Development of statistical models for improving efficiency of emergency evacuation in areas with vulnerable population

Reliability Engineering and System Safety 182 (2019) 233–249

Contents lists available at ScienceDirect

Reliability Engineering and System Safety journal homepage: www.elsevier.com/locate/ress

Development of statistical models for improving efficiency of emergency evacuation in areas with vulnerable population

T

Maxim A. Dulebenetsa, , Olumide F. Abioyeb, Eren Erman Ozguvenc, Ren Mosesd, Walter R. Boote, Thobias Sandof ⁎

a

Department of Civil & Environmental Engineering, Florida A&M University-Florida State University, 2525 Pottsdamer Street, Building A, Suite A124, Tallahassee, FL 32310-6046, USA b Department of Civil & Environmental Engineering, Florida A&M University-Florida State University, 2525 Pottsdamer Street, Building B, Suite B339, Tallahassee, FL 32310-6046, USA c Department of Civil & Environmental Engineering, Florida A&M University-Florida State University, 2525 Pottsdamer Street, Building B, Suite B313, Tallahassee, FL 32310-6046, USA d Department of Civil & Environmental Engineering, Florida A&M University-Florida State University, 2525 Pottsdamer Street, Building A, Suite A129, Tallahassee, FL 32310-6046, USA e Department of Psychology, Florida State University, 1107 W Call St., Suite B432, Tallahassee, FL 32306-4301, USA f School of Engineering, University of North Florida, 1 UNF Drive, Building 50, Suite 2102, Jacksonville, FL 32256, USA

ARTICLE INFO

ABSTRACT

Keywords: Emergency evacuation Evacuation routes Driving ability Driver characteristics Vulnerable population Natural hazard preparedness

Different parts of the world are characterized by frequent occurrences of natural hazards. As such, evacuation planning is an essential part of the natural hazard preparedness, especially in hazard-prone areas. Numerous research efforts have been directed towards improving the efficiency of the evacuation process. However, only a limited number of studies have specifically aimed to identify factors, influencing the driving ability of individuals under emergency evacuation and the occurrence of crashes along the evacuation routes. Furthermore, previous research efforts have focused on a relatively narrow range of factors (primarily driver and traffic flow characteristics). This study aims to fill the existing gap in the state-of-the-art by investigating the effects of a wide range of different factors (including driver characteristics, evacuation route characteristics, driving conditions, and traffic characteristics) on the major driving performance indicators under emergency evacuation. The considered driving performance indicators include travel time, lane deviation, crash occurrence, collision speed, average acceleration pedal pressure, and average braking pedal pressure. A set of statistical models is developed to identify the most significant factors that influence the major driving performance indicators. These models are tested using the data collected from the driving simulator and participants with various socio-demographic characteristics. The results indicate that age, gender, visual disorders, number of lanes, and space headway may substantially impact the driving ability of individuals throughout the emergency evacuation process. Findings from this research can be incorporated within the existing transportation planning models to facilitate the natural hazard preparedness, ensure safety of evacuees, including vulnerable populations, and reduce or even prevent the occurrence of crashes along the evacuation routes.

1. Introduction Natural hazards, such as hurricanes, floods, fires, tornadoes, severe freezes, thunderstorms, earthquakes, and others, occur relatively frequently in different parts of the world. According to the statistical information, provided by the Statistics Portal [1], the top three countries with the highest occurrence of natural hazards in 2015 include China (37 events), the United States of America (22 events), and India (21

events). Natural hazards may cause not only property damage and severe monetary losses but also pose a high risk to human lives. For example, Hurricane Katrina, one of the costliest hazards in the United States (U.S.) history, killed about 1,883 people directly or indirectly and left several million without power [2]. The total damage due to Hurricane Katrina in the U.S. was estimated to be $108 billion [2]. In case of an approaching natural hazard, the government agencies usually announce a mandatory evacuation from the areas, expecting the

Corresponding author. E-mail addresses: [email protected] (M.A. Dulebenets), [email protected] (O.F. Abioye), [email protected] (E.E. Ozguven), [email protected] (R. Moses), [email protected] (W.R. Boot), [email protected] (T. Sando). ⁎

https://doi.org/10.1016/j.ress.2018.09.021 Received 8 April 2018; Received in revised form 23 September 2018; Accepted 28 September 2018 Available online 05 October 2018 0951-8320/ © 2018 Elsevier Ltd. All rights reserved.

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

greatest impact [3–6]. The socio-demographic characteristics of individuals (e.g., age, gender, racial group, health conditions) may substantially affect their driving ability not only under normal driving conditions, but also under disruptive driving conditions (e.g., emergency evacuation). Significant perceptual and cognitive changes that occur with age may influence the driving performance of older adults (aged 65+) throughout the evacuation process [7]. The driving ability of an aging population is affected by changes in vision and visual disorders, hearing impairment, changes in attention and inhibition, reduced speed of processing, and slower response times. The effects of those perceptual and cognitive changes on the driving ability of an aging population can be drastically magnified under emergency evacuation [3,8]. The latter may further lead to some negative externalities, including headache, discomfort, heart attack, crashes on the evacuation routes, and others. It has been observed that during disruptive driving conditions (including emergency evacuation) many evacuees drive faster, more aggressively, and with smaller headways [9,10]. This bumper-to-bumper driving condition coupled with the stress, experienced by evacuees belonging to vulnerable population, significantly increases the odds of having a crash. Usually, it takes more time to respond to crashes during emergency evacuation due to a very dense traffic flow along the evacuation routes. A crash at the evacuation route may block one or several lanes, which will further result in congestion, significantly delay the evacuation process, and may ultimately result in casualties (i.e., injuries and/or fatalities as a result of a crash; injuries and/or fatalities, caused by a natural hazard in case if certain population groups were not able to evacuate in a timely manner). An increasing frequency of natural hazards and the aftermath underscore the need for efficient hazard preparedness to ensure organized and timely evacuation. Moreover, the emergency evacuation plans have to consider presence of older adults and other vulnerable population groups, which is expected to significantly increase in future [11]. In order to achieve the latter objectives, this study proposes a set of statistical models that will assist decision-makers with understanding the major factors that affect the evacuation process, including driver characteristics (e.g., age, gender, racial group, driving experience, marital status, health condition, etc.), evacuation route characteristics (number of travel lanes), driving conditions (time of the day, day of the week), and traffic characteristics (space headway, time headway). The required data are collected using the driving simulator and realistic emergency evacuation scenarios. Findings, revealed using the developed statistical models, can be incorporated within the existing transportation planning models to facilitate the natural hazard preparedness, ensure safety of evacuees, including vulnerable populations, and reduce or even prevent the occurrence of crashes along the evacuation routes. The remainder of the manuscript is structured as follows. The next section presents a state-of-the-art review of the literature, focusing on driving simulator studies and statistical models for crash analysis. The third section describes the methodology, which was adopted to collect the data, required for the development of statistical models. The fourth section presents the statistical models, which were developed for estimating various driving performance indicators during emergency evacuation, and discusses the approach, which was used to evaluate the statistical models. The fifth section describes the results, which were revealed using the developed statistical models, and outlines the major factors that may influence various driving performance indicators during emergency evacuation. The last section provides concluding remarks and outlines future research directions.

major concerns because of the resulting traffic breakdown they may cause. Due to limited availability of the traffic data during evacuation events, certain studies used driving simulators to develop scenarios that emulate the evacuation process and collect the data on driver behavior and crashes. In order to effectively capture previous research efforts, the literature review presented herein will focus on the following major aspects: (1) driving simulator studies; and (2) statistical models for crash analysis. A review of the collected studies, classified by the major aspects considered, is presented in the following sections of the manuscript. 2.1. Driving simulator studies Several studies used a driving simulator to assess the effects of various driver characteristics on safety-related performance indicators under normal driving conditions. For example, Bella et al. [12] used a driving simulator in their study and developed the linear regression model for predicting the effects of driver characteristics (such as age, gender, and driving experience), roadway characteristics, time of the day, and day of the week on the speed selected by drivers. The results demonstrated that visibility conditions, curve radius, and curve tangent length significantly affected the travel speed. Casutt et al. [13] examined the cognitive and on-road driving performance of elderly drivers using a driving simulator. They investigated the effects of age, gender, driving experience, medical condition, and road type (such as urban or rural) on the driver performance on-road versus in the simulator. It was found that behavior of the drivers during the simulation experiment was similar to their on-road driving behavior and cognitive performance. Furthermore, the study highlighted that the proposed methodology could be used for training unsafe older drivers to improve their driving skills and ensure safety on the roadways. Tuokko et al. [14] aimed to identify the driver characteristics, which could affect safety of drivers on the roadways. Using a driving simulator, they studied how driver characteristics (such as age, gender, health status, etc.) could influence the driving ability by time of the day. The analysis was conducted using the hierarchical regression model. It was found that age, among other factors, significantly affected the driving ability of individuals. Jurecki [15] conducted a study to determine various parameters, characterizing the driving performance, with a primary focus on the driver response time to simulated nearcollision events. The performance indicators, considered in that study, included the braking response time, the steering response time, the intensity of maneuvers, and others. The results showed a positive correlation between the driver response time and the time-to-collision. A number of other studies also modeled traffic flow and driver behavior under normal driving conditions using driving simulators [16–27]. Certain studies deployed driving simulators to investigate the effects of various factors on the performance of drivers during emergency evacuation. Xu et al. [28] studied the differences in driving characteristics between normal and emergency driving conditions and developed a car-following model, capturing emergency evacuation. A back-propagation neural network was simulated based on the data, collected from the driving simulator. The perception-reaction time (PRT) and the critical headway were used as the performance indicators. The analysis demonstrated that PRT followed a normal distribution under both normal and emergency situations. However, the PRT under the emergency situation was lower as compared to a normal situation. Hoogendoorn et al. [10] conducted a driving simulator experiment to assess the effects of longitudinal driving behavior, such as speed, acceleration, and spacing, on the traffic flow patterns. The authors showed that longitudinal driver behavior was adaptive during the emergency situation, and led to increasing capacity. However, the study suggested that future research should investigate the effects of static driver characteristics (such as age, gender, driving experience, health condition, etc.) on the driving ability, as it might affect the theoretical approach adopted. Hoogendoorn et al. [29,30] focused on modeling the

2. Literature review A number of studies investigated behavior of drivers and effects of various driver and roadway characteristics on the efficiency of emergency evacuation. Crashes during emergency evacuation are one of the 234

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

impact of emergency evacuation on traffic flow and driver behavior. Using a driving simulator, the study showed that emergency evacuation led to significant changes in speed, acceleration, and headway. Underwood et al. [31] deployed a driving simulator in order to assess how driving experience of individuals affected their ability to detect roadway hazards during disruptive driving conditions. The authors considered two types of hazard events, which include: (a) abruptonset hazards (i.e., sudden events); and (b) gradual-onset hazards (i.e., gradual events). The results demonstrated that, for gradual on-set hazards, driving experience significantly influenced hazard detection rates. Specifically, experienced drivers detected gradual-onset hazards faster. However, driving experience of individuals did not substantially impact the detection rates of abrupt-onset hazards. Ali et al. [32] examined the mandatory lane-changing behavior of individuals under disruptive driving conditions using a driving simulator. Regression models were developed to analyze various performance indicators. The results suggested that drivers might increase their initial speed, reject fewer gaps, and select relatively bigger gap sizes when a mandatory lane-change is required.

