THE ATTENTIONAL DEMAND OF AUTOMOBILE DRIVING REVISITED – Occlusion distance as a function of task-relevant event density in realistic driving scenarios

Précis


THE ATTENTIONAL DEMAND OF AUTOMOBILE DRIVING REVISITED -1
Occlusion distance as a function of task-relevant event density in realistic driving scenarios 2 3 A novel taxonomy defines driver inattention as "insufficient, or no attention, to activities 4 critical for safe driving" (Regan, Hallet & Gordon, 2011, p. 1775. Even if the taxonomy is a 5 highly valuable effort to standardize the use and operationalization of the construct, Regan (Senders et al., 9 1967). Five hundred milliseconds seemed to be a sufficient visual sampling time (visor open) 10 in between occluded periods for an experienced driver to keep the control of the vehicle in 11 the studied driving environments. 12 Concerning the qualitative questions of what and where do drivers require visual 13 information while driving, Rockwell (1970, 1972)  (2013), a task-relevant event state in driving is a source of visual information such that when 3 its value is changed significantly, a response is required from the driver in order to achieve a 4 subgoal in the driving task, for instance, to keep the vehicle in the lane. The task-relevant 5 event states in driving can include, for example, lane position, headway distance, visibility of 6 obstacles, signs or cues, as well as object trajectories, including one's own vehicle. The 7 significance of the change depends on the particular goals of the driving task but the safety-8 related goals can be assumed to be fairly general across drivers and drives. In occlusion 9 experiments, the expected rate of the significant task-relevant events in time (expectancies by 10 Wickens, Helleberg, Goh, Xu, & Horrey, 2001) is in inverse relationship to OT. 11 We argue that a limitation of OT is that it is a function of the event rate only in the 12 time domain, and cannot by itself (without considering speed) specify the density of task-13 relevant events in the spatial scenario. Because of the limitations of OT when applied to 14 realistic driving scenarios with voluntary speed control, we propose a new measure of visual 15 demand of driving environments, occlusion distance (OD). OD refers to the distance a driver 16 feels comfortable driving with his or her eyes shut when the driver is fully concentrating on 17 the driving task. 18 In order to illustrate the difference, Figure 1  of driving with various speeds on the road as a function of the task-relevant event rate in 1 time. With the same OT but at a higher speed, more OD is traveled blind. In this paper, we present support for our theoretical model of visual demand in driving 7 and the utility of occlusion distance as a function of task-relevant event density in realistic 8 traffic scenarios with driver-controlled speed and occlusion times. 9 Theoretical Model of Visual Demand in Driving 10 We define the visual demand of the driving task as the event rate at which the driver has to 11 update the focus of visual attention in order to decrease uncertainty of the task-relevant event 12 states in the immediate field of view to a preferred level. We specifically note that the event 13 rate can be either in the time domain or in the space domain. That is, the updating may occur 14 at specific time intervals, or at specific distance intervals. In the special case of constant 15 speed, these two will be perfectly correlated. 16 In the following, we assume a driver (a cognitive agent) k with a perfect expectancy 17 evaluation skill who pushes occlusion time to a constant maximum level of tolerated 18 uncertainty in all scenarios. 19 After Wortelen et al. (2013), a task-relevant event e(g, t) occurs if at time t 20 visual information, which is relevant for a goal g is used by the cognitive agent k to 21  t) occurs, if at time t a production rule is fired for goal g and 1 thus, the visual information is used by the cognitive agent. A production can process 2 perceived visual information from the environment, such as the headway distance, or features 3 of a stored dynamic visuospatial mental representation of the environment, such as the 4 imagined lane position of the vehicle. A production that processes visual information can also 5 fire without producing a motor response. This would correspond to a real-world behavior of a 6 driver perceiving something task-relevant in the environment such as a headway distance and 7 making a judgment that the current headway distance is sufficient and no response is needed. 8 By our definition, the visual demand of a driving scenario is a function of the total 9 number of events in the scenario per time or distance unit. With a perfect cognitive model of 10 driving (similar to, e.g., Salvucci, 2006), the visual demand, that is, the number of events in 11 the scenario per time or distance unit would correspond directly to the number of productions 12 firing, in which visual information is used. 13 For the cognitive agent k, the field of view at a point x i induces E(x i ) task-relevant 14 events. When the driver k moves along the road a distance ∆x, the total number of processed 15 The circles represent driving 16 task relevant targets (i.e., event states) in the road environment, such as a traffic sign or an 17 approaching car from the right at an intersection ahead. Each arrow represents task-relevant 18 visual information for an event that is processed by the driver, such as the observed speed of 19 the approaching car. Note that visual information of a single physical target can be processed 20 in multiple events. 