# Attention Horizon as a Predictor for the Fuel Consumption Rate of Drivers
## 2 Materials and Methods
### Extraction of Red Light-Approaching Trajectories
One possibility could be, for example, to investigate the impact of a bigger population of drivers and vehicles to see if the correlation values hold up. This might also smooth out even more noise and give a higher quality AH to work with. Another possible research avenue is to compare the extent to which AH explains different driving quality factors across populations, drivers, and vehicles. This implies measuring, for instance, how strong a predictor the AH is when one type of vehicle is used, as opposed to another type. Another option could be to compare the information value of AH across different populations of drivers, e.g., from different areas, occupations, or training background. Another facet that could be improved about our work is to look for a nonlinear relationship between AH and FCR. Correlation coefficients can only capture the linear component of relationships. Exploring the extraction of nonlinear components between AH and other driver quality metrics is a possible approach for future work. Finally, it is possible to work on a more sophisticated approach for calculating the AH, e.g., by involving other types of data into its determination. We found our approach to be effective enough but it does not exclude further research in this area. More specifically, in this first work we did not take advantage of machine learning techniques to analyze the data. The definition of attention horizon we used is, intentionally, very simple in order to be interpretable and intuitively understandable. However, using the power of machine learning to mine the available data, one will likely be able to much more precisely pinpoint the elusive point where the driver makes the _decision_ to stop at a red light. ## 5 Conclusions

In this paper, we introduced a new metric to analyze drivers' behavior. We called it attention horizon (AH), since it is inspired by the concept of driver awareness, i.e., how early the driver starts to react when forced to stop at a red traffic light. We presented an algorithm to automatically extract the AH of given positions of red traffic lights in the driving trajectory. The algorithm only needs data points with speed, acceleration and brake pedal positions, and geographical coordinates recorded at regular intervals. Past research on complex notions such as \"awareness\" typically required highly sensitive data from cameras and detailed human interpretations, while we demonstrate that it is, at least partially, possible to manage at scale with readily-available IoT data. With simple statistics and without the need for complex tools, we demonstrated that there is a correlation between the AH and fuel consumption rate (FCR) of the drivers in the timescale of weeks and months. This can be used to rank drivers, for example, in terms of their performance. Furthermore, we demonstrated the necessity of statistical normalization of AH for different traffic lights and normalization of the FCR by vehicle. We presented evidence that the absolute value of the median correlation grows by increasing length of the time periods for which the AH is calculated. In particular, it grows from 0.156 to 0.402 when moving from weekly to monthly periods. We also proposed that the AH could be a general driving quality metric; however, proving that remains to be achieved in future work. Such a metric as AH that is easy to calculate and straightforward to interpret could be employed as a tool to quantify drivers' awareness. This can be useful, especially when driving style alone has been shown to account for at least 6% of fuel consumption [38; 39], reduced driver vigilance contributes to 35% of motorway crashes [40], and inattentiveness after speeding is the biggest human error in road crashes [27]. In this work, our main focus was to establish AH as a well-founded metric. However, many interesting future research avenues exist based on the proposed AH metric, such as evaluating variance against consistency of the drivers, or analyzing how the AH of an individual driver changes over time, and more.