regression models that examined the effects of roadway geometric characteristics, weather, time of the day, environmental conditions, vehicle characteristics, pavement condition, and crash type on severity of crashes along the roadways over a period of nine years. The analysis results indicated that, although the data shared common features, the model parameters were not stable due to a considerable variation in crash trends over the considered time period. Moreover, snowy weather was found to be a statistically significant factor, influencing the crash occurrence and severity. Generally, inclement weather significantly reduces the operating speed [47] and capacity of roadways and also increases the risk of crash occurrence. Ulak et al. [48] focused on a spatial investigation of the crashes, involving older adults, in the Northwest Florida. A logistic-regression based approach was adopted to identify statistically significant factors that influenced the crash occurrence. The analysis results highlighted a strong correlation among the spatial allocation of aging populations and crash locations. 2.3. Contribution A detailed analysis of the collected literature indicates that many studies focused on modeling various driving performance indicators (e.g., anger, driving speed, reaction time, crash risk) using different methodologies, which include driving simulation, regression models, statistical analyses [10,13,29,30,33,35,43]. However, none of the conducted studies explicitly accounted for a wide range of different factors (including driver characteristics, evacuation route characteristics, driving conditions, and traffic characteristics) and the effects of those factors on the crash occurrence and other important driving performance indicators during emergency evacuation. In order to address the latter drawbacks, this study aims to develop a set of statistical models for assessing the effects of the aforementioned characteristics on the driving ability of individuals under emergency evacuation and the odds of having a crash. The required data will be collected using the driving simulator and realistic emergency evacuation scenarios. Findings from this study are expected to facilitate the natural hazard preparedness, ensure safety of evacuees, including vulnerable population groups, and reduce or even prevent the occurrence of crashes along the evacuation routes.

2.2. Statistical models for crash analysis Historically, investigation of crashes on roadways has received a lot of attention from researchers, although only a few studies have attempted to model crashes during emergency evacuation. Many studies relied on different statistical models to analyze the roadway crashes and identify the factors, which could cause the occurrence of those crashes. Note that this section of the manuscript presents some of the statistical models, which are commonly used for the roadway safety improvements and related to the theme of this research (e.g., models used for analysis of crashes that involve older adults; assessing the effects of driver, traffic flow, and roadway geometric characteristics on the crash occurrence), and discusses the relevant studies. For a more detailed review of the statistical models, applied in the crash analysis, this study refers to Lord and Mannering [33]. Coxon et al. [34] explored the factors that could influence the crash severity of older drivers using the generalized linear regression model. Findings indicated that age, health status, residency (rural or urban), driving frequency, and distance driven per week significantly affected the crash severity. Using the Poisson regression model, Huisingh et al. [35] showed that severe impairment in vision and useful field of view increased the rate of near crash involvement for older drivers. Moreover, visual disorders, such as impaired contrast sensitivity and far peripheral field loss in both eyes, were significant factors that influenced the occurrence of severe crashes and at-fault involvement among vulnerable individuals at the 95% confidence interval. Several studies attempted to capture the effects of traffic and roadway geometric characteristics on the collision severity. The effects of the roadway geometric factors, weather, and traffic conditions on the crash severity were modeled by Wang et al. [36] using the logit regression approach. It was found that minimum curve radius and the number of horizontal curves at the roadway influenced crash severity. The need for adequate design of horizontal curves on the roadways in order to reduce crashes was emphasized by Malyshkina and Mannering [37]. The Annual Average Daily Traffic (AADT) was identified as a significant factor that could increase the likelihood of multi-vehicle crashes [38]. Barua et al. [39] studied the correlation between spatial characteristics (such as the number of lanes, lane width, land use, etc.) and crash severity using the Poisson lognormal regression model. Other researchers have also modeled crash frequency by considering the effects of roadway geometric factors in their models [40,41]. The negative binomial regression model has been adopted by some researchers in modeling the effects of roadway and traffic characteristics on the crash occurrence [42,43] and crash frequency [44]. Also, the negative binomial regression model has been used to identify the driver and roadway geometric characteristics, affecting the crash frequency [37,45]. Behnood and Mannering [46] presented mixed logit

3. Methodology This section of the manuscript focuses on description of the methodology, adopted in this study for assessing the effects of major factors on the driving ability of individuals under emergency evacuation, developed emergency evacuation scenarios, and data collection. 3.1. Driving simulator The driving simulator was used in this study to model the emergency evacuation scenarios and collect necessary data (see Fig. 1). The simulator is a CDS250 model, manufactured by Drive Safety Company [49] in the U.S. This advanced driving simulator is a partial cabin of a Ford Focus sedan with an automatic transmission. The apparatus is equipped with an entertainment console (a functional radio/CD and MP3 player input) and standard automotive driver controls, which include a starter lock, accelerator and brake pedals, steering wheel, ignition, gear shift, wiper control switch, tachometer, speedometer, turn signals, and headlights. The simulated environment visual display is projected through three screens positioned in front of the driver, which offers a 110° field of view in the horizontal direction. Furthermore, the driving simulator has wide-angle mirrors with high-resolution (retina-limited) visual displays of 1040 × 1050 pixels, which provide real-time rear and side views. The simulator also offers a three-dimensional sound system, which produces tire and car engine noises. The simulator is connected to four network workstations, which manage input and output interface, audio, and graphics using the Drive Safety Hyper Drive software [49]. 235

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Fig. 1. The driving simulator.

3.2. Pilot study

asked to rate their medical condition, vision, and hearing using the following options: “poor”, “fair”, “good”, “very”, and “excellent”. Along with the latter health-related characteristics, the participants were requested to specify whether they had any visual disorders or chronic diseases. The driving ability of pilot study participants was assessed in terms of the following aspects: (1) ability to see road signs at a distance; (2) ability to see the speedometer and controls; (3) ability to avoid hitting curbs and medians; (4) ability to see vehicles coming up beside; (5) ability to move foot quickly from the gas to the brake pedal; (6) ability to make an over-the-shoulder check; (7) ability to make quick driving decisions; (8) ability to drive safely (avoid accidents); and (9) ability to react to a blowing horn from an approaching car. A detailed description of the socio-demographic data, which were collected from the pilot study participants, is provided in Appendix A.

A pilot study was conducted in order to collect necessary data using the driving simulator. The pilot study participants were recruited via leaflets and e-mail announcements. A monetary incentive of $25.00 was offered for each pilot study participant. A total of 115 drivers, residing in Tallahassee, the capital city of the State of Florida (USA), participated in the pilot study. Prior to the driving simulation experiments, all the participants were requested to complete the questionnaire, which aimed to gather the following information: (1) general information (such as age, gender, level of education, occupational status, marital status, income, and racial group); (2) driving experience under normal conditions (such as number of years of driving experience, driving frequency, and average distance driven per week); (3) driving experience under emergency evacuation; (4) health-related questions; (5) driving ability; and (6) experience driving the simulator (such as number of times the participants had driven a simulator before they took the pilot study experiments). The information, collected from the pilot study participants, was stored on a password-protected computer. In order to assess the driving experience under emergency evacuation, all the participants were requested to specify the number of times they had driven under emergency evacuation in the past. Also, the participants were asked to indicate (provide a yes/no response) whether they encountered any difficulties throughout emergency evacuation in the past, such as aggressive behavior of other drivers, causing collisions or near-collision events, traffic congestion, blockage of traffic lanes by fallen trees, and others. Moreover, all the pilot study participants were requested to indicate (provide a yes/no response) whether additional visual/technological evacuation aids were provided throughout emergency evacuation. One of the critical steps in the pilot study was to collect the information regarding the health-related characteristics of the pilot study participants. The participants were

3.3. Simulator experiments Three driving simulation scenarios were designed in this study using the driving simulator Drive Safety Hyper Drive software [49], including the following: (1) test drive scenario; (2) four-lane freeway evacuation scenario; and (3) six-lane freeway evacuation scenario. The driving simulation experiments were conducted between 9:00 a.m. and 5:00 p.m. daily. The time of the day and day of the week, when each pilot study participant was taking the driving simulation experiments, were recorded and further used as predictors in the development of statistical models (as discussed in Section 4.1.2 of the manuscript). Upon completion of the questionnaire, the purpose and requirements of the study, outlined in the consent form, were explained to the participants in details. All the participants were requested to read and sign the consent form. A copy of the signed consent form was stored on a passwordprotected computer, and the original was given to the participant. After signing the consent form, the pilot study participants were requested to 236

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

sit in the driving simulator and adjust the seat to ensure that they are comfortable. The driving simulator and its features were described for each participant. The participants were advised to indicate if they became nauseous or felt they couldn't complete the driving simulation experiments, so that the experiments could be stopped immediately. Also, the participants were advised to take a 10 min break, have light snacks, water, or soda between the driving simulation experiments to ensure that the participants remain comfortable and prevent any potential simulator sickness (i.e., when a participant starts experiencing a headache or becomes nauseous as a result of using the driving simulator). Before conducting the emergency evacuation experiments (which were used to collect the data, required for the development of statistical models), each participant was requested to complete a test drive. A test drive scenario, which lasted approximately 5 min, was developed to allow the participants become familiar with the driving simulation environment. The test drive was designed to enable the participants exercise the basic driving maneuvers, such as straight driving, acceleration, deceleration, complete stops, visualize the approaching vehicles using the available mirrors, and other driving skills. Upon completion of the test drive scenario, the pilot study participants were expected to complete two emergency evacuation scenarios, including the following:

65 mph and traffic density of 31 pc/mi/ln (passenger cars per mile per lane). The travel speed of vehicles was assumed to be uniformly distributed between 60 mph and 70 mph. Such travel speeds, which are close to the posted speed limit, are generally observed at early stages of emergency evacuation. Lower travel speeds are typically common at later stages of emergency evacuation due to increasing number of evacuees. Modeling traffic congestion along the evacuation routes is not included in the scope of this study and will be one of the future research directions. The traffic stream was composed of various types of vehicles, including cars, minivans, trucks, buses, and bikes. The vegetation was placed to make the evacuation scenarios more realistic. The vegetation was located at least 12 ft from the freeway shoulder for both evacuation scenarios. Additional triggers were inserted per mile for both evacuation scenarios, which caused the vehicle in front of the participant to brake suddenly. The purpose of introducing additional triggers was to determine how the participants would respond to sudden vehicle movements under emergency evacuation and avoid potential crashes with suddenly braking vehicles. Sudden vehicle movements and aggressive behavior of drivers have been frequently observed throughout the emergency evacuation process [9,10]. Note that the developed scenarios differ primarily by the number of travel lanes, while the rest of geometric and traffic characteristics remained the same (e.g., lane width, shoulder width, traffic density, travel speed of vehicles, etc.). The latter assumption can be justified by the fact that many of the published to date studies, relevant to this research, underlined that the number of lanes was the main roadway geometric feature, affecting the driving performance of individuals. Assessing the effects from altering the other geometric and traffic characteristics would necessitate development of additional scenarios. Each participant required approximately one hour to complete the test drive scenario and two emergency evacuation scenarios (including the time required for the basic instructions and completion of the questionnaire), and introduction of additional scenarios would significantly increase duration of the experiments. Increasing duration of experiments beyond one hour is not desirable, as the participants may start experiencing fatigue, which would negatively affect accuracy of the collected data. Moreover, as indicated in Appendix A of the manuscript, many individuals, participating in the pilot study, were aging adults, who are generally sensitive to the driving simulation environment and may develop simulator sickness due to increasing duration of the experiments. Development of additional emergency evacuation scenarios (which capture different evacuation route geometric and traffic characteristics) and organization of another pilot study will be one of the future research directions. Upon completion of each evacuation scenario, additional data were retrieved from the driving simulator, including the following: (1) duration of the experiment – the total travel time along the evacuation route (min); (2) lane deviation – the standard deviation of the vehicle

• Four-lane freeway evacuation segment: A straight 10 mile segment •

with level terrain, two lanes in each direction, 12 ft lanes, and 11 ft shoulders. Six-lane freeway evacuation segment: A straight 10 mile segment with level terrain, three lanes in each direction, 12 ft lanes, and 11 ft shoulders.