21 which is exact when ∆t is very small. V(x) is then the momentary velocity of the car. We 10 denote D(x) as the event density. It is the discrete version of the information density of the 11 road ("events per mile" rather than "bits per mile") as defined by Senders et al. (1967). The 12 driver can adjust the event rate by scanning freely ahead and adjust speed so that a 13 comfortable event rate is not exceeded. This is the key task in theoretical models of driving 14 such as Fuller (2005) and Summala (2007). 15 However, the occlusion method makes the mathematical interpretation more complex 16 compared to unoccluded driving. It is necessary to consider a new parameter: the driver's 17 uncertainty U(x) k of the task-relevant event states during occlusion (Senders et al., 1967). 18

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The uncertainty is hypothesized to be a function of the number of task-relevant events 1 induced by the field of view. Increases in the observed event density in the field of view adds 2 to the complexity of the stored dynamic visuospatial mental representation of the scenario 3 that must be processed during the following occlusion. The more events that have to be 4 processed while occluded, the faster the build-up of uncertainty. 5 Thus, uncertainty builds up in this model as a function of events, not time, as in the 6 work of Senders et al. (1967). We make the simplifying assumption that the uncertainty of 7 the task-relevant event states is linearly related to the number of processed (i.e., expected) 8 events during the occlusion: The driver k will ask for additional visual information as soon as the driver's 10 uncertainty of the task-relevant event states during the occlusion has reached the driver's 11 maximum level of uncertainty tolerated, U(x) k = Umax k . For our perfect cognitive agent k In this paper, we are interested in estimating D(x). In most occlusion studies so far 19 (Senders et al., 1967 However, these results would be limited, for example, to visual demand of negotiating 1 a curve with a constant speed. Driving on a road with realistic curvature with a forced static 2 speed is fundamentally a different task than driving the same road with a voluntary speed 3 control, at the operational level as well as from the perspective of visual demands. As an 4 example, in our upcoming data speed is strongly dependent on the curvature of the road, 5 since drivers decelerate when they enter a curve. 6 On the other hand, if both V and OT can vary, then OT can not be used to estimate 7 D(x) without considering changes in speed. For these cases, however, we can define a new 8 function that has not been used in earlier research: the occlusion distance OD(x) k , defined as 9 the distance the driver drives during an occlusion (see Figure 3). This is very close to 10 OT(x) k *V(x) k , but the relationship is not exact because the driver may accelerate or 11 decelerate during the occlusion (i.e., react according to the preceding unoccluded field of 12 view). 13 14 Figure 3. The relationships between U k , Umax k , OD k , and OT k . Driver k's uncertainty (U k ) 15 reaches k's maximum level of uncertainty tolerated (Umax k ) when the distance ∆x traveled 16 equals OD k and the time ∆t traveled equals OT k . 17 The occlusion distance combines the two driver-controlled variables in this setup into one: 18 and allows a prediction for driver behavior to be made: 20 We call the Umax k factor as the subjective uncertainty acceptance threshold that 2 should be fairly static for driver k across different traffic scenarios. It describes the threshold 3 at which the driver feels that the comfortable safety margins have been crossed (Summala, 4 2007). That is, the driver k is capable of processing (or willing to process) at most Umax k 5 events per OD(x) k . Umax k of a given driver can be estimated in a visual occlusion experiment 6 with a sufficient sample of drivers. 7 Both OT and OD are imperfect measures for visual demand, but each has its own 8 strengths. OT varies with the inverse of the task-relevant event rate in the time domain (i.e., 9 dynamic visual demands of driving), but cannot determine whether the changes are due to 10 changes in speed or to changes in the number of events in the scenario. OD varies with the 11 inverse of the event density in the space domain from one unoccluded view to another (i.e., 12 static visual demands of the driving environment), but does not give information on how the 13 driver is processing information in the time domain. 