# Attention Horizon as a Predictor for the Fuel Consumption Rate of Drivers
## 2 Materials and Methods
### Extraction of Red Light-Approaching Trajectories
## 3 Results

In order to test the link between the fuel consumption rate and attention horizon, we use heterogeneous naturalistic driving data collected from a fleet of heavy-duty vehicles collected over a timespan of three months. We set the \(L_{p}\) value to 150 m and \(N_{p}\) to 100; therefore, we resampled and analyzed the brake and acceleration sequences from the 150 m traversed before stopping at the traffic light with 100 equidistant resampled data points. As previously mentioned, we gathered the anonymized IDs of the vehicles' drivers throughout the time period. The IDs were employed to associate drivers with the paths with traffic light stops used in AH calculation. We also took advantage of the same IDs to associate drivers with their fuel consumption rate (FCR), i.e., fuel consumed per distance unit. Only 29 drivers had trajectories with stops at traffic lights that could be used to calculate the AH metric. To give some more insight regarding the calculation of AH, we created plots that show the changes in vehicle speed, and the sequence of positions for the acceleration and brake pedals, through the 150 m just before the vehicle stops at a traffic light. You can see examples of these plots from the same traffic light in Figure 2. Furthermore, we present statistics regarding these parameters at the vehicle approaches to multiple traffic lights in Figure 3. Different behaviors for different approaches to the traffic light can be observed. It is also clear that the AH is essentially the moment the driver stops to accelerate before the last brake. Our aim in this paper is to show that correlation exists between the AH metric and the overall driver behavior, more specifically one that is associated with long-term fuel consumption. We believe we can use this metric to identify inefficient driving patterns, which would be a very useful service for fleet operators. The operators can then use this information to provide incentives for more efficient and ecological driving and identify training needs, among others. However, to ensure that the influence of other important factors is minimized, we have performed some separate analysis on the AH and FCR values. to 100. To determine the variability of AH based on different factors, we measured its distribution across the traffic lights, and also across the drivers. First, we divided our AH samples based on the driver, and for each driver we calculated their individual average AH at different traffic lights. We created a box plot, capturing the distribution of the data for those drivers who have AH samples originating from more than one traffic light; this way we are showing the distribution of the average calculated AHs across different traffic lights. These box plots can be seen in Figure 4a. After that, we performed a similar analysis

Figure 3: Density histogram, median and mean for the speed, acceleration pedal position, and brake pedal position values for the data point on the traffic light approach sequences (all the data used for determining AH values). Brake and acceleration pedal positions have a possible value range from 0 to 100. Figure 2: The sequence of acceleration and brake pedal positions, as well as vehicle speeds, just before stops at traffic lights. Four examples from the same traffic light are presented. The calculated AH is shown at the dashed vertical line. Brake and acceleration pedal positions have a possible value range from 0 (fully released) to 100 (fully pressed). for traffic lights by grouping the AHs by traffic light and then calculating the average AH for different drivers that have stopped at each traffic light. We only created box plots for traffic lights with samples from more than one driver. The result is shown in Figure 4b. The comparison of Figure 4a,b shows a clear difference between the variability of the AH when grouped according to drivers and then averaged for different traffic lights, as opposed to grouped by traffic lights and then averaged for different drivers.