Before the beginning of the emergency evacuation experiments, the participants were instructed to imagine that there was an approaching natural hazard, and they were required to evacuate as quickly as possible. Also, the participants were warned that other vehicles, traveling along the evacuation route, might suddenly brake or start changing lanes. The emergency evacuation scenarios were alternated for the participants throughout the experiments. For example, participant A would take the four-lane freeway evacuation segment scenario for experiment 1, and the six-lane freeway evacuation segment scenario for experiment 2. Then, participant B would take the six-lane freeway evacuation segment scenario for experiment 1, and the four-lane freeway evacuation segment scenario for experiment 2. Such change in the scenario sequence was implemented throughout the experiments to eliminate potential practice and carryover effects. The driving simulation environment, emulated by the Drive Safety Hyper Drive software for both scenarios, is illustrated in Fig. 2. The design level of service (LOS) was set to “LOS D” with a speed limit of

Fig. 2. The Drive Safety Hyper Drive software simulation environment. 237

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

position across the lane (ft); (3) number of crashes – the total number of collisions with the other vehicles during the experiment (number of crashes); (4) collision speed – the travel speed of the vehicle at the moment of collision (mph); (5) average space headway – the average distance between the front bumper of the participant's vehicle and the rear bumper of the vehicle ahead throughout the experiment (ft); (6) average time headway – the average time between the participant's vehicle and the vehicle ahead throughout the experiment (s); (7) average acceleration pedal pressure – the normalized value, varying between 0.00 and 1.00, that shows the average degree of depression for the acceleration pedal during the experiment (0.00 – refers to the case when the acceleration pedal is not being depressed; 1.00 – refers to the case when the acceleration pedal is being depressed at the maximum); and (8) average braking pedal pressure – the normalized value, varying between 0.00 and 1.00, that shows the average degree of depression for the braking pedal during the experiment (0.00 – refers to the case when the braking pedal is not being depressed; 1.00 – refers to the case when the braking pedal is being depressed at the maximum). Note that the adopted driving simulator recorded ≈ 30 observations per second for space headway, time headway, acceleration pedal pressure, and braking pedal pressure (i.e., an observation for each one of the aforementioned indicators was transmitted every ≈ 1/30 of a second) for each participant and each driving simulation experiment. Such a high frequency of transmitting the data allowed estimating the driving performance indicators using the driving simulator with a high degree of accuracy. The data collected throughout the pilot study, including the driver characteristics (e.g., age, gender, level of education, occupational status, marital status, income, driving experience under normal and disruptive conditions), evacuation route characteristics (number of travel lanes), driving conditions (time of the day, day of the week), traffic characteristics (space headway, time headway), and driving performance indicators (e.g., travel time, lane deviation, crash occurrence, collision speed, average acceleration pedal pressure, and average braking pedal pressure) will serve as a foundation for the development of statistical models in this study.

insights regarding the driving ability of individuals under emergency evacuation and assess the factors, which may influence the occurrence of crashes along the evacuation routes. 4.1.2. Predictors The information for predictors of the statistical models was collected from the questionnaire, which was filled out by the pilot study participants, and retrieved from the driving simulator. The available predictors can be classified into four major groups, including the following: 1) Driver characteristics General information (age, gender, level of education, primary occupational status, marital status, income, racial group). Driving experience under normal conditions (number of years driving, driving frequency, average distance driven per week). Driving experience under emergency evacuation (number of times driven under emergency evacuation, any difficulties experienced during evacuation, presence of additional visual or technological aids during evacuation). Health-related characteristics (overall health rating, vision rating, hearing rating, presence of visual disorders, presence of chronic diseases). Driving ability (ability to see road signs at a distance, ability to see the speedometer and controls, ability to avoid hitting curbs and medians, ability to see vehicles coming up beside, ability to move foot quickly from the gas to the brake pedal, ability to make an over-the-shoulder check, ability to make quick driving decisions, ability to drive safely, ability to react to a blowing horn from an approaching car). Experience driving the simulator (number of times driven the simulator before). 2) Evacuation route geometric characteristics Number of lanes. 3) Driving conditions Time of the day. Day of the week. 4) Kinematic data obtained from the driving simulator Average space headway (ft): The average distance between the front bumper of the participant's vehicle and the rear bumper of the vehicle ahead throughout the experiment. Average time headway (s): The average time between the participant's vehicle and the vehicle ahead throughout the experiment. Minimum space headway (ft): The minimum distance between the front bumper of the participant's vehicle and the rear bumper of the vehicle ahead throughout the experiment. Minimum time headway (s): The minimum time between the participant's vehicle and the vehicle ahead throughout the experiment. Maximum space headway (ft): The maximum distance between the front bumper of the participant's vehicle and the rear bumper of the vehicle ahead throughout the experiment. Maximum time headway (s): The maximum time between the participant's vehicle and the vehicle ahead throughout the experiment.

• • • • •

• • • • •

4. Development of statistical models As highlighted in the literature review section of the manuscript, many studies relied on a large variety of regression models and the analysis of variance (ANOVA) approaches for estimation and analysis of various driving performance indicators under normal and disruptive driving conditions. The regression analysis is a statistical procedure, which is used for assessing the relationships that exist between variables. The candidate regression models, which have been frequently used for estimating various driving performance indicators in the stateof-the-art, will be adopted in this study. The following sections of the manuscript present a detailed description of the response variables and predictors that were used in the regression analysis, the candidate regression models that were considered in this study, and the approach that was adopted for evaluation of the statistical models.

• • • • •

4.1. Response variables and predictors 4.1.1. Response variables A total of six response variables (which will serve as driving performance indicators) were used in the development of statistical models, including the following: (1) travel time (min); (2) lane deviation (ft); (3) crash occurrence (number of crashes); (4) collision speed (mph); (5) average acceleration pedal pressure (from 0.00 to 1.00); and (6) average braking pedal pressure (from 0.00 to 1.00). A detailed description of each response variable is provided in Section 3.3 of the manuscript. The values of all six performance indicators were retrieved from the driving simulator using the Drive Safety Hyper Drive software for each participant and each emergency evacuation scenario. The considered response variables are expected to provide important

4.1.3. Predictor combinations A total of 18 predictor combinations were considered in order to develop the statistical models for estimating the response variables, listed in Section 4.1.1 of the manuscript. A detailed description of the predictor combinations is presented in Table 1. Additional two predictor combinations (i.e., predictor combinations 19 and 20, which include travel speed and lane deviation) were considered, when estimating the crash occurrence, as both travel speed and lane deviation may affect the crash occurrence (e.g., individuals, traveling at a higher speed, may have a higher collision likelihood; individuals, switching 238

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Table 1 Predictor combinations used in the statistical models. a/a

Description of the predictor combination

1

All the available predictors described in Section 4.1.2 of the manuscript (driver characteristics, evacuation route geometric characteristics, driving conditions, and kinematic data); Driver characteristics only; General participant information (from driver characteristics) only; Driving experience under normal conditions (from driver characteristics) only; Driving experience under emergency evacuation (from driver characteristics) only; Driving experience under normal conditions and emergency evacuation (i.e., combination of 4 and 5); Health-related characteristics (from driver characteristics) only; Driving ability (from driver characteristics) only; Experience driving the simulator (from driver characteristics) only; Driving experience under normal conditions, driving experience under emergency evacuation, and experience driving the simulator (i.e., combination of 4, 5, and 9); General participant information, driving experience under normal conditions, health-related characteristics (i.e., combination of 3, 4, and 7); Number of lanes (from evacuation route geometric characteristics) only; Time of the day (from driving conditions) only; Day of the week (from driving conditions) only; Time of the day and day of the week (i.e., combination of 13 and 14); Kinematic data only; Average space headway and average time headway (from kinematic data); Minimum space headway and minimum time headway (from kinematic data); All the available predictors described in Section 4.1.2 of the manuscript (driver characteristics, evacuation route geometric characteristics, driving conditions, and kinematic data), and travel speed; All the available predictors described in Section 4.1.2 of the manuscript (driver characteristics, evacuation route geometric characteristics, driving conditions, and kinematic data), travel speed, and lane deviation.

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

lanes frequently, may have a higher collision likelihood).

analysis are presented in Sections 4.3.1–4.3.3 of the manuscript.

4.2. Candidate statistical models

4.3.1. Goodness-of-fit estimation The log-likelihood was used in this study to assess the accuracy of the candidate regression models for both continuous and discrete response variables. The log-likelihood shows how well the parameters of a given regression model fit the available observations. Higher loglikelihood values indicate that the candidate regression model fits the data well and provides an accurate estimation of the response variable based on the considered predictors. Some background information regarding the likelihood and log-likelihood functions is provided next. Let x be a random variable, which has a probability mass function P(x|θ), where θ – is a parameter of the distribution. Denote x1, x2 , …, xn as observations from the given data sample, where n – is the total number of observations. Then, the likelihood function (or joint probability function) can be expressed as follows [60]:

As discussed in Section 2.2 of the manuscript, regression models have been widely used in the literature to estimate the effects of various factors on the driving ability of individuals. Based on the nature of variables (continuous or discrete), various statistical models were adopted in the literature, including linear regression model [13,34,50,51], logit regression model [52–54], hierarchical regression model [55–57], Poisson regression model [39,58], negative binomial regression model [37,44,45], to estimate different driving performance indicators. For this study, the candidate regression models considered were classified in two groups. The first group (group 1) of regression models will be applied for estimating continuous response variables, which include: (1) travel time; (2) lane deviation; (3) collision speed; (4) average acceleration pedal pressure; and (5) average braking pedal pressure. The candidate regression models that will be evaluated for group 1 include: (a) linear regression model; and (b) polynomial regression model. The second group (group 2) will be applied for estimating discrete response variables. Among the considered driving performance indicators, only crash occurrence falls under group 2. The candidate regression models that will be evaluated for group 2 include: (a) linear regression model; (b) logit regression model; (c) hierarchical logit regression model; (d) Poisson regression model; and (e) negative binomial regression model.