14 In the following, we seek to demonstrate that the three specific hypotheses supporting 15 our theoretical model are justified by the data set collected in two driving simulator 16 experiments with intersection, suburban, and highway scenarios: 17 H1. With self-determined speed and OT, median ODs will increase across environments of 18 progressively reduced event density from intersections to suburban to highway scenarios 19 whereas OTs will vary significantly less. Highways have larger built-in safety margins (e.g., 20 less curvature, no crossings, wider one-way lanes) to enable safe driving at higher speeds 21 than suburbs. Intersections have more task-relevant targets to scan for than the other two 22 scenarios, such as signs, lights, crossing roads, crosswalks, and lanes to select. H1 would 23 support the model of OD as a function of task-relevant event density in space and OT as a 24 function of the preferred task-relevant event rate. It would support the idea that drivers try to 25 H2. OD varies systematically with a nearly constant individual factor for the same driver 3 across driving scenarios. The finding would give support for the consistency of the subjective 4 uncertainty acceptance threshold Umax k within a driver and for the generalizability of OD 5 across driving scenarios. 6 H3. Curvature of the road ahead has a significant inverse relation to OD. The specific 7 environmental demands of road curvature should have an effect on OD if OD is a measure of 8 the task-relevant event density of the environment. 9 By validating these three hypotheses, we can demonstrate that OD can be effectively used to 10 define the environmental and driver-specific task-relevant event density with a generalizable 11 metric over a wide variety of drivers and dynamic real-world scenarios. 12 Questionnaire (SSQ, Kennedy, 1993). Thirty-three participants withdrew from the study or 23 had to be excluded from the data because of simulator sickness symptoms, or as outliers 24 (driving at least 30% of the time the scene was constantly unoccluded). The final sample 25 after a break a 15 minute Highway experiment, and finally 5 minute suburban experiment in 10 snowfall conditions (snowfall results not reported here). The driving scene was occluded by 11 default and participants were able to unocclude the scene for 500 milliseconds by pressing 12 the right-hand paddle behind the steering wheel. To keep the scene continuously unoccluded 13 the paddle had to be repeatedly pressed. 14 Page 15 of 41

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A speed limit of 60 km/h was instructed for the Suburban experiment and 80 km/h or 1 120 km/h for two different types of road in the Highway experiment. Driving directions were 2 provided by Finnish voice guidance at predetermined points on the tracks. The instructions 3 were given two times before each street corner or junction and the participant had the 4 possibility to ask the experimenter to repeat the instructions. In order to make the participants 5 focus on the driving task but still to try to maximize the comfortable occlusion time, they 6 were informed that the 30 most accurate participants in the driving task and with the least 7 unoccluded time would be rewarded with another movie ticket. Driving task accuracy was 8 defined by the number of lane excursions that were scored in real-time by the experimenter. 9 The accuracy of lane keeping was assessed by how many times the HUD speedometer 10 ( Figure 4) crossed a white lane marking, but this was not explicitly stressed in order to avoid 11 unnatural visual demand for an experienced driver through fixating on the lane markings . 12 In this setup, lane-keeping accuracy could be determined independently from the OD 13 because lane excursions were monitored covertly. Although it is not a direct measure of safe 14 driving as such, the lane-keeping accuracy differed dramatically from driver to driver (from 2 15 to 120 excursions). The accuracy parameter was thus defined as (120-number of 16 excursions)/120, being normalized between 0 and 1. Participants were also instructed to obey 17 traffic rules, to choose their preferred driving speed, beware of unexpected events and react 18 as in real situations. No completion time limits were given. Participants were told that they 19 could withdraw from the experiment whenever they wish. The data set consisted of two types of scenarios (Suburban and Highway, see Table  4 1). The tracks, that is, road segments, were divided into separate segments by defining trigger 5 points on the road at points where the user was instructed to turn at an intersection. Another 6 trigger point was set where the driver had cleared the intersection. The tracks were thus 7 defined as segments between the last trigger line marking the end of an intersection and the 8 first trigger line of the consecutive intersection. The drivers accelerated at the beginning of 9 each track in order to reach a velocity preferred by the driver. In total, there were 13 tracks 10 that were long enough to be usable to estimate the average behavior of drivers over the 11 tracks. Nine of these were Suburban (60 km/h speed limit) and four were Highway (80 or 120 12 km/h) tracks. In addition, 19 of the intersections were studied. These varied considerably, but 13 all contained an instruction for the driver to turn at an intersection. Driver behavior was 14 highly variable. Some stopped at some intersections, while others never did. This 15 confounding behavior could not be modeled. Therefore, the intersection data for speeds over 16 2 m/s were used for the OT-OD comparison, but not for a close-up analysis of the occlusion 17 data. For the Intersection data N=97.

