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Transportation Research Record: Journal of the Transportation Research Board, No. 2324, Transportation Research Board of the National Academies, Washington, D.C., 2012, pp. 20–28.DOI: 10.3141/2324-03

I. Zohdy, Center for Sustainable Mobility, Virginia Tech Transportation Institute, and H. A. Rakha, Charles E. Via, Jr., Department of Civil and Environmental Engi-neering, Virginia Polytechnic Institute and State University, 3500 Transportation Research Plaza, Blacksburg, VA 24061. Corresponding author: H. A. Rakha, hrakha@vt.edu.

cles at signalized intersections in different weather conditions is developed.

Most of the literature on the impact of weather has focused on collision risk, traffic volume variations, signal control, travel pattern, and traffic flow parameters. Datla and Sharma charac-terized highway traffic volume variations with severity of cold, amount of snowfall, and various combinations of cold and snow-fall intensities (1). Cools et al. quantified the impact of weather conditions on traffic intensity and volume variations (2). There have been few studies that directly address how adverse weather affects traffic flow variables, including speed, flow, density, head-way, and capacity. Brilon and Ponzlet quantified the impact of various weather conditions on the capacity and other traffic flow parameters on an autobahn in Germany (3). Rakha et al. quanti-fied the impact of inclement weather (precipitation and visibility) on traffic stream behavior and key traffic stream parameters includ-ing free-flow speed, speed at capacity, capacity, and jam density (4). Daniel et al. collected speed, flow, and density data under no adverse weather as well as under rain, snow, darkness, and sun glare conditions (5).

Gap acceptance or rejection behavior is considered one of the major factors that affect the capacity, saturation flow rate, and collision risk at signalized and unsignalized intersections. A gap is defined as the elapsed time interval between arrivals of successive vehicles in the opposing flow at a specified reference point in the intersection area. The minimum gap that a driver is willing to accept is generally called the critical gap. The Highway Capacity Manual defines the critical gap as the “minimum time interval between the front bump-ers of two successive vehicles in the major traffic stream that will allow the entry of one minor-street vehicle” (6). Attempts have been made in the literature to quantify the impact of various parameters on gap acceptance or rejection decisions. These factors include day and nighttime effects (7), the speed of the opposing vehicle (8, 9), the type of intersection control (yield versus stop sign) (10), the driver sight distance (11), the geometry of the intersection, the trip purpose, the expected wait time (12), and gap acceptance crash patterns at intersections (13). However, very few research efforts have attempted to quantify the impact of adverse weather on gap acceptance behavior (14–16).

Driver gap acceptance behavior is considered a decision-making process in which the driver could misjudge the offered gap size and thus collide with the opposing vehicle. Consequently, an intelligent system that provides driver guidance and assistance can reduce crashes during adverse weather conditions. This research effort develops an intersection decision support (IDS) system that can assist drivers to make better decisions.

Framework for Intersection Decision Support in Adverse Weather ConditionsUse of Case-Based Reasoning Algorithm

Ismail Zohdy and Hesham A. Rakha

The impact of inclement weather on driver behavior can be signifi-cant and may lead to erroneous driver decisions. Consequently, the research being presented used sensor information to assist opposed left-turning vehicles at signalized intersections under various weather conditions. The research proposed a new framework for a real-time intersection decision support system for left-turning vehicles entitled IDS-W. The proposed system was tested with data from a signalized intersection in Christiansburg, Virginia. The intersection was equipped with four video cameras and an on-site weather station. Nine thousand fifty-eight observations covering various weather conditions were gath-ered. Each observation consisted of the driver decision (accept or reject), weather condition (dry, rain, or snow), illumination (day or night), gap size, and gap-offered location (lane number). The observed decisions and the corresponding gap variables were aggregated to build the IDS-W database, which was developed by fusing data from roadside sensors (input data) and provided a decision (accept or reject the offered gap) to the driver. A case-based reasoning approach was used to provide the gap acceptance decision. The approach’s cycle starts with the entering of a new case (the combination of the gap size and the corresponding independent variables) and ends with the proposed decision (accept or reject the gap). The model was developed with 80% of the data to deduce the appropriate decision (accept or reject) and validated with the remaining 20% of the data through a Monte Carlo simulation. The results demonstrate the potential for delay reductions at the signalized intersection.