P (x1, x2, …, x n | ) = P (x1 | )·P (x2 | ) P (xn | )

(1)

The likelihood function L(θ) can be also re-written as follows: n

L ( ) = P (x1, x2, …, x n | ) =

P (x i | ) i=1

(2)

Based on Eq. (2), the likelihood function L(θ) is estimated as a product of probability mass functions, which can be relatively difficult to calculate. Therefore, the logarithm of the likelihood function or the log-likelihood function LL(θ) is generally used in the statistical analysis for evaluation of regression models. The log-likelihood function can be computed based on the following relationship [60]:

4.3. Evaluation of statistical models

n

The statistical analysis was conducted using MATLAB® 2015b software [59] on a computer, running a Windows 10 operating system. The candidate regression models of group 1 were applied for continuous response variables, while the candidate regression models of group 2 were applied for discrete response variables within the MATLAB environment. The goodness-of-fit of the candidate regression models was assessed based on the accuracy of the models in estimating various driving performance indicators. The backward elimination and correlation analysis were conducted for the regression model with the highest goodness-of-fit for each one of the considered response variables. Details regarding estimation of the goodness-of-fit for the candidate regression models, backward elimination, and correlation

LL ( ) =

log [P (x i | )] i=1

(3)

Additional performance indicators were provided by MATLAB for some of the regression models (and the model predictors), including the following: (1) R2-value (for the model); (2) p-value (for the model and the model predictors); 3) t-statistic (for the model predictors); and (4) deviance (for the model). 4.3.2. Backward elimination The stepwise backward elimination was implemented for the regression model with the highest goodness-of-fit value (i.e., the 239

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Pseudocode 1 Backward elimination (BackwdElim).

Table 2 Descriptive statistics for the considered response variables.

tol tol BackwdElim (X , Y , ppred , pmod )

Response variable

Mean

SD

Variance

Minimum

Maximum

tol in: X - set of predictors; Y - set of response variables; ppred - tolerance on p-values of

Travel time (min) Lane deviation (ft) Crash occurrence (number of crashes)* Collision speed (mph) Average acceleration pedal pressure (from 0 to 1) Average braking pedal pressure (from 0 to 1)

11.00 1.40 1.72

0.95 0.44 2.49

0.90 0.19 6.19

6.18 0.79 0.00

13.22 3.18 14.00

13.91 0.39

17.10 1.41

292.36 1.99

0.00 0.04

111.33 1.00

0.06

0.09

0.01

0.00

0.85

tol - tolerance on p-value of the model the predictors; pmod

out: Xupt - updated set of predictors 0: Xupt ← X ⊲ Initialize the updated set of predictors 1: [ppred, pmod] ← RegModel(Xupt, Y) ⊲ Execute the model with the initial set of predictors max 2: ppred max (ppred ) max tol tol > ppred 3: while ppred and pmod < pmod do

4: i ← argmax(ppred) Xupt 5: Xupt 6: Xupt

Xupt

⊲ Determine the predictor with the highest p-value ⊲ Store a copy of the set of predictors

Notes: SD – standard deviation. ⁎ Note that certain pilot study participants could have several crashes per scenario, which can be explained by the fact that the driving simulator does not stop the experiment after each crash, and a participant is allowed to continue driving after colliding with the other vehicle(s). The validity of the latter assumption can be justified by the fact that minor rear-end and sideswipe collisions (which were the most common types of collision during the driving simulator experiments) are highly unlikely to cause complete vehicle stops, considering the fact that the participants were instructed to evacuate as quickly as possible due to approaching life-threatening hazard.

⊲ Remove predictor i from the set of predictors

{i}

7: [ppred, pmod] ← RegModel(Xupt, Y)⊲ Execute the model with the updated set of predictors max 8: ppred max (ppred ) 9: if pmod 10: Xupt

tol then pmod

Xupt

updated set 11: end if 12: end while 13: return Xupt

⊲ Replace the updated set of predictors with a previously

which has the highest correlation value, would be kept in the model as those predictors are closely related). The regression model for each response variable was re-run after filtering out the closely related predictors, and the final regression model was analyzed to determine the statistically significant factors that may influence the major driving performance indicators under emergency evacuation. Upon completion of the correlation analysis, the Cohen's D-values were estimated to identify whether there is a significant difference between the average value of a given response variable and the average values of corresponding predictors [61].

maximum log-likelihood value) for each one of the considered response variables. The backward elimination procedure was applied in order to remove the predictors, which do not affect the response variable sigtol nificantly (i.e., have p-values that exceed a pre-defined tolerance – ppred ) and ensure that the model p-value does not increase drastically (i.e., tol more than a pre-defined tolerance – pmod ). The key steps of the backward elimination procedure are presented in Pseudocode 1. In step 0, the updated set of predictors is initialized. In step 1, the regression model with the initial set of predictors is executed. In step 2, the maximum p-value over the available predictors is determined. Then, the procedure enters the loop (steps 3–12), where the predictor with the highest p-value is identified in step 4. In step 5, a copy of the set of predictors is stored. After that, the predictor with the highest p-value is removed from the set of predictors in step 6. In step 7, the regression model with the updated set of predictors is executed. In step 8, the maximum predictor p-value is determined for the updated set of predictors. Then, the procedure checks whether the removal of the predictor with the highest p-value caused a significant increase in the model p-value. If the updated model p-value is greater or equal to a tol certain tolerance value ( pmod pmod ), then the updated set of predictors is replaced with a previously updated set (i.e., with the predictor set that still contains the predictor with the highest p-value). In the latter case, the procedure will be terminated in the next iteration. Otherwise, the procedure will continue until all predictors with p-values greater than a certain tolerance value have been removed from the regression model. In this study, the tolerances on p-values of the model and pretol tol = ppred = 0.0500 . The backward elimdictors were assumed to be pmod ination was critical for the analysis of the regression model with the highest goodness-of-fit value, as more than 30 different predictors were considered for each response variable (see Section 4.1.2).

5. Analysis results Before developing the regression models, a statistical analysis of the available observations, recorded during the pilot study for the participants, was performed for all the considered response variables. The mean, standard deviation, variance, minimum, and maximum values of all observations were estimated, and the results are presented in Table 2. Note that the number of observations, collected throughout the pilot study, was found to be sufficient for the development of statistical models for the considered driving performance indicators, as all of the developed models were found to be statistically significant at 0.0500 significance level (more details will be provided in Sections 5.1.1–5.1.6 of the manuscript). All the considered regression models (described in Section 4.2), which have been frequently used in the literature for estimating various driving performance indicators (i.e., linear regression model – LN; polynomial regression model – PN; binary logit regression model – BLG; multinomial logit regression model – MLG; hierarchical logit regression model – HLG; Poisson regression model – PM; and negative binomial regression model – NB), were evaluated in terms of their goodness-of-fit in estimating the considered response variables (described in Section 4.1.1) based on various predictor combinations (described in Section 4.1.3). Detailed results of the conducted regression analysis are presented in Sections 5.1.1-5.1.6, while important findings are discussed in Section 5.2 of the manuscript.

4.3.3. Correlation analysis After backward elimination, a correlation analysis was conducted to determine the correlation between the response variables and predictors. The correlation value and the p-value for correlation between the response variables and predictors were also estimated. The closely related predictors were determined and the predictor with the highest correlation value was kept, while the other related predictors were removed from the regression model (e.g., if minimum time headway and average time headway were found to be statistically significant predictors after backward elimination, only one of the predictors,

5.1. Regression models 5.1.1. Travel time All candidate regression models of group 1 were evaluated for the collected travel time observations. Note that the total travel time in this study refers to the total time, required by a given pilot study participant 240

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Table 4 Coefficient information for predictors of the final travel time regression model LN1.

to drive through a 10-mile freeway evacuation segment (please see Section 3.3 of the manuscript for more details). Three predictor combinations, yielding the highest log-likelihood values for the candidate regression models, where the travel time was treated as a response variable, are presented in Fig. 3. The following notation was used for the regression models in Fig. 3 (and other relevant figures for the remainder of the manuscript): “type of regression model” & “predictor combination”. For example, the model LN1 refers to the linear regression model with predictor combination 1. Based on the analysis results, the model LN1 was found to have the highest log-likelihood value (LL = −217.5), when compared with the other models, which indicates that it fits the data best. Next, the backward elimination was executed for the model LN1 to remove the predictors, which do not affect the travel time response variable significantly. After that, the correlation analysis was performed to determine whether additional closely related predictors could be removed from the regression model. Based on the correlation analysis results (see Table 3), it was observed that the average space headway had the highest correlation and was kept in the final regression model, while the average time headway and minimum time headway with lower correlation values were removed from the list of significant predictors. Furthermore, the majority of predictors had Cohen's D-values exceeding 0.8, which indicates a statistically large difference between the average travel time and the average values of corresponding predictors. The final model was re-run. Detailed information for the coefficients of statistically significant predictors with p-value ≤ 0.0500, retrieved from the final travel time regression model, is presented in Table 4. Based on the analysis results, the travel time was found to be

p-value

Cohen's Dvalue

Age Driving frequency Distance driven per week Difficulty evacuating Ability to make quick decisions Simulator experience

0.2192 0.1427 0.0754 0.0373 0.1754

0.0020** 0.0454* 0.2923 0.6028 0.0137*

2.3906 4.3956 1.7538 12.8903 9.3567

0.3701

2.7938

Average space headway Average time headway Minimum time headway

0.2269 0.0358 0.1967

< 0.0001** 0.0013** 0.6179 0.0056**

t-stat

p-value

Intercept

11.9658

0.5605

21.3473

Age Driving frequency Distance driven per week Difficulty evacuating Ability to make quick decisions Simulator experience

0.0107 −0.0649 −0.0286 −0.4187 −0.2555 −0.0625

0.0038 0.0260 0.0123 0.2019 0.0903 0.0119

2.8175 −2.4916 −2.3240 −2.0732 −2.8279 −5.2682

Average space headway

0.0015

0.0008

1.9069

< 0.0001 0.0053 0.0136 0.0212 0.0395 0.0052 < 0.0001 0.0480

significantly affected with age (greater travel time was generally recorded for aging individuals), driving frequency (greater travel time was generally recorded for individuals, who drive less frequently), distance driven per week (greater travel time was generally recorded for individuals, who do not drive far), and difficulties experienced while evacuating in the past (greater travel time was generally recorded for individuals, who experienced difficulties during emergency evacuation in the past). Other factors, such as the self-reported ability of drivers to make quick decisions (greater travel time was generally recorded for individuals with lower rating for the self-reported ability to make quick decisions), simulator experience (greater travel time was generally recorded for individuals, who do not have a lot of experience driving the simulator), and average space headway (greater travel time was generally recorded for individuals, who prefer to keep greater average space headway) also substantially influenced the travel time at 0.0500 significance level. 5.1.2. Lane deviation All candidate regression models of group 1 were evaluated for the collected lane deviation observations. Three predictor combinations, yielding the highest log-likelihood values for the candidate regression models, where the lane deviation was treated as a response variable, are presented in Fig. 4. Based on the analysis results, the model LN1 was found to have the highest log-likelihood value (LL = −13.1), when compared with the other models, which indicates that it fits the data best. Next, the backward elimination was executed for the model LN1 to remove the predictors, which do not affect the lane deviation response variable significantly. After that, the correlation analysis was performed to determine whether additional closely related predictors could be removed from the regression model. Based on the correlation analysis

Table 3 Correlation analysis summary: response variable – travel time. Correlation values

S.E.

