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The main objective of this study was to assess the effectiveness of several countermeasures at bicycle crossroads on drivers’ behavior during the driver–cyclist interaction (a cyclist that crosses the road) by the use of a driving simulator. Three treatments of the cyclist crossroads were investigated: baseline condition (no treatment), raised island, and the colored paved markings. Forty-two participants drove a suburban scenario with several bicycle crossroads having difference configurations and presence/absence of cyclist. Overall, 252 speed profiles were plotted from 150 m before each crossroad of which 23 showed non-yield events: 12 for the baseline condition, 6 for the colored paved markings, and 5 for the raised island. The method of the survival analysis was applied to model the driver speed reduction time (the elapsed time to pass from the initial speed to the minimum speed during the yielding maneuver) with the use of the Weibull distribution. The model identified the average deceleration, the drivers’ age, and the countermeasure condition as significant explanatory variables. The survival curves highlighted that for the colored paved markings the driver adopted longer values of the speed reduction times and then a less aggressive driver’s braking behavior. Moreover, the outcomes of the questionnaire confirmed that the colored paved markings were considered to be the most effective in terms of driving aid.

The use of the bicycle as viable alternative to the traditional transport systems has continuously increased in the past years as a consequence of the environmental cause, the impact of the pollution on human health, and the cities congestion [e.g., [

The critical issues of the driver–cyclist interaction at crossroads need to be sought in the driver’s behavior and the poor layout of the crossroad, which does not always ensure adequate safety levels for cyclists. For example, a study of Wood et al. [

According to the literature, interactions between vehicles and cyclists at bicycle crossroads are dangerous situations, in which the driver has to be influenced in order to adapt his speed if the cyclist is present, avoiding the occurrence of accidents and improving the cyclist safety.

For these reasons, the objective of this study is analyzing and comparing the driver performance at bicycle crossroads in the presence of several countermeasures, which are aimed at allowing the driver to adapt his speed and, thus, improving the ability of the driver to yield to cyclist. The parameter speed reduction time (SRT) was used for the evaluation of the effects on driver performance.

SRT gives a measure of the driver’s braking behavior to avoid a potential conflict event at the bicycle crossroad [

Two countermeasures were analyzed in the present study: colored paved markings and raised island. The first is a bicycle crossroad provided with a red pavement and its aim is to highlight the presence of the crossroads and focus the attention of the approaching vehicles on it, contributing to the speed reduction [

The survival analysis is based on a probabilistic method which is used to analyze data in the form of time from a well-defined time origin until the occurrence of some particular event of an end point [

In this study, the speed reduction time (SRT) is the duration variable.

The speed reduction time is a continuous random variable T whose

The accelerated failure time (AFT) model was used to model SRT. The AFT model is a parametric approach that allows incorporating the influence of covariates on a hazard function. More specifically, it allows the covariates to accelerate time in a baseline survivor function, which is the survivor function when all covariates are zero [

The AFT assumption allows a simple interpretation of results because the estimated parameters quantify the corresponding effect of a covariate on the mean survival time [

In the AFT model, the natural logarithm of the duration variables, ln

where

which leads to the conditional hazard function

where _{0} are the baseline hazard and the baseline survival function, respectively.

Equations (

To estimate the hazard and the survival function in a fully parametric setting, a distribution assumption of the duration variable is needed. Common distribution alternatives include Weibull, lognormal, exponential, gamma, log-logistic, and Gompertz distribution [

This study was conducted by the use of the interactive fixed-base driving simulator of the Department of Engineering, Roma Tre University. It was previously tested, calibrated, and validated for speed research on two-lane rural roads [

The hardware interfaces (wheel, pedals, and gear lever) are installed on a real vehicle. The driving scene is projected onto three screens: one in front of the vehicle and one on either side, which provide a 135° field of view. The resolution of the visual scene is 1024x768 pixels with a refresh rate of 30 to 60 Hz. The system is also equipped with a sound system that reproduces the sounds of the engine.

The experimental road scenario was a two-lane suburban road about 7.6 Km long in which also the cyclist that crosses the road was simulated. Nine bicycle crossroads (3 for each of the 3 types described in the following) were present along the alignment. To ensure the same approaching condition, a signalized intersection was placed in advance of each bicycle crossroad.