Adverse weather conditions negatively affect surface transportation and accordingly affect roadway operating conditions, safety, and mobility. Weather events are considered one of the factors that affect roadway surface conditions, vehicle performance, and driver behavior and consequently reduce capacity. Adverse weather could be mainly precipitation (rain or snow), surface condition (wet, icy, or snowy), strong winds, fog, or storms. The impact of different weather con-ditions could be significant and lead to erroneous decision making by the driver. Consequently, driver assistance for left-turning vehi-

Zohdy and Rakha 21

StUdy OBjeCtive

The main objective of the study is to propose a new framework for an IDS system for left-turning vehicles in different weather con-ditions based on field data. The proposed system is called IDS-W (IDS in adverse weather conditions). This framework uses a case-based reasoning (CBR) algorithm that accounts for the impact of inclement weather, illumination (day or night), gap size, and gap-offered location (lane number) on gap acceptance behavior.

Initially the study site and data acquisition procedures are presented followed by a description of the data analysis procedures and a sum-mary of the preliminary results. An overview of the IDS definition, background, and applications is then presented. Subsequently, the proposed IDS system is presented along with the CBR algorithm and then the proposed system validation is discussed.

StUdy Site deSCRiptiOn And dAtA ACqUiSitiOn eqUipment

The study site that was considered in this study was the signalized intersection of Depot Street and North Franklin Street (Business Route 460) in Christiansburg, Virginia. A schematic of the intersection

is shown in Figure 1a. It consists of four approaches at approxi-mately 90-degree angles. The posted speed limit for the eastbound and northbound approaches was 35 mph and for the westbound and southbound approaches was 25 mph at the time of the study.

The traffic signal included three phases: two phases for Depot Street north and south (one phase for each approach) and one phase for Route 460 (two approaches discharging during the same phase) with a permissive left-turn movement. Figure 1a illustrates the movement of vehicles during the green phase of Route 460 and the dashed lines show the left-turning vehicle trajectory in which drivers are facing a gap acceptance or rejection situation. The dashed line is opposed by the through movements at three conflict points, P1, P2, and P3. Each conflict point presents the location of a possible collision with the through opposing movement.

The data acquisition hardware for the study site consisted of two components:

1. Video cameras to collect the visual scene (Figure 1b). Four cam-eras were installed at the intersection (one camera for each approach) to provide a video feed of the entire intersection environment at 10 frames per second.

2. Weather station (Figure 1c). The weather station provided weather information every minute. The collected weather data

FIGURE 1 Study setup: (a) layout of intersection, (b) video surveillance system, and (c) weather monitoring system.

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included precipitation, wind direction, wind speed, temperature, barometric pressure, and humidity level.

Data analysis Process anD Data reDuction results

The data were collected over a 6-month period (from the beginning of December 2009 until the end of May 2010). The data output per day consisted of 15 hourly video files and the corresponding weather measurements. The video data were reduced manually by record-ing the time instant at which a subject vehicle initiated its search to make a left-turn maneuver, the time stamp at which the vehicle made its first move to execute its left-turn maneuver, and the time the left-turning vehicle reached each of the conflict points. In addi-tion, the time stamps at which each of the opposing vehicles passed the conflict points were identified. Unfortunately, it was not pos-sible to identify the type of vehicle because of the low quality of video data especially under inclement weather and nighttime conditions.

Each rejected or accepted gap was recorded as an observation in the reduced data set and the corresponding variables for each obser-vation were also recorded. The total data set consisted of 9,058 gap observations (10.5% accepted gaps and 89.5% rejected gaps). The reduced variables for each observation were as follows:

• Gap size,• Weather condition,• Weather station measurements (precipitation, wind speed,

barometric pressure, and temperature),• Waiting time for each offered gap,• Illumination (day or night),• Lane number of the offered gap, and• Decision of the driver regarding the offered gap (accept or reject).

The gap size g is a continuous variable measured in seconds and defined as the time headway difference between the passage of the front bumper of a lead vehicle and the following vehicle at a refer-ence point (P1, P2, or P3) in the opposing direction as presented in Figure 1a. The analysis assumed that left-turning vehicles heading for South Depot Street were similar in gap acceptance behavior to left-turning vehicles heading for North Depot Street. The reduced data set was classified into three main categories for weather conditions

depending on the precipitation type and roadway surface condition (Table 1).

The collected data were divided into three main weather catego-ries as shown in Table 1: DD, RW, and SS. Figure 2 presents screen-shots from the recorded videos at the studied intersection showing the different weather categories.