Notes: S.E. – standard error; t-stat – t-statistic. *Final model LL = −244.0834; Final model p-value < 0.0001.

Fig. 3. Log-likelihood estimates for the fittest regression models with the travel time as a response variable.

Predictors

Coefficient

3.0965 2.0985 0.0541

Notes: The absolute values of the correlation coefficients and Cohen's D-values are reported. *p-value ≤ 0.0500, **p-value ≤ 0.0100 (p-values are presented for the correlation analysis).

Fig. 4. Log-likelihood estimates for the fittest regression models with the lane deviation as a response variable. 241

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

reported ability to avoid hitting curbs). Also, the self-reported ability to see vehicles coming beside (greater lane deviation was generally recorded for individuals with higher rating for the self-reported ability to see vehicles coming beside), the self-reported ability to drive safely (greater lane deviation was generally recorded for individuals with lower ratings for the self-reported ability to drive safely), simulator experience (greater lane deviation was generally recorded for individuals, who have a lot of experience driving the simulator), number of lanes (greater lane deviation was generally recorded for the four-lane evacuation route scenarios as compared to the six-lane evacuation route scenarios), and minimum space headway (greater lane deviation was generally recorded for individuals, who prefer to keep lower minimum space headway) substantially influenced the lane deviation at 0.0500 significance level.

Table 5 Correlation analysis summary: response variable – lane deviation. Predictors

Correlation values

p-value

Cohen's Dvalue

Gender Driving experience under normal conditions Health rating Visual disorders Ability to avoid hitting curbs Ability to see vehicles coming beside Ability to drive safely Simulator experience Number of lanes Average time headway Minimum space headway Minimum time headway

0.2414 0.5343

0.0006** < 0.0001**

0.2839 1.7024

0.1326 0.4167 0.1170 0.0440

0.0633 < 0.0001** 0.1016 0.5390

3.7542 0.6930 3.4419 3.4887

0.1951 0.3395 0.1269 0.0850 0.5137 0.0988

0.0060** 0.0001** 0.0756 0.2351 < 0.0001** 0.1670

3.9308 0.1146 2.3480 1.3681 0.9800 0.1186

5.1.3. Crash occurrence All candidate regression models of group 2, except the Poisson regression model, were evaluated for the collected crash occurrence observations. The Poisson regression model was excluded from the list of candidate regression models of group 2 due to the fact that, based on the statistical analysis of the available observations, the mean crash occurrence was found to be lower than the crash occurrence variance – see Table 2 (while the Poisson model is typically applied for analysis of the datasets, where the sample mean is approximately equal to the sample variance over the collected observations – [33]). Note that the binary logit regression model (BLG) was used to estimate the crash occurrence for each pilot study participant during each emergency evacuation experiment (i.e., binary response variable: 0 – no crashes have been observed during the experiment; 1 – crashes have been observed during the experiment), while the rest of regression models of group 2 were used to calculate the number of crash occurrences or crash frequency (i.e., how many crashes each pilot study participant had during each emergency evacuation experiment). Three predictor combinations, yielding the highest log-likelihood values for the candidate regression models, where the crash occurrence was treated as a response variable, are presented in Fig. 5. Although, the model BLG20 does not have the highest log-likelihood value (LL = −43.4), it gives more information regarding the effects of predictors on the crash occurrence response variable (models MLG14, MLG12, and MLG13 with the highest log-likelihood values did not have any statistically significant predictors at 0.0500 significance level); and, therefore, the model BLG20 will be further used in the analysis. The backward elimination was executed for the model BLG20 to remove the predictors, which do not affect the crash occurrence response variable significantly. After that, the correlation analysis was performed to determine whether additional closely related predictors could be removed from the regression model. Based on the correlation analysis results (see Table 7), no predictors were removed from the crash occurrence regression model BLG20. Furthermore, the majority of predictors had Cohen's D-values exceeding 0.8, which indicates a statistically large difference between the average crash occurrence and the average values of corresponding predictors. Detailed information for the coefficients of statistically significant predictors with pvalue ≤ 0.0500, retrieved from the final crash occurrence regression model, is presented in Table 8. Based on the analysis results, the crash occurrence was found to be significantly affected with age (the odds of having a crash increase for younger individuals and decrease for aging adults). Furthermore, the crash occurrence was also significantly influenced with gender (the odds of having a crash generally increased for males as compared to females), visual disorders (the odds of having a crash increased for individuals with visual disorders), and minimum space headway (the odds of having a crash generally increased for individuals, who prefer to keep lower minimum space headway).

Notes: The absolute values of the correlation coefficients and Cohen's D-values are reported. **p-value ≤ 0.0100 (p-values are presented for the correlation analysis).

Table 6 Coefficient information for predictors of the final lane deviation regression model LN1.

(Intercept) Gender Driving experience under normal conditions Health rating Visual disorders Ability to avoid hitting curbs Ability to see vehicles coming beside Ability to drive safely Simulator experience Number of lanes Minimum space headway

Coefficient

S.E.

t-stat

p-value

1.8673 −0.0879 −0.0051

0.2076 0.0443 0.0013

8.9958 −1.9813 −3.8667

< 0.0001 0.0489 0.0001

0.0570 0.2054 −0.1073 0.1098

0.0251 0.0456 0.0472 0.0532

2.2691 4.5030 −2.2725 2.0659

0.0243 < 0.0001 0.0241 0.0401

−0.1348 0.0247 −0.1000 −0.0157

0.0484 0.0043 0.0424 0.0032

−2.7880 5.7643 −2.3603 −4.9236

0.0058 < 0.0001 0.0192 < 0.0001

Notes: S.E. – standard error; t-stat – t-statistic. *Final model LL = −41.8304; Final model p-value < 0.0001.

results (see Table 5), it was observed that the minimum space headway had the highest correlation and was kept in the final regression model, while the average time headway and minimum time headway with lower correlation values were removed from the list of significant predictors. Furthermore, the majority of predictors had Cohen's D-values exceeding 0.8, which indicates a statistically large difference between the average lane deviation and the average values of corresponding predictors. The final model was re-run. Detailed information for the coefficients of statistically significant predictors with pvalue ≤ 0.0500, retrieved from the final lane deviation regression model, is presented in Table 6. Based on the analysis results, the lane deviation was found to be significantly affected with gender (greater lane deviation was generally recorded for males as compared to females), driving experience under normal conditions (greater lane deviation was generally recorded for individuals, who have less driving experience under normal conditions), health rating (greater lane deviation was generally recorded for individuals, who have higher health rating), visual disorders (greater lane deviation was generally recorded for individuals without visual disorders as compared to individuals, who have visual disorders), and the self-reported ability to avoid hitting curbs (greater lane deviation was generally recorded for individuals with lower rating for the self242

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Fig. 5. Log-likelihood estimates for the fittest regression models with the crash occurrence as a response variable. Table 7 Correlation analysis summary: response variable – crash occurrence.

Table 9 Correlation analysis summary: response variable – collision speed.

Predictors

Correlation values

p-value

Cohen's D-value

Predictors

Correlation values

p-value

Cohen's D-value

Age Gender Visual disorders Minimum space headway

0.4809 0.1289 0.1444 0.5013

< 0.0001** 0.0710 0.0430* < 0.0001**

3.0455 0.1088 1.0067 0.8772

Age Gender Distance driven per week Vision Minimum space headway

0.4325 0.3100 0.2210 0.0490 0.4381

< 0.0001** < 0.0001** 0.0019** 0.4943 < 0.0001**

1.6349 1.0234 0.7381 0.8497 0.5384

Notes: The absolute values of the correlation coefficients and Cohen's D-values are reported. *p-value ≤ 0.0500, **p-value ≤ 0.0100 (p-values are presented for the correlation analysis).

Notes: The absolute values of the correlation coefficients and Cohen's D-values are reported. **p-value ≤ 0.0100 (p-values are presented for the correlation analysis).

Table 8 Coefficient information for predictors of the final crash occurrence regression model BLG20.

Table 10 Coefficient information for predictors of the final collision speed regression model LN1.

(Intercept) Age Gender Visual disorders Minimum space headway

Coefficient

S.E.

t-stat

p-value

6.7142 −0.0627 −0.8151 −0.8182 −0.2258

1.3429 0.0130 0.4256 0.4118 0.0327

4.9996 −4.8087 −1.9151 −1.9872 −6.9048

< 0.0001 < 0.0001 0.0455 0.0469 < 0.0001

(Intercept) Age Gender Distance driven per week Vision Minimum space headway

Notes: S.E. – standard error; t-stat – t-statistic. *Final model LL = −73.7398; Final model p-value < 0.0001.

Coefficient

S.E.

t-stat

p-value

42.1500 −0.2704 −5.6654 0.9172 −1.9500 −0.7253

5.8600 0.0553 1.9962 0.1894 1.0390 0.1362

7.1928 −4.8878 −2.8380 4.8438 −1.8768 −5.3268

< 0.0001 < 0.0001 0.0050 < 0.0001 0.0420 < 0.0001

Notes: S.E. – standard error; t-stat – t-statistic. *Final model LL = −843.4041; Final model p-value < 0.0001.

5.1.4. Collision speed All candidate regression models of group 1 were evaluated for the collected collision speed observations. Three predictor combinations, yielding the highest log-likelihood values for the candidate regression models, where the collision speed was treated as a response variable, are presented in Fig. 6. Based on the analysis results, the model LN1 was found to have the highest log-likelihood value (LL = −777.8), when compared with the other models, which indicates that it fits the data best. Next, the backward elimination was executed for the model LN1 to remove the predictors, which do not affect the collision speed response variable significantly. After that, the correlation analysis was performed to determine whether additional closely related predictors could be removed from the regression model. Based on the correlation analysis results (see Table 9), no predictors were removed from the collision speed regression model LN1. Furthermore, the majority of predictors had Cohen's D-values exceeding 0.8, which indicates a statistically large difference between the average collision speed and the average values

Fig. 6. Log-likelihood estimates for the fittest regression models with the collision speed as a response variable. 243

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Fig. 7. Log-likelihood estimates for the fittest regression models with the average acceleration pedal pressure as a response variable.