Each driver was obligated to stop at the signalized intersection, due to the red light that turned on when the driver was at approximately 100 m from the intersection. The distance between the signalized intersection and bicycle crossroad was equal to 400 m, which allowed the drivers to reach a congruous speed for the simulated scenario. The posted speed limit was 50 Km/h while the cross-section was 10 m wide, formed by two 3.00 m wide lanes, two paved shoulders 0.50 m wide, and two curbs 1.50 m wide, according to the Italian road design guidelines [

(a) Baseline condition; (b) colored paved markings; (c) raised island.

Figure

Bicycle crossroads as seen by drivers during the experiment: (a) baseline condition; (b) colored paved markings; (c) raised island.

At six bicycle crossroads (2 for the baseline condition, 2 for the colored paved markings, and 2 for the raised island) a cyclist coming from driver right side crossed the road. The cyclist was set to start the crossing at 20 m from the collision point when the driver was at 50 m from it. The speed of the cyclist was 20 Km/h. Assuming the driver speed equal to 50 Km/h, in such condition the driver and cyclist have the same time to arrive (3.6 s) to the collision point. It should be noted that this condition is representative of a theoretical driver–cyclist interaction, which occurs only if the driver adopts the hypothesized speed value.

To avoid a potential effect of the order on the driver’s behavior, 3 road scenarios that have a different sequence of the 9 combinations of bicycle crossroad (baseline condition, colored paved markings, and raised island) x cyclist (cyclist absence and two conditions in which the cyclist was crossing the road) were implemented in the driving simulator. The participants were divided into 3 groups and each group was assigned to only one road scenario (see next section on participants). Thus, each group experienced a different presentation sequence of the 9 combinations of crossroad layout x cyclist condition.

For the analysis of the present study, only the conditions in which the cyclist was present were used (6 combinations: 3 countermeasures x 2 cyclist conditions presence).

The driver did not experience interaction with other vehicles in their driving lane. On the opposing lane, a slight amount of traffic was present to induce the driver not to drift to the incoming traffic lane. The simulated vehicle was a standard medium-class car with automatic gears. The data recording system acquired all of the parameters at spatial intervals of 2 m. The experiment procedure consisted of the following steps: (a) communicating to the driver about the duration of the driving and the use of the simulated vehicle tools; (b) training at the driving simulator on a specific alignment with a length of approximately 5 Km to become familiar with the steering wheel, accelerator, and brake pedal; (c) filling in a form with personal data, years of driving experience, and average annual distance driven; (d) driving one of the three road scenarios with a specific bicycle crossroads-cyclist sequence; (e) filling in a questionnaire about the discomfort that is perceived during driving, to eliminate from the sample driving performed under anomalous conditions. This questionnaire consisted of 5 questions, in which each question addressed a type of discomfort: nausea, giddiness, daze, fatigue, and other. A score from 1 to 4 in proportion to the level of discomfort experienced could be selected: null, light, medium, and high. The null and light level for all four types of discomfort are considered to be the acceptable condition for driving; (f) filling in a questionnaire about how the driver perceived the countermeasures. For this question, the participant could choose between (a) driving aid and (b) obstacle; for each of them, the driver could answer by a score from 0 to 3 in proportion to the perceived effectiveness. Drivers were instructed to drive as they normally would in the real world.

Forty-two drivers (24 men and 18 women), whose ages ranged from 24 to 59 (mean = 29.3; SD = 8.5) and who had regular European driving licenses for at least three years (mean = 11.0; SD = 8.0), were selected to perform the driving in the simulator. The participants were chosen from students, faculty, and staff of the University and volunteers from outside of the University. The drivers had no prior experience with the driving simulator and had an average annual driven distance of at least 2500 km. According to the questionnaire on perceived discomfort, no participant was excluded from the analysis due to the perceived discomfort. Thus, the sample used for the analysis consisted of all 42 drivers, which were divided into 3 groups; the 3 groups drove different scenarios, which were characterized by a specific sequence of bicycle crossroad/cyclist.

To obtain the explanatory variables of the driver behavior, for each participant and for each configuration of the bicycle crossroad, the speed profile of the last 150 m in advance of the bicycle crossroad was plotted. Overall, 252 speed profiles were obtained from the driving tests (42 participants x 6 bicycle crossroads). The following variables were determined from each speed profile:

SRT: speed reduction time, which is the elapsed time to pass from the initial speed to the minimum speed.

Table

Descriptive statistics of drivers’ speed profiles variables.