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The study closest to ours, Tsimhoni and Green (1999), had the following restrictions: a 4 simple predefined road with a radius of curvature measured at just a few points, constant 5 speed, no other cars, and the participant only varying the occlusion time. The level of visual 6 demand was defined as 0.5/(0.5+OT), and a linear model of visual demand with a radius of 7 curvature and age was determined by averaging values over all drivers for the four well-8 defined curvature points. 9 In contrast, in our experiments the driver drove on simulated real-world roads that 10 were not designed to prove any hypotheses and the driver was able to vary vehicle speed 11 (only a nominal maximum for the road was defined) as well as the occlusion time. 12 Furthermore, the driver was told to drive carefully and to obey traffic regulations. 13 Additionally, other traffic in the form of cars controlled by artificial intelligence algorithms 14 (AI cars) could move in the same or opposite direction ( Figure 5: 1, 2) and there were 15 intersections with potential traffic (Fig. 5: 1, 6), traffic lights ( Fig. 5: 6), and various other 16 signage ( Fig. 5: 1, 2). The downside of this naturalistic driving simulation was that it 17 introduced variables that could not be modeled. We suspect that intersections, zebra 18 crossings, and road signs, in particular, may have caused highly variable effects, since the 19 drivers were asked to be vigilant of crossing traffic and pedestrians. 20 Calculation of Winding. The calculation of road curvature for real-world roads is a 21 numerically unstable parameter, a fact that could be ignored in Tsimhoni and Green (1999) 22 where the simulated road was designed specifically for the purpose of the analyses of 23 curvature on occlusion time. In addition, they only measured road curvature at four points, 24 whereas we needed to measure it continuously. 25

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The radius of curvature R of a natural road is not constant, but rather is constantly 1 varying as the driver moves in and out of a curve. To improve measurements, we defined a 2 related parameter we coined Winding, denoted by W. It is a measure of how much the driver 3 needs to turn the steering wheel while driving along the track. 4 We suggest that the number of task-relevant events on a winding road is related to the 5 amount of steering a driver anticipates as being required ahead. The Winding is related to the 6 radius of curvature R, but is dimensionless and numerically more stable. For any infinitesimal 7 distance dx, the dimensionless lateral deflection is dx/R(x). The total lateral deflection over a 8 long distance L is then given by: 9 The integral is divided by L in order to make W dimensionless and independent of the 11 chosen value of L. The distance L must be defined empirically, but we found 100 meters to 12 be practical. This is also consistent with the result of Tsimhoni and Green

W is dimensionless but can be defined as (meters deflection)/(meters distance). 18
Qualitatively, it describes how many meters the path is deflected per each meter that is 19 traveled forward. 20 Effects of other cars. The effect of AI cars on driver behavior could not be 21 meaningfully evaluated. Some of the tracks had AI traffic going in the same or opposite 22 direction as the driver, but this had no practical effect on the results. The lead cars drove at 23 the nominal speed limit of the scenario, while test subjects almost always drove at lower 24

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H1. With self-determined speed and OT, median ODs will increase across environments 4 of progressively reduced event density from intersections to suburban to highway 5 scenarios whereas OTs will vary significantly less. Median and mean OTs, ODs, and 6 speeds per track are listed in Table 1. Over all the drivers, median ODs seem to vary in a 7 similar systematic fashion between the tracks in Table 1 as median OT * median speed 8 (Pearson's r(11)=.98, p<.001). This suggests that it is sufficient to approximate that 9 OD(x)=V(x)*OT(x) although the exact distance travelled during OT is then somewhat under-10 or overestimated. It is, however, more interesting to look at the underlying distributions. 11