Fig. 8. Log-likelihood estimates for the fittest regression models with the average braking pedal pressure as a response variable.

of corresponding predictors. Detailed information for the coefficients of statistically significant predictors with p-value ≤ 0.0500, retrieved from the final collision speed regression model, is presented in Table 10. Based on the analysis results, the collision speed was found to be significantly affected with age (greater collision speed was generally recorded for younger individuals as compared to aging adults), gender (greater collision speed was generally recorded for males as compared to females), distance driven per week (lower collision speed was generally recorded for individuals, who do not drive far), vision (greater collision speed was generally recorded for individuals with lower vision rating), and minimum space headway (greater collision speed was generally recorded for individuals, who prefer to keep lower minimum space headway).

make quick decisions; however, they tended to press the acceleration pedal more often and complete the driving simulation experiments faster as compared to older adults. 5.1.6. Average braking pedal pressure All candidate regression models of group 1 were evaluated for the collected average braking pedal pressure observations. Three predictor combinations, yielding the highest log-likelihood values for the candidate regression models, where the average braking pedal pressure was treated as a response variable, are presented in Fig. 8. Although, the model LN1 does not have the highest log-likelihood value (LL = −250.5), it gives more information regarding the effects of predictors on the average braking pedal pressure response variable (the model LN10 with the highest log-likelihood value had only one statistically significant predictor at 0.0500 significance level); and, therefore, the model LN1 will be further used in the analysis. Next, the backward elimination was executed for the model LN1 to remove the predictors, which do not affect the average braking pedal pressure response variable significantly. After that, the correlation analysis was performed to determine whether additional closely related predictors could be removed from the regression model. Based on the correlation analysis results (see Table 12), it was observed that the maximum space headway had the highest correlation and was kept in the final regression model, while the average space headway, average time headway, and maximum time headway with lower correlation values were removed from the list of significant predictors. Furthermore, the majority of predictors had Cohen's D-values exceeding 0.8, which indicates a statistically large difference between the average braking pedal pressure and the average values of corresponding

5.1.5. Average acceleration pedal pressure All candidate regression models of group 1 were evaluated for the collected average acceleration pedal pressure observations. Three predictor combinations, yielding the highest log-likelihood values for the candidate regression models, where the average acceleration pedal pressure was treated as a response variable, are presented in Fig. 7. Based on the analysis results, the model LN1 was found to have the highest log-likelihood value (LL = −330.5), when compared with the other models, which indicates that it fits the data best. Next, the backward elimination was executed for the model LN1 to remove the predictors, which do not affect the average acceleration pedal pressure response variable significantly. After the backward elimination, only one predictor (the self-reported ability to make quick decisions), which was statistically significant at 0.0500 significance level, remained in the regression model. As a result of the correlation analysis, it was found that the self-reported ability to make quick decisions was the predictor with the highest correlation value. Detailed information for the remaining predictor of the average acceleration pedal pressure regression model is presented in Table 11. Based on the analysis results, it was found that greater acceleration pedal pressure was generally recorded for individuals with lower rating for the self-reported ability to make quick decisions. The latter finding can be explained by the fact that many young participants put a relatively low rating for their ability to

Table 12 Correlation analysis summary: response variable – average braking pedal pressure.

Table 11 Coefficient information for predictors of the final average acceleration pedal pressure regression model LN1.

(Intercept) Ability to make quick decisions

Coefficient

S.E.

t-stat

p-value

1.2973 −0.2766

0.4823 0.1434

2.6896 −1.9290

0.0077 0.0451

Predictors

Correlation values

p-value

Cohen's Dvalue

Ability to avoid hitting curbs Ability to see vehicles coming beside Day of the week Number of lanes Average space headway Average time headway Maximum space headway Maximum time headway

0.0496 0.0810

0.4885 0.2578

6.7596 7.0531

0.2002 0.1699 0.1838 0.1984 0.2058 0.1532

0.0048** 0.0170* 0.0097** 0.0052** 0.0037** 0.0316*

3.0370 6.7906 3.2744 1.8695 0.3485 0.9218

Notes: The absolute values of the correlation coefficients and Cohen's D-values are reported. *p-value ≤ 0.0500, **p-value ≤ 0.0100 (p-values are presented for the correlation analysis).

Notes: S.E. – standard error; t-stat – t-statistic. *Final model LL = −368.0443; Final model p-value = 0.0451. 244

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

of individuals to see vehicles coming beside. The results from the conducted statistical analysis also demonstrate that health-related characteristics of individuals substantially affect their driving ability under emergency evacuation. Visual disorders and lower vision rating impacted the ability of individuals to maneuver and switch lanes along the evacuation route, increased the odds of having a crash, and increased the collision speed in case of crash occurrence. The emergency evacuation experience was also found to be an important factor. Individuals, who experienced difficulties during emergency evacuation in the past, tended to drive more carefully and took longer time to evacuate from the virtual emergency area. The latter finding can be explained by the fact that emergency evacuation is a quite challenging task, and individuals, who previously experienced difficulties during emergency evacuation (e.g., crashes, unexpected maneuvers from other drivers that almost resulted in crashes, slippery surface of the evacuation routes due to adverse weather), preferred to drive more carefully to avoid or mitigate any potential evacuation difficulties. Moreover, the driving simulator experience was found to be a statistically significant factor for certain driving performance indicators. Typically, individuals, who used the driving simulator before (even the model that was different from the one, adopted in this study), were able to evacuate from the virtual emergency area faster and maneuver along the evacuation route more efficiently.

Table 13 Coefficient information for predictors of the final average braking pedal pressure regression model LN1.

(Intercept) Ability to avoid hitting curbs Ability to see vehicles coming beside Day of the week Number of lanes Maximum space headway

Coefficient

S.E.

t-stat

p-value

0.0747 0.0256 −0.0275 −0.0111 0.0235 0.0012

0.0515 0.0127 0.0136 0.0042 0.0115 0.0006

1.4511 2.0195 −2.0228 −2.6546 2.0443 2.4140

0.1483 0.0448 0.0444 0.0086 0.0422 0.0167

Notes: S.E. – standard error; t-stat – t-statistic. *Final model LL = −270.4768; Final model p-value = 0.0003.

predictors. The final model was re-run. Detailed information for the coefficients of statistically significant predictors with p-value ≤ 0.0500, retrieved from the final average braking pedal pressure regression model, is presented in Table 13. Based on the analysis results, the average braking pedal pressure was found to be significantly affected with the self-reported ability of individuals to avoid hitting curbs (greater braking pedal pressure was generally recorded for individuals with higher rating for the self-reported ability to avoid hitting curbs) and the self-reported ability to see vehicles coming beside (greater braking pedal pressure was generally recorded for individuals with lower rating for the self-reported ability to see vehicles coming beside). Moreover, the average braking pedal pressure was also significantly influenced with day of the week, when the participants were taking the experiment (greater braking pedal pressure was generally recorded for individuals, who were taking the experiment in the first part of the week), number of lanes (greater braking pedal pressure was generally recorded for the six-lane evacuation route scenarios as compared to the four-lane evacuation route scenarios), and maximum space headway (greater braking pedal pressure was generally recorded for individuals, who prefer to keep greater maximum space headway).

5.2.2. Evacuation route characteristics The evacuation route geometric characteristics were found to be statistically significant for certain driving performance indicators. Specifically, the pilot study participants were more comfortable to switch lanes more often during the four-lane evacuation route experiment as compared to the six-lane evacuation route experiment primarily due to the fact that they were surrounded by fewer vehicles. Moreover, the pilot study participants tended to use braking pedal more often during the six-lane evacuation route experiment as compared to the four-lane evacuation route experiment. 5.2.3. Driving conditions Another interesting finding consists in the fact that greater braking pedal pressure was generally recorded for individuals, who were taking the experiment in the first part of the week. More specifically, based on the data collected form the driving simulator, greater braking pedal pressure was generally recorded for the participants, taking the experiments on Mondays and Tuesdays, as compared to Wednesdays, Thursdays, and Fridays. Generally, denser traffic flow is observed in the first part of the week for the area, where the pilot study was conducted (i.e., Tallahassee Metropolitan Area, the state of Florida, USA). Therefore, the participants, who had to travel to the driving simulator laboratory throughout the peak hours during the days with larger traffic volumes tended to drive more defensively and use the braking pedal more often throughout the driving simulator experiments as compared to the participants, who had to travel to the driving simulator laboratory throughout the off-peak hours during the days with lower traffic volumes.

5.2. Discussion Based on statistical analysis of the data, collected as a result of the driving simulator pilot study, a number of important findings have been discovered regarding the major factors, influencing the driving ability of individuals under emergency evacuation. Certain findings can be considered as rather expected, while the others were not that intuitive. The discovered findings were classified in several groups (including driver characteristics, evacuation route characteristics, driving conditions, and traffic characteristics) and are presented in the following sections of the manuscript. 5.2.1. Driver characteristics The results from the conducted statistical analysis show that greater travel time was recorded for aging adults, as compared to their younger counterparts. Younger individuals tended to drive faster along the evacuation route and change travel lanes more often (especially males). However, such frequent changes of lanes increased the number of collisions with other vehicles for younger adults. Driving experience and self-reported driving ability of individuals were found to be important factors throughout the emergency evacuation process. Specifically, individuals with higher rating for the self-reported ability to make quick decisions were able to evacuate the virtual emergency area faster, while individuals with higher rating for the self-reported ability to see vehicles coming beside were able to maneuver more efficiently along the evacuation route. Furthermore, the vehicle acceleration patterns throughout emergency evacuation were primarily affected with the selfreported ability of individuals to make quick decisions, while the vehicle braking patterns were primarily affected with the self-reported ability of individuals to avoid hitting curbs and the self-reported ability

5.2.4. Traffic characteristics The space headway was found to be an important factor during emergency evacuation, as it was statistically significant for many of the considered driving performance indicators. The results from the statistical analysis indicate that increasing space headway increased the travel time, but reduced the lane deviation, the odds of having a crash, and the collision speed (in case of crash occurrence). Some findings from this study can be classified as “general” (e.g., findings regarding the effects of age, gender, driving experience, healthrelated characteristics, and evacuation route geometric characteristics on the driving ability of individuals under emergency evacuation), while other findings are more “study-specific” (e.g., greater braking pedal pressure was generally recorded for the participants, taking the 245

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

experiments on Mondays and Tuesdays, as compared to Wednesdays, Thursdays, and Fridays; the latter finding can be classified as “studyspecific”, since the braking pedal pressure may be influenced with driving conditions of a given metropolitan area). Findings, which were revealed as a result of this study (especially, the ones of the general interest), can be incorporated within the existing transportation planning models to facilitate the natural hazard preparedness and ensure safety of evacuees, including vulnerable population.

speed in case of crash occurrence. The space headway was found to be another important factor, as increasing space headway increased the travel time, but decreased the lane deviation, the odds of having a crash, and the collision speed (in case of crash occurrence). Also, the evacuation route geometric characteristics were found to be statistically significant for certain driving performance indicators. The pilot study participants were typically more comfortable to switch lanes more often during the four-lane evacuation route experiment as compared to the six-lane evacuation route experiment mainly due to the fact that they were surrounded by fewer vehicles. Furthermore, health-related characteristics of individuals also substantially affected their driving ability under emergency evacuation. Visual disorders and lower vision rating impacted the ability of individuals to maneuver along the evacuation route and increased the odds of having a crash. The conducted statistical analysis indicated that the vehicle acceleration and braking patterns were primarily influenced with the driving ability characteristics of individuals. The developed statistical models are expected to facilitate the natural hazard preparedness, ensure safety of evacuees, including vulnerable population, reduce or even prevent the occurrence of crashes along the evacuation routes, and ultimately preserve human lives. Findings from this research will be important for various agencies, which are involved at the natural hazard preparedness stage, including state authorities, Federal Emergency Management Agency, Department of Homeland Security, United States Coast Guard, and others. The scope of future research for this study includes the following: (1) develop additional emergency evacuation scenarios by changing traffic flow characteristics, evacuation route geometric characteristics, weather conditions, and others; (2) assess the effects of additional visual and technological aids throughout emergency evacuation; (3) increase the number of participants to ensure accuracy of the statistical models; (4) account for the unobserved heterogeneity to improve accuracy of the developed statistical models; (5) apply certain advanced statistical methods to the available dataset in order to enhance the prediction accuracy of the developed statistical models and reduce potential errors due to the sample size; (6) based on the study findings, develop a set of optimization models and solution algorithms for assigning evacuees to the available evacuation routes and emergency shelters; and (7) apply the developed optimization models and solution algorithms for real-life emergency evacuation scenarios, considering natural hazards that recently struck coastal areas of the United States (e.g., Hurricane Matthew in 2016, Hurricane Harvey in 2017, Hurricane Irma in 2017).

