## 2 Materials and Methods  
### Simulation Settings  
As previously stated, in a simulation, we have fast and slow vehicles. The fast vehicles are represented by the \(p_{1}\) percentage and their speed tendency is \(sp_{1}\). The slow vehicles are represented by the \(p_{2}\) percentage and their speed tendency is \(sp_{2}\). The speed tendency (or desired speed) is the speed that a driver aims to reach and tries to maintain, without exceeding it. Moreover, the fast drivers' desired speed is assumed to be the legal speed limit (or posted speed), and is selected in the range of 60 to 90 km/h. The slow drivers' desired speed is the half of their counterpart (fast drivers), and is selected in the range of 30 to 45 km/h. The desired speed values are selected in a range that will provide meaningful results for different traffic scenarios. The simulation scenario is a two-lane one-direction avenue segment of \(d=500\) m length, with constant flow and no entry points, and (looking for general results) without considering specific road geometry or environmental issues. The input of a simulation are fast and slow speed tendency, \(sp_{1}\) and \(sp_{2}\), respectively, and fast and slow vehicles' percentage, \(p_{1}\) and \(p_{2}\), respectively. The output of a simulation are the fast vehicles' travel times. This outcome depends on the percentage of fast and slow vehicles and their speed tendencies. For simulating we use the simulator tool presented in [2], which integrates the microsimulation model for accelerating (decelerating) in free driving and following another vehicle, as well as for overtaking. Thus, the fast vehicles' percentage and speed tendency can take a value from the sets {90%,80%,...,20%} and {60 km/h, 65 km/h, 70 km/h,..., 90 km/h}, respectively. \(p_{2}\) can take a value from the set {10%,20%,...,80%}, while \(sp_{2}\) can take a value from the set {30 km/h, 32.5 km/h, 35 km/h,..., 45 km/h}. Recalling that \(p_{1}=100\%-p_{2}\) and \(sp_{2}=sp_{1}/2\), a \(p_{2}\) value fixes \(p_{1}\), and a \(sp_{1}\) value fixes \(sp_{2}\). In a simulation, the fast vehicles' travel time to complete the 500 m distance is being measured, which is influenced by the slow vehicles, because these force the fast vehicles to perform overtaking maneuvers. We have eight simulations (the possible values of \(p_{2}\)) for each of the seven \(sp_{1}\) cases, thus 56 simulations were performed. We use the output data of 40 simulations (hereafter, data for modeling) for modeling, in these simulations \(sp_{1}\) is a value from [60; 65; 75; 85; 90]. We use the output data of 16 simulations (hereafter, data for validating) for validating, in these simulations \(sp_{1}\) is a value from \(\{70,80\}\). The data for modeling and validating conform the total observed data. The simulation time of a single simulation is 600 s, thus the total simulation time was 33600 s, or 9.3333 h. For all simulations, we set the time lapse (\(f\)) between vehicles' arrival per lane to be \(f=6\) s, i.e., one vehicle arrives per lane each 6 s. Table 1 shows the parameters' values for setting a simulation. As the flow is constant, the time of day and day of week, which are variables related with demand, were out of the scope of this study. Instead, variables \(p_{2}\) and \(sp_{1}\) (and their counterparts, \(p_{1}\) and \(sp_{2}\), respectively) shape the traffic outcome (travel times). When a vehicle is generated in a simulation, we need to establish if it will be a fast or a slow one. In any simulation, for each 10 vehicles generated (a group), it is guaranteed that the percentages of fast and slow vehicles of that group are equal to the percentages' values (\(p_{1}\) and \(p_{2}\), respectively) of the simulation settings. This generation process seeks to avoid patterns between groups in the order by which the fast and slow vehicles are generated, but there is also randomness involved.