The distributions of the recorded (accepted, rejected, and total) gaps corresponding to different weather categories are shown in Figure 3. For the on-site weather station, the measurements were extracted each minute and synchronized with the gap acceptance or rejection decision. In the reduced data set, the snow precipita-tion ranged from 0.025 cm/h to 0.25 cm/h and the rain precipitation ranged from 0.025 cm/h to 1 cm/h as presented in Figure 3, d and e. The average recorded measurements for wind speed, barometric pressure, and temperature were 3.45 km/h, 106 mbar, and 3°C, respectively.

In addition, the waiting time for each observation (i.e., each offered gap) was recorded in the data set as shown in Figure 3f. The illumina-tion (day or nighttime) condition corresponding to each gap accep-tance or rejection was also recorded; day–night was considered as a binary variable (1 for day and 0 for night). The lane number variable indicates the location of the offered gap with respect to the left-turning vehicle. The lane number variable was flagged as 1, 2, or 3 cor-responding to the conflict point P1, P2, or P3, respectively. At the end, the gap decision was recorded as a binary variable (0 = rejection and 1 = acceptance) and modeled as the response variable. The observed decision making (accept or reject the offered gap) and the correspond-ing variables were aggregated in one database, which will be used for the IDS proposed system as will be described later.

TABLE 1 Weather Condition Categories

Weather Condition

Weather Category PrecipitationRoadway Surface

Number of Observations

Category 1 (DD) Dry Dry 1,348

Category 2 (RW) Rain Wet 4,694

Category 3 (SS) Snow Snowy 3,016

Note: DD = dry precipitation and dry surface; RW = rain precipitation and wet surface; SS = snow precipitation and snowy surface.

(a) (b) (c)

FIGURE 2 Screenshots from recorded videos of intersection showing different weather conditions.

Zohdy and Rakha 23

idS OveRview

There are several traditional countermeasures for reducing crossing-path crashes at controlled intersections. One countermeasure entails installing signs that warn drivers on the major roadway of possible merging or crossing traffic. Other countermeasures focus on the minor movements (e.g., permissive left-turning vehicles). Warning or advisory signs are some of the ways to increase drivers’ awareness and would help drivers entering from the minor roadway in choosing an appropriate gap to enter the intersection. The integration of infra-structure and vehicle systems offers new possibilities to improve traffic safety, throughput, and quality of life (17).

In early 2009, the U.S. Department of Transportation (U.S. DOT) re-branded the infrastructure and vehicle systems initiative as

“IntelliDrive” (18). The re-branding involved more than just chang-ing the name of the initiative. U.S. DOT also changed some of the basic assumptions related to how vehicles and infrastructure compo-nents of the system would communicate. One major change relaxed the constraint that all vehicle-to-vehicle and vehicle-to-infrastructure communications would use dedicated short-range communication radios and protocols (18). U.S. DOT recently changed the name “IntelliDrive” to “Connected Vehicle Research Program”; however, the same concepts and motivations of the IntelliDrive initiative were retained. The main Connected Vehicle Research Program purposes are to provide connectivity among vehicles (vehicle to vehicle, vehicle to infrastructure, and vehicle to hand-held devices) for crash prevention, safety, mobility, and environmental benefits. The safety applications have the potential to reduce crashes through advisories

FIGURE 3 Data set distributions: (a) accepted gap size, (b) rejected gap size, (c) total accepted and rejected (Acc 1 Rej) gap size, (d) snow intensity, (e) rain intensity, and (f) waiting time.

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and warnings for decision guidance. Consequently, IDS is considered one of the main aspects of the Connected Vehicle Research Program safety application for driver guidance to accept or reject an offered gap and prevent crashes and reduce delays.

The FHWA-sponsored Infrastructure Consortium in 2003 (18) consisted of state departments of transportation and universities from California, Minnesota, and Virginia. The consortium created the IDS project, which was formed and given the task of developing technologies and approaches to mitigate the intersection crash prob-lem (18). Three problems were addressed as part of this initiative and divided among California, Minnesota, and Virginia. Virginia addressed signalized and stop-controlled intersection violations and crashes. California studied violations of left turn across path and opposite direction, primarily in urban and suburban settings (19). Minnesota was elected to address crashes at rural through-stop inter-sections because in rural Minnesota, approximately one-third of all crashes occur at intersections (18, 20).