6. Concluding remarks and future research Efficient natural hazard preparedness is very important to reduce negative externalities, associated with natural hazards, including not only property damages, but also loss of human lives. In case of an approaching natural hazard, the population is required to evacuate the emergency area promptly. Emergency evacuation is a quite challenging task, especially for vulnerable population (e.g., aging adults, individuals with medical conditions, individuals with disabilities), due to the associated traffic surge potential, stress caused by the approaching natural hazard, bottlenecks on the evacuation routes, and unexpected maneuvers from other evacuees, which may further result in crashes along the evacuation routes. Vulnerable population groups may require additional time in order to evacuate the emergency areas after the evacuation warning. A lot of studies were conducted in the past, aiming to identify the major factors, influencing the occurrence of crashes on the roadways under normal driving conditions. However, only a limited number of studies focused on the factors, influencing the driving ability of individuals and the occurrence of crashes during emergency evacuation. Moreover, those studies accounted for a relatively narrow range of factors (primarily driver and traffic flow characteristics). Considering a frequent occurrence of natural hazards in different parts of the world, negative externalities that could be caused by natural hazards, bottlenecks and traffic breakdowns as a result of crashes along the evacuation routes, this study focused on development of statistical models, which accounted for the effects of a wide range of different factors (including driver characteristics, evacuation route characteristics, driving conditions, and traffic characteristics) on the driving ability of individuals under emergency evacuation, including potential occurrence of crashes along the evacuation routes. The required data were collected using the driving simulator and realistic emergency evacuation scenarios. A total of 115 participants with various socio-demographic characteristics were involved in the driving simulator pilot study. The information regarding the socio-demographic characteristics of participants and the data, collected from the driving simulator, were used as a foundation for the developed statistical models. A total of six driving performance indicators were considered, including travel time, lane deviation, crash occurrence, collision speed, average acceleration pedal pressure, and average braking pedal pressure. Age was found to be one of the statistically significant factors, influencing the driving ability of individuals under emergency evacuation. Generally, younger individuals tended to drive faster along the evacuation route and change lanes more often (especially males). The latter reduced the travel time, required to evacuate the virtual emergency area, but increased the odds of having a crash and the collision

Acknowledgments This study was supported by United States Department of Transportation grant DTRT13-G-UTC42, and administered by the Center for Accessibility and Safety for an Aging Population (ASAP) at the Florida State University (FSU), Florida A&M University (FAMU), and University of North Florida (UNF). The opinions, results, and findings expressed in this study are those of the authors and do not necessarily represent the views of the United States Department of Transportation, the Center for Accessibility and Safety for an Aging Population, the Florida State University, the Florida A&M University, or the University of North Florida.

Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ress.2018.09.021. Appendix A. Socio-demographic data for the pilot study participants This section of the manuscript provides a detailed description of the socio-demographic data, which were collected from the pilot study participants. The distribution of the pilot study participants by age and gender is presented in Fig. 9. The age of participants ranged from 18 years to 87 years (M = 45.34 years, SD = 19.59 years; where M – is a notation used for the sample mean, SD – is a notation used for the sample standard deviation). As for gender, 43% of participants were males, while 57% of participants were females. Fig. 10 illustrates the distribution of the pilot 246

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Fig. 9. Distribution of the pilot study participants by age and gender.

study participants by level of education, occupational status, marital status, driving experience, driving frequency, and average distance driven per week. From the analysis of responses, it was found that most of the participants had a bachelor's degree (36 participants or 31%), a master's degree (33 participants or 29%), and an associate's degree (21 participants or 18%). Also, 16 participants (or 14%) had a doctoral degree, 7 participants (or 6%) were high school graduates, and 2 participants (or 2%) took a vocational training. Therefore, all the participants had a formal education and graduated from a high school. As for the primary occupational status, 37 participants (or 32%) were working full-time, 36 participants (or 31%) were retired, 33 participants (or 29%) were students, and 6 participants (or 5%) worked part-time. Only one participant was a homemaker. The participants were asked to indicate their marital status as either being single, married, separated, divorced, or widowed. A blank space was provided for any participant, who did not belong to any of the aforementioned marital status groups. Based on the collected information, 53 participants (or 46%) were married, 48 participants (or 42%) were single, 10 participants (or 9%) were divorced, while 3 participants or (3%) were widowed. One participant filled in the blank space as “separated”. Also, the participants were requested to specify how long they had been driving. It was found that the driving experience of participants ranged from 1 year to 66 years (M = 20.48 years, SD = 27.48 years). To get a proper distribution, the data were sorted into 10-year classes. The results of the analysis show that 38 participants (or 33%), 21 participants (or 18%), and 18 participants (or 16%) had about 0–9 years, 50–59 years, and 40–49 years of driving experience, respectively. A high variation in the years of driving experience among the participants can be explained by a significant difference in age. All the participants were requested to indicate how often they drive per week. Based on the analysis of responses, it was found that 54 participants (or 47%) drive at least 11 times a week, and 35 participants (or 30%) drive between 5–10 times per week. Also, 14 participants (or 12%) drive 2–4 times a week, while 12 participants (or 10%) drive once a week. Therefore, most of the participants of the pilot study are active drivers. As for the average distance driven per week, the results from the analysis of the collected data show that 55 participants (or 48%) drive 30 miles or more per week, and 40 participants (or 35%) drive between 10 and 30 miles per week. On the other hand, 9 participants (or 8%) drive between 6 to 10 miles per week, 6 participants (or 5%) drive between 2 to 6 miles per week, and 5 participants (or 4%) drive less than 2 miles per week. The participants were asked to state the number of times they had driven under emergency evacuation. A total of 82 participants (or 71%) reported that they had never driven under emergency evacuation. Also, 28 participants (or 24%) said they had driven under emergency evacuation between one and five times, 4 participants (or 3%) responded that they had driven under emergency evacuation between six and ten times, and one participant had driven under emergency evacuation about 100 times. The latter response (i.e., driving more than 100 times under emergency evacuation) seems out of the ordinary. It can be the case that the participant perceived heavy rain or other adverse weather conditions as disruptive events (therefore, the participant's response was not used in the development of statistical models). The participants were also requested to specify (provide a yes/no response) whether they encountered any difficulties during emergency evacuation in the past, such as traffic congestion, aggressive behavior of other drivers, causing collisions or near-collision events, blockage of traffic lanes by fallen trees, and others. Also, the participants were asked to indicate (provide a yes/no response) whether additional visual/technological evacuation aids were provided to facilitate emergency evacuation. Furthermore, all the pilot study participants were requested to indicate their annual household income in the participant form. It was found that 32 participants (or 28%) earn $80,000 or more, 26 participants (or 23%) earn between $20,000 and $39,000, 16 participants (or 14%) earn between

Fig. 10. Distribution of the pilot study participants by driver characteristics and driving experience. 247

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al.

Table 14 Distribution of the pilot study participants by the self-reported health-related characteristics. Characteristic\Rating

Poor

Fair

Good

Very good

Excellent

Medical condition Vision Hearing

5.2% 1.7% 1.7%

4.3% 7.0% 7.8%

23.5% 43.5% 32.2%

36.5% 27.8% 27.8%

30.4% 20.0% 30.4%

Table 15 Distribution of the pilot study participants by the self-reported driving abilities. Driving ability feature\Rating

Poor

Fair

Good

Very good

Ability Ability Ability Ability Ability Ability Ability Ability Ability

1.7% 0.9% 0.9% 0.0% 0.9% 0.0% 0.9% 0.0% 0.9%

9.6% 1.7% 8.7% 9.6% 4.3% 13.9% 9.6% 4.3% 12.2%

45.2% 33.9% 42.6% 47.0% 47.0% 47.8% 48.7% 47.8% 46.1%

43.5% 63.5% 47.8% 43.5% 47.8% 38.3% 40.9% 47.8% 40.9%

to see road signs to see the speedometer and controls to avoid hitting curbs and medians to see vehicles coming up beside to brake quickly to make an over-the-shoulder check to make quick driving decisions to drive safely to react to a blowing horn

$10,000 and $19,000, and 13 participants (or 11%) earn between $40,000 and $59,000. Also, 10 participants (or 9%) earn between $60,000 and $79,000, and 7 participants (or 6%) earn less than $10,000. Moreover, 6 participants (or 5%) did not know for certain what their annual household income was, while 5 (or 4%) said they do not wish to answer. The participants were also requested to indicate their primary racial group in the participant form. The analysis of the collected responses shows that 72 participants (or 63%) were White/Caucasian, and 27 participants (or 23%) were Black/African American. A total of 10 participants (or 9%) were Hispanic/Latino, 2 participants (or 2%) were Multi-racial, and one participant was a Native Hawaiian/Pacific Islander. Before the beginning of driving simulation experiments, all the participants were requested to answer a number of questions related to their health-related characteristics, including the self-reported medical condition, vision, and hearing. The following options were provided to rate the aforementioned health-related characteristics: “poor”, “fair”, “good”, “very”, and “excellent”. The distribution of the pilot study participants by the self-reported health-related characteristics is presented in Table 14. Along with the self-reported health-related characteristics, the participants were asked to specify whether they had any visual disorders or chronic diseases. A total of 36 participants reported that they had visual disorders, while 14 participants indicated that they had chronic diseases. Furthermore, the pilot study participants were requested to rate their driving ability in terms of the following aspects: (1) ability to see road signs at a distance; (2) ability to see the speedometer and controls; (3) ability to avoid hitting curbs and medians; (4) ability to see vehicles coming up beside; (5) ability to move foot quickly from the gas to the brake pedal; (6) ability to make an over-theshoulder check; (7) ability to make quick driving decisions; (8) ability to drive safely (avoid accidents); and (9) ability to react to a blowing horn from an approaching car. The distribution of the pilot study participants by the self-reported driving abilities is presented in Table 15. Finally, all the participants were requested to indicate the number of times they had driven a simulator before they took the pilot study experiments. The analysis of responses shows that 81 participants (or 70%) had never driven a simulator before the pilot study, while 28 participants (or 24%) had driven a simulator once or twice. Also, 4 participants (or 3%) had driven a simulator about three to five times, and only 2 participants (or 2%) had driven the simulator more than ten times.