Countermeasure | No of driver-cyclist interactions | | | | | ^{2}] | SRT [s] | No of failed | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

mean | SD | mean | SD | mean | SD | mean | SD | mean | SD | mean | SD | |||

| 72 | 11.88 | 3.02 | 40.23 | 10.39 | 4.76 | 3.2 | 20.64 | 9.91 | 2.75 | 1.56 | 2.15 | 1.04 | 12 |

| ||||||||||||||

| 79 | 11.79 | 2.71 | 41.47 | 11.33 | 4.89 | 3.05 | 20.84 | 11.23 | 2.64 | 1.69 | 2.38 | 1.06 | 5 |

| ||||||||||||||

| 78 | 11.39 | 2.63 | 45.69 | 10.25 | 4.88 | 2.82 | 26.07 | 10.93 | 2.58 | 1.57 | 2.77 | 1.03 | 6 |

| ||||||||||||||

| |

Thus, a total of 229 observations of the driver braking behavior were used for the analysis.

For a reliable modeling of the speed reduction time, a Pearson's product-moment correlation (PPMC) analysis was performed (Table

Results of Pearson’s product-moment correlation analysis.

Variable | | | | | | driver’s age | driver’s gender |
---|---|---|---|---|---|---|---|

| - | ||||||

| - 0.254 | - | |||||

| 0.290 | 0.213 | - | ||||

| - 0.474 | 0.822 | - 0.044 | - | |||

| - 0.429 | 0.393 | 0.407 | 0.230 | - | ||

driver’s age | - 0.057 | 0.013 | 0.908 | 0.013 | - 0.059 | - | |

driver’s gender | -0.003 | 0.022 | 0.240 | -0.017 | 0.068 | - 0.119 | - |

The outcomes of the PPMC analysis are reported too. The analysis showed that there were a moderate positive correlation between

Finally, there was a strong positive correlation between

Therefore, considering the outcomes of the PPMC analysis, only the dynamic variable average deceleration

Finally, the PPMC analysis showed that there was no correlation between the average deceleration and the drivers’ age, r (227) = -0.059, p>0.10 and the drivers’ gender, r (227) = 0.068, p>0.10.

Therefore, to model the drivers’ speed reduction time, the continuous variables, driver’s average deceleration (mean value and standard deviation were 2.67 m/s^{2} and 1.60 m/s^{2}, respectively), drivers’ age (mean value was equal to 29.3 years and the standard deviation was 8.5 years), and the categorical or indicator variables countermeasure and drivers’ gender, were used.

The distribution of the survival function was selected comparing AIC (Akaike information criterion) and BIC (Bayesian information criterion). Table

Summary of information criteria results.

Survival function distribution | AIC | BIC |
---|---|---|

| 222.07 | 245.63 |

| ||

| 284.51 | 311.44 |

| ||

| Convergence not achieved | Convergence not achieved |

| ||

| 244.54 | 271.46 |

| ||

| Convergence not achieved | Convergence not achieved |

Considering the values of AIC and BIC, the distribution for the selected survival function to model the SRT was the Weibull function.

The hazard function of the Weibull duration model is expressed as

and the survival function of the Weibull duration model is expressed as

where

The location parameter, with the introduction of explanatory variables, has the following expression:

where each

The exponential value of each explanatory variable coefficient

In addition, three models based on the Weibull distribution were also tested with different combination of the independent variables and compared with the information criteria. In the table (Table

Summary of information criteria comparison of three Weibull regression models.

Model | Independent variables | AIC | BIC | Log – Likelihood (LL) |
---|---|---|---|---|

| Countermeasure | 225.39 | 245.98 | -106.63 |

| ||||

| Countermeasure | 227.25 | 250.83 | -106.64 |

| ||||

| Countermeasure | 222.07 | 245.63 | -104.04 |

Table

The application of the duration model as specified in Section

The first model fits the standard duration model and then adjusts the standard error estimates to account for the possible correlations induced by the repeated observations within individuals [

Weibull regression model with shared frailty allows taking into account the correlation among observations obtained from the same driver and maintains independence among observations across different drivers.

