Numerical Data

The purpose of this numerical study is not to investigate real driving behavior, but to illustrate the appropriateness of the proposed choice-based driver attention allocation model. Thus, a set of hypothetical data was generated for demonstration purposes. Working with hypothetical data, generated data based on certain rules and characteristics, can effectively illustrate how the model works and how its results can be applied. To be effective, the estimated model results should be able to recover the rules and parameters of data generation.

Two types of parameters must be identified, which are the glance duration and the transition probability. This study treated the process of attention allocation as the successive choices of the next focal point. Therefore, continuous data of attention allocation must be transferred into discrete counterparts (time stages) every 250 ms.

Figure 3-5 shows the data generation procedure. The three outputs of data generation used to estimate the proposed attention allocation model were the focal point chosen in time stage k (Fj,k), the glance duration of glancing at each focal point (Duri,k) and the focal point chosen in the time stage k - 1 (Prevk).

The duration of glancing at each focal point (T) was randomly generated from a normal distribution. Under normal conditions, the mean glance duration of each focal point is between 400 ms to 700 ms (Chapman et al. 2002, Underwood et al. 2002a, Underwood 2007, Konstantopoulos et al. 2010). When driving in a demanding situation with heavy traffic, the sampling rate of each glance will be higher due to psychological pressure. This means that the glance duration would be shorter than that in normal conditions, which is about 400 ms to 500 ms (Chapman et al. 2002, Underwood et al. 2002a). When driving in hazardous situations in which crashes may occur, the mean glance duration would increase significantly to one second, since drivers must pay close attention to hazardous objects (Underwood 2007).

Initial State points is not identical, the mean glance duration was set between 1.5 to 3 time stages (375 ms to 750 ms). Among the focal points, the frontal side (perception domain of the current driving lane) attracted the most drivers’ attention (Underwood et al. 2002a, Underwood et al. 2003b, Underwood 2007, Levin et al. 2009). Therefore, the mean duration of glancing at F3 was set as three time stages. By contrast, drivers pay less attention to the perception domain of the adjacent lane (F6), and the critical domains of the current driving lane (F1) and adjacent lane (F4). Drivers usually glance at these areas quickly, and then shift their visions to other focal points. Therefore, the mean durations of glancing at F1, F4 and F6 were set as 1.5 time stages. In addition, glancing at mirrors and roadside signs required more effort to identify the object in the mirror and the message on the sign. Previous research illustrated that drivers spend an average of 400 ms to 650 ms glancing at roadside signs and mirrors

(Underwood et al. 2002a, Crundall et al. 2006). Therefore, the mean durations of glancing at mirrors and roadside signs were set to 2 time stages.

Table 3-1 Parameters for data generation

Origin Focal Point

Glance Duration (250 ms) Probability of Focal Point Transition (%) Mean Std. F₁ F₂ F₃ F₄ F₅ F₆ F₇ F₈

F₁ 1.5 0.75 0 5 70 5 5 5 5 5

F₂ 2 1 7 0 50 7 15 7 7 7

F₃ 3 1.5 2 30 0 2 30 32 2 2

F₄ 1.5 0.75 5 5 40 0 10 5 30 5

F₅ 2 1 6 20 40 7 0 6 15 6

F₆ 1.5 0.75 8 8 45 8 8 0 15 8

F₇ 2 1 5 5 70 5 5 5 0 5

F₈ 2 1 5 5 70 5 5 5 5 0

When drivers end the glance at a current focal point, they must choose a new focal point. Table 3-1 illustrates the probability of shifting attention from one focal point to another that was hypothesized in this study for data generation. The hypothetical driver was assumed as an experienced driver who fits the “normal driving pattern”. The hypothesized driver was considered as having no particular intention, such as looking for road signs. Figure 3-6 shows the three types of scan paths considered in this study. Each block represents a focal point that a vision glance can cover. The arrows between blocks represent the origin and destination focal point of scan paths.

Scan Path 1 Scan Path 2 Scan Path 3

F1 F2 F3

F4 F5 F6

F8

F7

Figure 3-6 Hypothetical scan paths

The first type of scan path represented the frontal area dominating the attention allocation. Drivers usually focus on the farthest point of the current driving lane (F3).

Since the driving task discussed in this case study is driving forward without changing lanes, shifting attention away from this focal point will cause the unawareness of leading traffic and increase the risk. Therefore, drivers will have a higher probability

to shift attention back to F3 after shifting away. Hence, seven paths originated from the other seven focal points to F3 were created. The second type of scan path illustrated the attention demand of the neighboring transition. Considering that the invested effort increases with the distance between consecutive focal points, drivers tend to transit vision between neighboring areas. This study considered 6 neighboring transition paths, as shown in Figure 3-6. The third type of scan path represented the attention allocation for roadside areas and information acquisition from road signs. In this study, drivers did not have an intention to search the roadside actively for information. However, roadside areas are occasionally glanced due to situational awareness or neighboring search. Since the driver was assumed to drive on the inner lane, the three focal points on the adjacent lane (F4 to F6) are closer to the roadside than the other focal points. Therefore, the three scan paths of neighboring transitions from the adjacent lane to the roadside (F7) are generated.

In total, 8,001 samples were generated. The first sample was removed due to data unavailability for the previous focal point. The average glance duration was 590.1 ms, which was within the reasonable range obtained from previous studies. Figure 3-7 illustrates the percentage of time and frequency of transiting vision on the 8 focal points in this hypothetical case. As shown in Figure 3-7 (a), the farthest area of the current driving lane attracted the most attention. Meanwhile, drivers paid the least attention to the area closest to the vehicle. The proportion of time spent on each focal point, including the length of the glance duration fits well with the general driving behavior. Figure 3-7 (b) illustrates that the number of glances (101.76 per minute) was similar to the results in Underwood et al. (2003b).

45.0 %

(a) Percentage of time spending on focal points (b) Number of glances per minute

Figure 3-7 Statistics of a hypothesis data set of drivers’ glances