[12] Bella F, Calvi A, D'Amico F. Analysis of driver speeds under night driving conditions using a driving simulator. J Safe Res 2014;49:45–52. [13] Casutt G, Martin M, Keller M, Jancke L. The relation between performance in onroad driving, cognitive screening and driving simulator in older healthy drivers. Transp Res Part F 2014;22:232–44. [14] Tuokko H, Myers A, Jouk A, Marshall S, Man-Son Hing M, Porter MM, Bedard M, Gelinas J, Korner-Bitensky N, Mazer B, Naglie G, Rapaport M, Vrkjlan B. Associations between age, gender, psychosocial and health characteristics in the Candrive II study cohort. Accid Anal Prev 2015;61:267–71. [15] Jurecki R. An analysis of collision avoidance maneuvers in emergency traffic situations. Arch Automov Eng 2016;72(2):73–93. [16] Man-Son-Hing M, Marshall SC, Molnar FJ, Wilson KG. Systematic review of driving risk and the efficacy of compensatory strategies in persons with dementia. J Am Geriatr Soc 2007;55(6):878–84. [17] Yan X, Abdel-Aty M, Radwan E, Wang X, Chilakapati P. Validating a driving simulator using surrogate safety measures. Accid Anal Prev 2008;40:274–88. [18] Shanmugaratnam S, Kass JS, James EA. Age differences in cognitive and psychomotor abilities and simulated driving. Accid Anal Prev 2010;42(3):802–8. [19] Boer E, Cleij D, Dawson J, Rizzo M. Serialization of vehicle control at intersections in older drivers. Proceedings of the sixth international driving symposium on human factors in driver assessment, training and vehicle design. 2011. p. 17–23. [20] Thompson KR, Johnson AM, Emerson JL, Dawson DJ, Boer ER, Rizzo M. Distracted driving in elderly and middle-aged drivers. Accid Anal Prev 2012;45(5):711–7. [21] Haufe S, Meinecke F, Gorgen K, Dahne S, Haynes J, Blankertz B, Bießmann F. On the interpretation of weight vectors of linear models in multivariate neuroimaging. NeuroImage 2014;87:96–110. [22] Belanger A, Gagnon S, Stinchcombe A. Crash avoidance in response to challenging driving events: the roles of age, serialization, and driving simulator platform. Accid Anal Prev 2015;82:199–212.

References [1] The Statistics Portal. https://www.statista.com/statistics/269652/countries-withthe-most-natural-hazardhazards. Accessed 09/18/2017. [2] Knabb, RD, Rhome JR, Brown DP. Tropical cyclone report. Hurricane Katrina. National Hurricane Center; 2005. [3] Ozguven EE, Horner M, Kocatepe A, Marcelin JM, Abdelrazig Y, Sando T, Moses R. Metadata-based needs assessment for emergency transportation operations with a focus on an aging population: a case study in Florida. Transp Rev 2016;36(3):383–412. [4] Van Manen S, Brinkhuis M. Quantitative flood risk assessment for Polders. Reliab Eng Syst Safe 2005;90(2-3):229–37. [5] Jonkman S, Lentz A, Vrijling J. A general approach for the estimation of loss of life due to natural and technological disasters. Reliab Eng Syst Safe 2010;95(11):1123–33. [6] Lv Y, Yan X, Sun W, Gao Z. A risk-based method for planning of bus–subway corridor evacuation under hybrid uncertainties. Reliab Eng Syst Safe 2015;139:188–99. [7] Boot W, Stothart C, Charness N. Improving the safety of aging road users: a minireview. Gerontology 2014;60:90–6. [8] Wolfe B, Dobres J, Rosenhltz R, Reimer B. More than the useful field: considering peripheral vision in driving. Appl Ergon 2017;65:316–25. [9] Hamdar SH, Mahmassani HS, Chen RB. Aggressiveness propensity index for driving behavior at signalized intersections. Accid Anal Prev 2008;40:315–26. [10] Hoogendoorn R, Hoogendoorn S, Brookhuis K. Driving behavior in emergency situations. Transp Res Rec 2012;2316:11–9. [11] Ortman JM, Velkoff VA. Current population reports. An Aging Nation: The Older Population in the United States. U.S. Census Bureau, 2014. 2014.https://www. census.gov/prod/2014pubs/p25-1140.pdf Accessed 09/18/2016.

248

Reliability Engineering and System Safety 182 (2019) 233–249

M.A. Dulebenets et al. [23] Cheng Y, Gao L, Zhao Y, Du F. Drivers’ visual characteristics when merging onto or exiting an urban expressway. PLoS Clin Trials 2015;11(9). e0162298. [24] Perrier J, Bertran F, Marie S, Couque C, Bulla J, Denise P, Bocca M. Impaired driving performance associated with effect of time duration in patients with primary insomnia. Sleep 2015;37:1565–73. [25] Calvi A, Bella F, D'Amico F. Diverging driver performance along deceleration lanes: driving simulator study. Transp Res Rec 2015;2518:95–103. [26] Gaspar G, Ward N, Neider MB, Crowell J, Carbonari R, Kaczmarski H, Ringer RV, Johnson AP, Kramer FA, Loschky L. Measuring the useful field of view during simulated driving with gaze-contingent displays. Hum Factors 2016;58(4):630–41. [27] Martinussen LM, Holler MH, Prato C, Haustein S. How indicative is a self-reported driving behaviour profile of police registered traffic law offences? Accid Anal Prev 2017;99:1–5. [28] Xu Z, Yang XK, Zhao XH, Jie LL. Differences in driving characteristics between normal and emergency situations and model of car-following behavior. J Transp Eng 2012;138(11):303–1313. [29] Hoogendoorn RG, Arem Bv, Brookhuis KA. Longitudinal driving behavior in case of emergency situations: an empirically underpinned theoretical framework. Procedia 2013;80:341–69. [30] Hoogendoorn RG, Arem Bv, Brookhuis KA. Longitudinal driving behavior in case of emergency situations: an empirically underpinned theoretical framework. Transp Res Part C 2013;36:581–603. [31] Underwood G, Ngai A, Underwood J. Driving experience and situation awareness in hazard detection. Safe Sci 2013;56:29–35. [32] Ali Y, Zheng Z, Haque M. Connectivity's impact on mandatory lane-changing behaviour: evidences from a driving simulator study. Transp Res Part C 2018;93:292–309. [33] Lord D, Mannering F. The statistical analysis of crash-frequency data: a review and assessment of methodological alternatives. Transp Res Part A 2010;44:291–305. [34] Coxon K, Chevalier A, Lo S, Ivers R, Brown J, Keay L. Behind the wheel: predictors of driving exposure in older drivers. J Am Geriatr Soc 2015;63(6):1137–45. [35] Huisingh C, Levitan EB, Irvin MR, MacLennan P, Wadley V, Owsley C. Visual sensory and visual-cognitive function and rate of crash and near-crash involvement among older drivers using naturalistic driving data. Invest Ophthalmol Vis Sci. 2017;58(7):2959–67. [36] Wang C, Quddus MA, Ison GS. Predicting accident frequency at their severity levels and its application in site ranking using a two-stage mixed multivariate model. Accid Anal Prev 2011;43(6):1979–90. [37] Malyshkina N, Mannering F. Empirical assessment of the impact of highway design exceptions on the frequency and severity of vehicle accidents. Accid Anal Prev 2010;42(1):131–9. [38] Yu R, Abdel-Aty M. Multi-level Bayesian analyses for single- and multi-vehicle freeway crashes. Accid Anal Prev 2013;58:97–105. [39] Barua S, El-Basyouny K, Islam T. A Full Bayesian multivariate count data model of collision severity with spatial correlation. Anal Methods Accid Res 2014;3-4:28–43. [40] Aguero-Valverde J, Jovanis PP. Spatial correlation in multilevel crash frequency models: effects of different neighboring structures. Transp Res Rec 2010;2165:21–32. [41] Aguero-Valverde J. Multivariate spatial models of excess crash frequency at area level: case of Costa Rica. Accid Anal Prev 2013;59:365–73. [42] Abdel-Aty MA, Radwan E. Modeling traffic accident occurrence and involvement.

Accid Anal Prev 2000;32:633–42. [43] Abdel-Aty M. Analysis of driver injury severity levels at multiple locations using ordered probit models. J Safe Res 2003;34(5):597–603. [44] Abdel-Aty M, Pande A. Crash data analysis: collective vs. individual crash level approach. J Safe Res 2007;38(5):267–76. [45] Coruh E, Bilgic A, Tortum A. Accident analysis with aggregated data: the random parameters negative binomial panel count data model. Anal Methods Accid Res 2015;7:37–49. [46] Behnood A, Mannering F. The temporal stability of factors affecting driver-injury severities in single-vehicle crashes: some empirical evidence. Anal Methods Accid Res 2015;8:7–32. [47] Koglbauer I, Holzinger J, Eichberger A, Lex C. Drivers’ interaction with the adaptive cruise control on dry and snowy roads with various tire-road grip potentials. J Adv Transp 2017;2017:1–10. [48] Ulak MB, Ozguven EE, Spainhour L, Vanli A. Spatial investigation of aging-involved crashes: a GIS-based case study in northwest Florida. J Transport Geogr 2017;58:71–91. [49] Drive Safety. Advanced Driving Simulators, Tools for Recovery and Mobility. 2017http://drivesafety.com/ [Accessed 15 April 2017]. [50] Borowsky A, Shinar D, Oron-Gilad T. Age, skill, and hazard perception in driving. Accid Anal Prev 2010;42(4):1240–9. [51] Li X, Yan X, Wu J, Radwan E, Zhang Y. A rear-end collision risk assessment model based on drivers’ collision avoidance process under influences of cell phone use and gender—a driving simulator based study. Accid Anal Prev 2016;97:1–18. [52] Di Stefano M, Macdonald WA. Assessment of older drivers: relationships among onroad errors, medical conditions and test outcome. J Safe Res 2003;34(4):415–29. [53] Wickens CM, Mann RE, Stoduto G, Butters JE, Ialomiteanu A, Smart RG. Does gender moderate the relationship between driver aggression and its risk factors? Accid Anal Prev 2012;45:10–8. [54] Wickens CM, Mann RE, Ialomiteanu AR, Stoduto G. Do driver anger and aggression contribute to the odds of a crash? A population-level analysis. Transp Res Part F 2016;42(2):389–99. [55] Rapoport M, Naglie G, Weegar K, Myers A, Cameron D, Crizzle A, Korner-Bitensky N, Tuokko B, Bedard M, Porter M, Mazer B, Gelinas I, Man-Son-Hing M, Marshall S. The relationship between cognitive performance, perceptions of driving comfort and abilities, and self-reported driving restrictions among healthy older drivers. Accid Anal Prev 2013;61:288–95. [56] Cuenen A, Jongen W, Brijs T, Brijs K, Lutin M, Vlierden VK, Wets G. The relations between specific measures of simulated driving ability and functional ability: new insights for assessment and training programs of older drivers. Transp Res Part F 2016;39:65–78. [57] Gilliath O, Canterberry M, Atchley P. Attachment as a predictor of driving performance. Transp Res Part F 2017;45:208–17. [58] Wang K, Ivan J, Ravishanker N, Jackson E. Multivariate Poisson lognormal modeling of crashes by type and severity on rural two-lane highways. Accid Anal Prev 2017;99:6–19. [59] MathWorks (R2015b). MATLAB (Matrix Laboratory) software. [60] Vinaitheerthan R. Maximum likelihood estimation and likelihood ratio test revisited. 2017.http://www.vinaitheerthan.com [Accessed 24 June 2018]. [61] Walker I. Null hypothesis testing and effect sizes. 2018.http://staff.bath.ac.uk/ pssiw/stats2/page2/page14/page14.html [Accessed 4 July 2018].

249