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The mean difference in OT between Suburban and Highway scenarios is only .27 4 seconds, and the difference is to an opposite direction than in OD. The mean difference in OT 5 between the Intersection and Highway scenarios is only .07 seconds. These findings suggest 6 that even if OT is able to differentiate the high Intersection demands, OT varies as a function 7 of task-relevant event rate in time and is not able to differentiate the spatial task-relevant 8 event density between the Suburban and Highway environments that are built to allow safe 9 driving at significantly different speeds. On the other hand, OD can indicate the differences 10 in the expected spatial demands between the scenarios. However, OD cannot indicate that the 11 visual demand of driving near the nominal speed limits in Suburban and Highway scenarios 12 are nearly at the same level, with slightly higher demands on Highway driving and 13 approaching the demands of the Intersection scenarios. Hence the two measures provide 14 complementary information. 15 These findings support H1 and thus support the model of OD as a function of task-16 relevant event density in space whereas OT seems to be a function of preferred task-relevant 17 event rate in time. The findings suggest, as expected, that by controlling speed according to 18 the experienced event density, the drivers tend to keep the occlusion times on a similar 19 comfortable range of approximately .50 to 1.00 seconds across different driving scenarios. 20 The data and our theoretical model can provide an explanation why drivers' preferred range 21 of off-road glance durations seem to reside within this time frame across driving scenarios 1 (Wierwille, 1993). The task-relevant event densities of constructed real-world road 2 environments are in a linear relationship with the drivers' preferred speeds in these 3 environments such that the preferred off-road glance durations (a function of the task-4 relevant event rate) rarely exceed 2.00 seconds. 5 H2. OD varies systematically with a nearly constant individual factor for the 6 same driver between driving scenarios. The Highway scenario differed from the others in 7 that the Winding is extremely low (see Figure 7), there were no intersections to worry about, 8 and driving was not affected by AI cars because in almost all cases the AI lead cars drove 9 much faster than the participants. The within-scenario visual demand is thus for all practical 10 purposes near constant. Any variations in the highway scenario should be due to individual 11 differences. To eliminate issues with possible AI lead cars, we removed the first 200 meters 12 of the highway tracks from the analysis. Therefore, in all except a few cases the lead cars had 13 driven off, and do not confound the analysis of the visual demand. The median highway OD was 13.7 m, and the 15th and 85th percentiles were 7.1 and 23.4 m 5 (see Figure 8). The median OT was .71 s, and the 15th and 85th percentiles were .36 and 1. 10 6 s. The median OD (as well as OT) can thus vary by up to a factor of three between drivers. 7 Since the drivers in the highway scenario did not modulate the speed rapidly (i.e. did not 8 apply brakes sharply), the OD and OT are closely correlated (r(91)=.95, p<.001). The scenario-dependent visual demand in all the Highway scenarios was assumed to be 3 constant, and the significant variations seen in OD thus show differences in the drivers' 4 perceptions of the task-relevant event density, which are in fact not present in the objective 5 distribution of the events in the external scenario. Based on our theoretical framework, we 6 interpret these differences to describe the subjective uncertainty acceptance threshold Umax k , 7 so that for any individual driver k on the Highway scenario OD(x,highway) k =Umax k *13.7. 8 H2 suggests that across scenarios OD(x) varies systematically (because the event 9 density varies with the distance x), and that across subjects Umax k varies systematically. Let  OD(x,highway) k and OD(x,suburban) k for the driver k are: 3 Then we can rewrite OD(x, suburban) k as a linear function of OD(x, highway) k using the 6 above equations: 7 Now we can show that for any individual driver, the value of Umax k remains almost constant 9 across all scenarios. Figure 9 shows a scatter plot of the per-driver relative values for the two 10 scenarios (Highway and Suburban). The data points are normalized to the median OD for all 11 drivers in the scenario. It is seen that a driver with a low OD on the Highway tracks will also 12 have a low OD on the Suburban tracks (r(91)=.85, p<.001). The correlation between 13 Highway and Intersection tracks is slightly lower (r(93)=.71, p<.001). However, we can state 14 that the measured value of Umax k for a given driver will be relatively constant over different 15 scenarios. Interestingly, drivers' median OD and driver accuracy were significantly inversely 1 correlated (r(93)=-.64, p<.001) in the Suburban scenarios. Figure 10 shows the OD-accuracy 2 relationship by experience category, together with the least-squares fits for each experience 3 category. 4 5 Figure 10. Lane-keeping accuracy in the Suburban scenarios by OD (m, median) and the 6 driving experience category. 