work (described in Section 4).  
The simulation refers to a specific intersection in Castelo Branco, a small Portuguese city, with six inbound lanes, as can be seen in Figure 1. This intersection has been chosen for the simulation because it is a key intersection that regulates traffic to/from the city centre.  
The traffic profiles used in the simulation were created in the traffic profile creator tool, from base statistical parameters, gathered from the direct observation of traffic at the intersection. Four different traffic profiles were generated, with a time frame of one hour each:  
* A normal traffic profile corresponds to the regular traffic observed on weekdays, during the middle of the morning (10 a.m. to 12 a.m.) and afternoon (2 p.m. to 5 p.m.).
* A high traffic profile corresponds to the traffic observed on weekdays, in the first hours of the morning (8 a.m. to 10 a.m.) and end of afternoon (5 p.m. to 7 p.m.).
* A low traffic profile corresponds to the traffic observed in the early morning (from 6 a.m. to 8 a.m.) and night (from 8 p.m. to 11 p.m.).
* A very low traffic profile corresponds to the traffic observed during the night, from 11 p.m. of one day to 6 a.m. of the next day.  
To define the base statistical parameters for these profiles, each lane was observed for one hour during the profile time span, and the traffic was registered and classified. As an example, Table 1 contains the statistical parameters observed at the intersection that were used to generate the normal traffic profile. There are no categories for battery electric vehicles (BEVs) or hybrid vehicles (HVs), because currently the percentage of BEV and HV vehicles in Portugal is so low that for the purpose of this study they can be ignored.  
Then, each traffic profile was simulated by a passive routing strategy (fixed timing cycle), which mimics the existing traffic light system, and by a smart routing algorithm, especially designed to optimize CO\({}_{2}\) emissions. The CO\({}_{2}\) emissions, average speed, and waiting time for each simulation were registered and compared. The final step of the work was the assessment of the gains obtained with the smart routing algorithm, for different traffic densities, daily patterns, and a whole year of traffic.  
Figure 1: The intersection and its inbound lanes.  
Both the reliability and validity of the findings strongly depend on the overall reliability and accuracy of the simulator. For this reason, the simulator makes use of well-known and proven mathematical modelling (thoroughly described in Section 4) of the energy that is required for specific vehicle kinematics and real-world data about the fuel that are needed to generate that amount of energy, considering the fuel type and vehicle class and mass. Moreover, the simulator has been tested with a single vehicle of each class, for different dynamic profiles, and the reported fuel consumption is consistent with expected reasonable values.