In general, the concept of a left-turning vehicle assistance system (i.e., IDS) has been addressed in several literature sources under various names but with one ultimate goal: reduction of intersection crashes by providing drivers with information to support their crossing decisions. As an example, the intelligent cooperative inter-section safety system generates warning messages to support road users at intersections (17); this system is considered one of the infrastructure-based applications of the European research project SAFESPOT for preventing road accidents by extending the drivers’ awareness in space and time. In addition, the INTERSAFE sub-project within the European research project PREVENT had a similar aim (21), although it was considered a vehicle-based appli-cation. INTERSAFE incorporated different types of vehicle sensors to identify and track vehicle motions and warn drivers of potential conflicts. The U.S. Cooperative Intersection Collision Avoidance Systems (CICAS) program also uses vehicle- and infrastructure-based technology and communication systems to transmit warnings between the infrastructure and equipped vehicles (22). Misener et al. presented the concept of CICAS–SLTA (Cooperative Intersection Collision Avoidance System–Signalized Left Turn Assistance) as a part of the California Partners for Advanced Transit and Highways

(PATH) program (23). The CICAS–SLTA project addressed the sen-sor testing, field data collection, human factors, and simulation for left-turning vehicles using naturalistic data. The research showed that no evidence was found to rule out the potential for providing decision support to drivers through either infrastructure or an in-vehicle display (23).

In a trade-off study for wireless communications technologies that could be implemented in the IDS application, technologies were compared and analyzed by Virginia Tech Transportation Institute (24) in 2006. The feasibility of several wireless communications technolo-gies was evaluated for intersection-based safety system applications. These technologies were considered independent of their use in sig-nalized or stop-controlled intersections. The report recommended dedicated short-range communications as the method to be used for critical safety applications that require both high availability and low latency communications (i.e., for decision support systems) (19).

The IDS system proposed in this paper is considered an infrastructure-based application in which the warnings are generated at the infrastructure by using sensor information and weather station input. However, the proposed system could be extended to send a warning from the infrastructure directly to an equipped vehicle in the future.

pROpOSed idS SyStem, idS-w

The proposed IDS-W system provides the left-turning driver with the appropriate decision (accept or reject the offered gap) taking into consideration the impact of weather condition (dry, rain, and snow), gap size, gap location, and illumination (day or night). The advisory (guidance) decision may be displayed as a green arrow for accepting the gap and a red arrow for rejecting the gap (Figure 4), under given assumptions, as follows:

• The intersection is fully equipped with roadside sensors for detecting the speed of vehicles;• The infrastructure-based receivers are able to detect the

trajectories of approaching vehicles for gap size estimation;

(a) (b)

FIGURE 4 Different decision guidance outputs for left-turning vehicles during green light phase of approach for IDS-W: (a) accept offered gap and (b) reject offered gap.

Zohdy and Rakha 25

• The IDS-W display indicates to the driver that it is safe to turn (could proceed with the turn) but leaves the turning initiative to the driver;• The design logic or problem-solving algorithm is suitable for

a large fraction of the driving population and the solution process is completed in milliseconds (i.e., a real-time system);• The system is able to operate under different weather (dry, rain,

or snow) and illumination (day or night) conditions;• The system is applicable for the same range of traffic speeds

(≈35 mph) and flows that would be expected at intersections with permissive left turns; and• The system is able to learn and to update the stored database.

Consequently, with the premise that the driver’s attention has been captured, the IDS-W system will provide a driver with timely and relevant information regarding unsafe conditions. The IDS-W system (infrastructure based) will be provided with data from mul-tiple sensors that measure the gap size offered to each driver and the corresponding weather condition. The IDS-W device will process the information gathered from the sensors (input data) in order to estimate the decision guidance (output data), that is, accepting or rejecting the offered gap, by using the collected field data set. In integrating the input, the output, and the stored database, the model uses CBR as a problem-solving algorithm.

CBR AlgORithm

CBR is a problem-solving paradigm that has been used in many disciplines over the past years. No consistent CBR method is suit-able for every domain of application; however, the main concept of CBR is to solve a problem (case) by remembering previous similar cases and by reusing the corresponding information and knowledge. In CBR terminology, a case usually denotes a prob-lem situation (25). An important feature of CBR is its ability to learn from a previously experienced situation (stored case) that can be reused in the solving of future problems. Consequently, the CBR method is considered quite different from other major artificial intelligence approaches since it depends on specific knowledge of previous experience and not on general knowledge or attributes (25).

The roots of CBR in artificial intelligence are found in the work of Schank on dynamic memory and the central role that a reminder of earlier situations (episodes, cases) and situation patterns (scripts, measures of performance) has in problem solving and learning (26). Central tasks that all CBR methods have to deal with are to identify the current problem situation, find a past case similar to the new one, use the case to suggest a solution to the current problem, evaluate the proposed solution, and update the system by learning from this experience.