7 As noted earlier, there was no direct correlation between driving experience and OD 8 (or OT). Based on our theoretical framework, we interpret this result to suggest that the 9 subjective uncertainty acceptance threshold Umax k of a driver is not in a direct relationship 10 with driving experience. A higher OD seemed to systematically lead to a lower lane-keeping 11 accuracy regardless of the level of driving experience. However, higher level of driving 12 experience may result in better lane-keeping accuracy for a given OD value. No other 13 individual effects could be found. 14 H2 is supported by the data. The findings suggest that OD is a generalizable measure 15 across the studied driving scenarios and the consistency of the subjective uncertainty 16 we know a driver's Umax k value, we can make predictions of the driver's visual behavior in 2 road environments with known median OD values. 3 H3. Curvature of the road ahead has a significant inverse relation to OD. Next, 4 we modeled the dependence of OD on scenario parameters. This analysis was made with only 5 the Suburban tracks. To eliminate between-subject differences, ODs of the individual driver k 6 were normalized by dividing by the median OD of the driver k for the Suburban scenarios: 7 ODN(x, suburban) k = OD(x, suburban) k / median(OD(x, suburban) k ) (9) 8 Thus, whether the driver is high-OD or low-OD, the normalized ODN for that driver will be 9 centered at a value of 1. 10 The tracks were digitized at ten-meter intervals. For each of the 10-meter intervals, an 11 average Winding W(x) was then calculated. The normalized OD values of all drivers were 12 also averaged, giving a single value 13 In this paper, we studied the utility of occlusion distance as a function of task-relevant event 2 density in realistic dynamic driving scenarios with driver-controlled speed and occlusion 3 times by testing three hypotheses (H1-H3). 4 The fairly short range of mean OTs for the different driving scenarios (670-950 5 milliseconds) is in the ballpark with the visual sampling model by Wierwille (1993). 6 According to Wierwille, in most real world self-paced driving scenarios drivers try to keep 7 off-road glances between 500 to 1,600 milliseconds. OT as well as OD indicated that the 8 Intersection scenarios were the most demanding ( Figure 6), although the mean difference in 9 OT between the Intersection and Highway scenarios was only 70 milliseconds. 10 However, ODs as well as driving speeds varied considerably more than OTs between 11 all the scenarios. According to OD, the Intersection scenarios had the highest event density, 12 followed by Suburban, and then Highway scenarios (means 3.8-9.9-15.5 meters, Figure 6). 13 These findings give support to our model of OD as a function of task-relevant event density 14 in space and that by controlling speed according to the experienced event density, the drivers 15 tend to keep the event rate in time on a similar comfortable range across different driving 16 scenarios (H1 supported). Near the road speed limits, the OTs for the different scenarios will 17 be close to each other either because of the built-in scalability of safety margins (and thus, of the curve, as in the earlier driving models (e.g., Salvucci, 2006). The more the road is 2 winding ahead, the higher the event density, that is, the more visual targets have to be 3 processed in order to ensure a safe path of travel and to track the variable tangent point for 4 steering. 5 The objective task-relevant event density is not however the only factor behind the 6 preferred OD level. The current data indicates that OD varies systematically with a nearly 7 constant individual factor for the same driver across driving scenarios (Figure 9, H2 8 supported). This finding gives support to the consistency of the subjective uncertainty 9 acceptance threshold Umax k in our theoretical model and thus, for the generalizability of OD 10 across driving scenarios. A driver's maximum level of tolerated uncertainty of the task-11 relevant event states is defined by psychological factors. 12 The more experienced drivers were able to achieve more accurate lane-keeping 13 performance with similar ODs than the least experienced drivers. The road familiarity effect 14 observed by Mourant and Rockwell (1970)  in the level of uncertainty tolerated among both the least and the more experienced drivers. 3 Also the experienced high-OD drivers overestimated their capabilities if we assume 4 that they tried to drive accurately: higher ODs led to lower lane keeping accuracy regardless 5 of the level of experience ( Figure 10). External motives and emotions, such as prizes for the 6 most occluded drivers in our experiments, can push drivers towards risk-taking (Summala, 7 1988;Näätänen & Summala, 1974). Only about 10% of the participants were able to drive 8 with median ODs of 30 meters comparable to J.W.S.' in Senders et al. (1967) in the Highway 9 scenarios (Figures 1 and 8, Table 2 We claim that OD is a function of the subjectively experienced task-relevant event 12 density of the driving environment. OD does not refer to distance to hazards or headway 13 distance but varies with the inverse of the spatial density of expected task-relevant events 14 requiring processing from the driver in order to achieve one's current goals of driving, in 15 accordance with Wortelen et al. (2013). From the safety point of view, OD is related to the 16 construct of safety margin (Summala, 1988), but there are also other events that can be 17 relevant for achieving a subgoal in the driving task, such as noticing the correct exit in order 18 to find the way to a destination. 