The shared frailty model can be expressed by modifying the conditional hazard function (see (

where_{ij} is the hazard function for the _{i} is the shared frailty, which is assumed to be gamma or inverse-Gaussian distributed, with mean 1 and variance

Weibull regression model with clustered heterogeneity and Weibull regression model with shared frailty were then compared by the likelihood ratio statistics [

The development of the Weibull accelerated failure time (AFT) for the speed reduction times (SRT) was carried out using the statistical software STATA version 14.1. After the selection of the best fit distribution and the significant independent variables, the Weibull AFT model with clustered heterogeneity and the Weibull AFT model with shared frailty were tested. The frailty was gamma-distributed. The two models were compared with their likelihood ratio statistics and with the AIC and BIC tests. The likelihood ratio statistic of the Weibull AFT model with clustered heterogeneity was -104.04 while that for the shared frailty model was -104.54, highlighting that the first was preferable. The AIC and BIC tests also confirmed the better fit of the model; for the clustered heterogeneity model and for the shared frailty model the AICs were 222.07 and 223.08, while BICs were 245.63 and 246.65, respectively. Thus, comparing the likelihood ratio statistics, AIC and BIC, the Weibull AFT model with clustered heterogeneity was the preferable option for modeling the speed reduction times of the drivers in response to a cyclist that is crossing at the bicycle crossroad, under different conditions of safety measures.

Table ^{3166-1}). The scale parameter P higher than 1 implies that the hazard function of the speed reduction times was monotone and with positive duration dependence; this is consistent with the hypothesis of the applied model.

Estimates of the Weibull AFT model with clustered heterogeneity for SRT.

Variable | Estimate | SE | z - Statistic | p-value | Exp ( | 95% Conf. Interval | |
---|---|---|---|---|---|---|---|

^{2}] | -0.142 | 0.018 | -7.85 | 0.000 | 0.867 | -0.176 | -0.107 |

Drivers’ age [years] | 0.006 | 0.003 | -2.15 | 0.031 | 1.006 | 0.001 | 0.012 |

Countermeasure | |||||||

| - | - | - | - | - | - | - |

| 0.052 | 0.061 | 0.85 | 0.349 | 1.053 | -0.067 | 0.171 |

| 0.211 | 0.059 | 3.53 | 0.000 | 1.235 | 0.094 | 0.328 |

Constant | 1.432 | 0.127 | 11.30 | 0.000 | 1.184 | 1.681 | |

P | 3.166 | 0.307 | 2.618 | 3.829 | |||

| |||||||

Log–likelihood at convergence (Pseudo) | -104.04 | ||||||

Log–likelihood at zero | -138.11 | ||||||

AIC | 222.07 | ||||||

BIC | 245.63 | ||||||

No of observations | 229 | ||||||

No of groups | 42 |

The model identified that the driver average deceleration (^{2} increase of the driver’s average deceleration, the time required to complete the yielding maneuver was approximately 13% lower

Among the countermeasure conditions, the model identified significant coefficient estimates for the colored paved markings (P= 0.000) while for the raised island the effect on the survival model was not statistically significant (P=0.349). For the coefficient estimate of the baseline condition the model did not provide a coefficient estimate, because this condition was set by the model as the reference one.

The pairwise comparison with Bonferroni’s correction showed that, for the baseline condition and the raised island, the values of SRT (equal to 4.76 and 5.01s for null survival probability, respectively) were statistically significantly shorter than that for the colored paved markings (5.88 s; mean difference = 1.12s, P=0.001; mean difference = 0.87s, P=0.006, respectively). More specifically, for the colored paved markings, the SRT was 23.5% longer than that for the baseline condition

The use of the Weibull AFT model with clustered heterogeneity allowed a comparison of the driver’s speed reduction time for the yielding maneuver, under different configurations of the bicycle crossroad. The representation of the drivers’ speed reduction patterns was possible by plotting the survival curves with the use of the estimated coefficients of the average deceleration and the countermeasures condition.

The estimation of the survival curves was provided by (^{2}), drivers’ age (29.3 years), and the estimated coefficients of the average deceleration, driver’s age, and countermeasure conditions in Table

Using this method, the survival curve for each countermeasure (baseline condition, raised island, and colored paved markings) was plotted (Figure

Survival curves of SRT.

The results of the questionnaire showed that 71% of the drivers (30 of 42) reported the highest score of “driving aid” for the colored paved markings, while only 19% of the drivers (8 of 42) reported the same score of “driving aid” for the raised island. For the baseline condition, the highest score of “driving aid” was reported by 40% of the drivers (17 of 42). Consistently with this outcome, 79% (33 of 42) of the drivers reported the lower score of the “obstacle driving effect” for the colored paved markings, while only 31% (13 of 42) of the drivers reported the lower score of the “obstacle driving effect” for the raised island. For the baseline condition, the lower score of the “obstacle driving effect” was reported by 76% of drivers (32 of 42).