CBR has been successfully applied to a wide variety of applica-tion areas including philosophy and psychology (27–29), diagnostic systems (30, 31), and real-time control problems (32). CBR has also been applied in many transportation problems (33–38); however, a novel application is presented here for the CBR algorithm in the IDS system for left-turning vehicles.

In general, as mentioned before, the CBR process is a case database that stores previous instances of problems and their derived solutions. The CBR cycle starts with entering a new case (input) followed by four main steps (25):

1. Retrieve the most similar case or cases,2. Reuse the information and knowledge in that case to solve the

problem,3. Revise the proposed solution, and4. Retain the parts of this experience likely to be useful for future

problem solving.

For this study, the case is defined as the gap size offered to the left-turning vehicle with its corresponding attributes. The input information for each case in the CBR cycle consists of the offered gap size, the lane number (location) of the offered gap, day or night (for visibility indication), and the corresponding weather category (DD, RW, or SS). The proposed system is anticipated to be applied on the same studied intersection after the collected data set has been stored for the matching step with any new case input.

For future application to different intersections, the stored cases data set will be empty in this situation and the system will begin to record cases to build the database (learning stage). As well, the col-lected data set in the studied intersection of this paper may be used as an initial (reference) data set to other intersections while a new case database is built. Figure 5 summarizes the CBR algorithm for estimating the output decision from an input case with the collected field data as a stored database.

The given input combinations create a new entry case and lead to the first step of the CBR cycle, the retrieve case. First the CBR system compares the new problem with the stored cases in the collected field data, and the result will be that a matching case is found or not found. Since the retrieved case is likely to be somewhat different from the current case, a CBR system typically adapts the retrieved solution to closely suit the new problem during the reuse step by searching for the closest case (case with the least gap difference).

After the initial decision output from the reuse case is estimated, the following step would be the revise case. In this step, the deci-sion output is validated and tested to overcome irrational outputs by using the following rules. If the decision output for the input case is “accept the gap” and the decision corresponding to any larger gap in the stored database is “reject the gap,” the final decision output would be changed to “reject the gap.” Similarly, when the initial decision is “reject the gap” and the decision for a smaller gap is the opposite, the final decision will change to “accept the gap.” In all other cases, the initial decision will remain the same. Simultaneously, in the case of offering a gap smaller than 2 s, the default output for the system is “reject the gap” and if it is larger than 12 s, the decision is “accept the gap.” After the initial decision is revised and the final output is estimated, the retain case in the final stage confirms the output and stores the case as a learned case in the database for future use. At the end, as mentioned before, it is assumed that the CBR cycle will be accomplished in milliseconds to providing the driver with real-time decision guidance.

idS-w SyStem vAlidAtiOn

In order to validate the IDS-W system framework, 80% of the collected field data (randomly selected) was used as the stored case database and the proposed framework was applied on the remaining new cases (20% of the data). The 80/20 split is typically used in the literature when training and validation data sets are needed. This step was repeated 1,000 times using a Monte Carlo simulation and the waiting time was recorded at each time and compared with the original (observed) waiting time stored in the data set. The difference

26 Transportation Research Record 2324

between the new recorded waiting time (with the IDS-W system) and the observed waiting time in the original data set (without the IDS-W system) is considered the waiting time reduction for each vehicle.

In the collected (stored) data set, many observations could be found with the same gap size and sometimes with inconsistent decisions (accept and reject). Therefore, in order to choose the appropriate decision guidance, the system is set to select the adequate percentile of the stored decision list corresponding to the input case. However, there is a trade-off between selecting a high percentile that leads to a reduction in the delay time (waiting time) but increases the colli-sion risk and the opposite case in the selection of a low percentile. Consequently, the percentile of the chosen decision from the stored

list of decisions (corresponding to the same case) is varied in the validation process. Figure 6 shows the relative frequency of the average waiting time reduction values per vehicle after application of the Monte Carlo simulation for different percentiles of the stored decisions list.

It is observed that by increasing the selected percentile (i.e., the system is more biased to the aggressive drivers’ stored decisions), the waiting time decreases (reduction in waiting time increases) for each vehicle. The waiting time reduction values on average are as follows: 4.20 s, 6.12 s, 7.51 s, and 7.67 s for the 50th, 75th, 95th, and 99th percentiles, respectively. Consequently, it could be stated that in general the IDS-W would be able to reduce delays for crossing vehicles at intersections in addition to increasing drivers’ awareness in severe weather conditions.