19 To summarize, the individual task-relevant event density in space is determined in the 20 interaction of both environmental factors as well as psychological factors through the level of 21 uncertainty the driver experiences and tolerates. For any given driver k, our Suburban model 22 can be written as OD(x,suburban) k =Umax k *(10.7-9.1*W), where Umax k is a driver-specific 23 constant that we interpret here as the subjective uncertainty acceptance threshold. 24 Our tentative model so far focuses on the effects of the environmental factor of road 1 winding. Even if Winding together with the Umax k -factor could perhaps explain the observed 2 differences between the scenarios, these differed in many other aspects as well. Further 3 research should be done on the effects of relevant environmental factors such as visibility, 4 weather, signs, and proximity of traffic as well as on building a more accurate model for 5 predicting ODs in other road environments than Finnish suburban roads. 6 A significant implication of our findings is that our theoretical model enables 7 predictions. The median OD value of a given road environment can be predicted 8 approximately, if its Winding is known. Even more importantly, it is possible to predict how 9 an individual driver with a known uncertainty acceptance threshold Umax k will respond to 10 the road environment, and in terms of speed selection, in particular. 11 The other advantage of OD relates to experimental design. Only one drive per driver 12 with self-determined speeds and OTs is required for mapping the experienced event density 13 of a road environment for the driver. With this information collected from a large driver 14 sample, for example, the populations' 85 th percentile OTs for any speed on the road can be 15

estimated. 16
This line of work can be utilized in the development of proactive distraction 17 mitigation systems. The current findings indicate that because of the fairly static OT range 18 across different driving scenarios, the general 2-second glance limit of acceptable in-vehicle 19 glance duration (NHTSA, 2013) seems to make sense as the maximum limit for any situation.  For a practical and acceptable proactive distraction warning application, we would 1 want to define a warning threshold time (WT), that equals the time it takes to travel the 2 longest distance the majority of drivers would choose to drive comfortably without vision 3 when fully concentrating on the driving task in an occlusion experiment, that is, WT = OD / 4 speed. To determine WT, we should use the 85th percentile margin that is a common design 5 standard in traffic engineering (TRB, 2003). The median OD for the 85th percentile driver for 6 the Suburban tracks was 14.4 meters. This corresponds to a WT of .86 seconds at 60 km/h. It 7 is important to note that this WT applies only for the specific scenario used for the 8 calculation (empty roads, speed limit 60 km/h) and the effect of Winding should be taken into 9 account. 10 Besides alerting purposes, dynamic WTs could be utilized as appropriate individual 11 in-car glance limits for any given driving scenario and a driver with a known uncertainty 12 acceptance threshold Umax k . These would enable general verification criteria for in-vehicle 13 infotainment and telematics systems for distracted glancing behaviors with in-car tasks. Other Occlusion distance seems to be an informative measure for assessing task-relevant 2 event density in realistic traffic scenarios with self-controlled speed and occlusion 3 time. 4

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There are systematic differences in the preferred occlusion distances between 5 individual drivers and driving scenarios. 6 • The more experienced drivers were able to achieve more accurate lane-keeping 7 performance than the least experienced drivers with similar ODs. However, driving 8 experience does not seem to be a major factor on the preferred ODs. 9

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Occlusion distance can be utilized in the development of context-aware distraction 10 mitigation systems, human -automated vehicle -interaction, road speed design, 11 prediction of driver speed selection, and in the testing of visual in-vehicle user 12 interfaces. 13