As expected, the survival probability for the speed reduction time during the yielding maneuver in response to a cyclist that is crossing decreases with the elapsed time (Figure

The survival curves for different countermeasure conditions show that, for a fixed value of the elapsed time, the higher survival probability of SRT was obtained for the colored paved markings while the lower survival probability of SRT was obtained for the baseline condition. For example, after 2.5 seconds, the speed reduction time survival probability for colored paved markings was about 56%, while for raised island and the baseline condition it was approximately 39% and 33%, respectively.

The event duration, that is, the speed reduction time (obtained for null value of the survival probability), was 5.88s for the colored paved markings, while it was 1.12 s shorter (statistically significant) for the baseline condition (4.76s) and 0.86s shorter (statistically significant) for the raised island (5.02s).

Overall, the outcomes of the Weibull AFT model highlight that when the bicycle crossing was reorganized with the colored paved markings, the driver adopted more time to complete the braking maneuver.

It should be noted that speed reduction time values represent different times of yielding maneuvers in response to a cyclist that is crossing the road. This means that longer values of the speed reduction times are linked to smoother yielding maneuver. The results of the Weibull AFT model showed that, for the colored paved markings, the longer time to pass from the initial speed to the minimum speed was required. This finding suggests that, in this condition of bicycle crossroad, the drivers are able to advance the yielding maneuver and the consequence is that they adopt a less aggressive braking behavior.

This result can reasonably be due to a better visibility of the bicycle crossing, which effectively gained the driver’s attention allowing him to adopt a less abrupt maneuver. This aim is consistent with previous results of Bella and Silvestri [

Consistently with the improvement of the driver performance, also an increase of the trend of the yielding behavior was recorded for the colored paved markings. For this countermeasure, the driver did not yield in 7.1% (6 of 84) of the interactions with the cyclist, while for the baseline condition the failed yielding rate was the 14.3% (12 of 84) (Table

The Weibull AFT showed also a slightly positive effect of the raised island on SRT compared with the baseline condition, but not as effective as that for the colored paved markings.

Finally, the drivers’ SRT was affected in a statistically significant way by the average deceleration

The present study aimed at the investigation of how the reorganization with safety countermeasures of the bicycle crossroads affects the drivers’ braking behavior in response to a cyclist that crosses the road. The safety countermeasures implemented in the driving simulator scenario were the raised island and the colored paved markings. The drivers’ SRT (the elapsed time to pass from the initial speed

The analysis was carried out by the Weibull AFT duration model, which identified the average deceleration

The better visibility of the bicycle crossroad provided by the presence of the colored paving allowed the driver to adopt smoother braking maneuver to yield to the cyclist. It should be also noted that the benefits of a less aggressive brake can lead to a decrease of the probability that a rear-end collision occurs.

The increase of the cyclist safety provided by the colored paved markings was also highlighted by the low number of events in which the driver did not yield compared to that recorded for the baseline condition. Finally, the effectiveness of this countermeasure was also confirmed by the outcomes of the questionnaire, which revealed that 71% of drivers reported the highest score for driving aid when the bicycle crossroad was provided with the colored pavement.

The experiment of the present study was carried out by the use of the driving simulator of the Roma TRE University, Department of Engineering. Therefore, the caveats that usually referred to driving simulator studies must be raised. Among these, the main one referred to the possibility that the driving tests can result in a drivers’ behavior that is different from the actual behavior in the real world.

The driving simulator used in the present study was previously validated for the study of the drivers’ behavior on two-lane rural world [

However, for the objective of the present experiment (comparing the driver performance at bicycle crossroads in the presence of several countermeasures, without the claim to provide valuations in absolute terms of the driver behavior), only the relative validity (which refers to the correspondence between the effects of different variations in the driving situation) is required [

the obtained results in the present study are in line with those recorded in fields studies by Leden et al. [

the recorded data showed that the drivers reacted differently at the different crossroad layouts and cyclist condition, giving reasonable results

In addition, the results based on the drivers’ behavior recorded during the simulations were fully confirmed by the subjective ratings acquired through the questionnaire about the effectiveness of the countermeasures.

In light of this, the obtained results can be considered as reliable in terms of relative effects induced by countermeasures and cyclist condition on the driver’s behavior during the interaction with a cyclist that crosses the road.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This research was financially supported by the Italian Ministry of Education, Research and Universities.