COnClUSiOnS And ReCOmmendAtiOnS fOR fURtheR wORk

The research presented developed a driver support system that assists drivers in their gap acceptance decisions for permissive left-turning movements under different weather conditions. As a result, a new framework is proposed for a real-time IDS system for left-turning vehicles that uses collected field data for different weather conditions: IDS-W.

The system was tested with a data set collected from the sig-nalized intersection of Depot Street and North Franklin Street in Christiansburg, Virginia. The intersection was equipped with four video cameras and an on-site weather station that collected the gap acceptance or rejection observations. Each observation consisted of the driver decision, weather condition (dry, rain, or snow), illumina-tion (day or night), gap size, and gap offered location (lane number). The observed decision (to accept or reject the offered gap) and the corresponding variables were fused and aggregated in one database to develop the IDS-W system. The developed system provides the driver with timely, relevant information regarding unsafe conditions. The IDS-W system (infrastructure based) is expected to include mul-tiple sensors that measure the gap size offered to each driver and the corresponding weather condition.

The IDS-W device would process the information gathered from the sensors (input data) in order to compute a decision (output data), that is, to accept or reject the offered gap, using the collected field data. A CBR approach is used to solve the problem. The CBR principle con-sists in solving a new problem, for which the solution is unknown, by using similar problems from historical information.

In validating the framework, 80% of the collected data set was randomly selected and stored as the historical cases. The algorithm was then used to provide guidance on the remaining 20% of the data. This approach was repeated 1,000 times with a Monte Carlo simulation. Because of intra- and interdriver variability, contradictory decisions may exist (e.g., accept a smaller gap or reject a larger gap) in the input database. In resolving these contradictory decisions vari-ous percentile decisions were considered (50th, 75th, 95th, and 99th), where a higher percentile would result in more risk associated with a decision but less delay. The system validation demonstrated that the system was capable of reducing the average wait time significantly while at the same time providing drivers with safe gap acceptance decisions.

For future applications, the proposed system could be applied in different gap acceptance situations (merging onto freeways, stop-sign-controlled intersections, roundabouts, etc.); however, the system

FIGURE 5 CBR algorithm for estimating output decision in IDS-W framework.

Zohdy and Rakha 27

will first need to gather and store cases as part of the learning process. The necessary time and data required to develop a learning database is an area of research that requires further analysis. Consequently, it is recommended that this framework be tested at different inter-sections and for different gap acceptance applications before the system is ready for field implementation.

ACknOwledgmentS

The authors acknowledge the valuable input of Roemer Alfelor and David Yang of FHWA and Daniel Krechmer of Cambridge Sys-tematics, Inc. The authors also acknowledge funding from the U.S. Department of Transportation for gathering the field data and from the Mid-Atlantic University Transportation Center for developing the proposed framework.

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13. Caird, J. K., and P. A. Hancock. Left-Turn and Gap Acceptance Crashes. In Human Factors in Traffic Safety (R. E. Dewar and P. Olson, eds.), Lawyers & Judges Publishing, Tucson, Ariz., 2002, pp. 613–652.

14. Zohdy, I., S. Sadek, and H. A. Rakha. Empirical Analysis of Wait Time and Rain Intensity Effects on Driver Left-Turn Gap Acceptance Behavior. In Transportation Research Record: Journal of the Transportation Research Board, No. 2173, Transportation Research Board of the National Academies, Washington, D.C., 2010, pp. 1–10.

15. Rakha, H., S. Sadek, and I. Zohdy. Modeling Stochastic Left-Turn Gap Acceptance Behavior. Presented at 89th Annual Meeting of the Trans-portation Research Board, Washington, D.C., 2010.

16. Zohdy, I., H. A. Rakha, R. Alfelor, C. Y. D. Yang, and D. Krechmer. Impact of Inclement Weather on Left-Turn Gap Acceptance Behavior of Drivers. In Transportation Research Record: Journal of the Transporta­tion Research Board, No. 2257, Transportation Research Board of the National Academies, Washington, D.C., 2011, pp. 51–61.

FIGURE 6 Relative frequency of average waiting time reduction values per vehicle attributed to IDS-W system with percentiles of stored decision list.

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cy50th percentile of the stored decisions75th percentile of the stored decisions95th percentile of the stored decisions99th percentile of the stored decisions

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The Intelligent Transportation Systems Committee peer-reviewed this paper.