Development of Left-Turn Lane Warrants for Unsignalized Intersections (2013)

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61 CHAPTER 4 DRIVER BEHAVIOR STUDY BACKGROUND While many intersections in urban environments are signalized, numerous intersections are unsignalized and have considerable left-turn activity. Particularly in areas with dense development, left-turn movements can be problematic because a wide variety of activity (through traffic, pedestrian traffic, parking maneuvers, etc.) usually occurs in a confined space and competes for the driver’s attention. The confined space in many dense urban developments also generally prohibits the addition of left-turn lanes where none currently exist; in other locations, the road surface is restriped to create a left-turn lane alongside narrower through lanes. As a result, left turns in dense urban environments take place in conditions where drivers must consider many factors in making the decision to complete a left-turn maneuver; drivers’ responses to these factors are reflected in their behavior. Some of these behavioral evidences (e.g., positioning in the lane, accepted gap, time to complete the turn, time spent waiting to turn at the head of the queue, etc.) can be measured and subsequently analyzed for patterns and trends. For this project, videotaped observations recorded vehicle and pedestrian operational characteristics. Video recording permits review and data reduction after the actual crossing event occurs—a valuable approach when trying to measure turning events or gaps accepted. STUDY OBJECTIVES The objectives of the driver behavior study were to: • Obtain needed data for calibrating the simulation model and • Obtain data to update the Harmelink (1) procedure. STUDY LOCATION To conduct this research, left-turn movements were studied at 30 sites that were located in the following metropolitan areas: • College Station/Bryan, Texas; • Houston, Texas; • Staten Island, New York; and • Phoenix, Arizona. The sites were selected based on a variety of intersection arrangements and geometric characteristics, including: • Number of lanes on the major roadway—two or four lanes; • Presence of a left-turn lane—yes or no;

62 • Signal coordination—location is near enough to a signal to be affected or far enough from a signal to result in random arrival; and • Approach speed range—low or high speed, with posted speed limits between 25 and 40 mph being defined as low speed and posted speed limits of 45 mph or more being defined as high speed. Table 38 lists the 30 sites used in this study and their corresponding geometric characteristics. DATA COLLECTION At the Texas sites, the data were collected through the use of video cameras mounted on a data collection trailer. The cameras were raised approximately 30 ft high to record a bird’s-eye view of the study area. Figure 13(a) shows the trailer with the mast arm extended at one of the sites. At the Arizona and New York sites, camcorders were used. Figure 13(b) illustrates one installation. The video recorded the movements at the intersection for at least 4 hours, observing the advancing/opposing traffic and left-turn movement. A time stamp was imprinted on the video so that the precise times of each turning movement could be reduced from the video. In addition to the video, site-specific data about the intersection were collected, including the geometric characteristics and measurements as well as detailed photographs of the intersection. DATA REDUCTION Following the data collection, each site’s data were reduced to obtain the necessary information for the analysis. The reduction process began with reviewing the site video and obtaining turning movement counts using 5-minute intervals. The goal for each site was to obtain data for a minimum of 100 left-turning vehicles whose drivers had to make a decision based on the available gaps in the opposing traffic. In most cases, a 1-hour time interval provided the desired sample size. However, some sites did not have 100 left-turning vehicles within the 1-hour timeframe; therefore, additional hours were reduced for those sites. The turning movement counts were reviewed to determine which time period to reduce. Within that time period, actions of interest for each left-turning vehicle and opposing vehicle were recorded. In addition to the time of arrival of the opposing vehicles, the following times for each left- turning vehicle were recorded: • Time at the back of the queue, • Time at the front of the queue, • Time at the start of the left-turn maneuver, • Time to clear the approaching lane, • Time to clear the median and/or median lane (where applicable), • Time to clear opposing lane 1, and • Time to clear opposing lane 2 (where applicable).

63 Table 38. Site characteristics. Site Legs Left- Turn Lane? Median Opposing Crossing Width (ft) Opposing Lanes Posted Speed Limit (mph) Signal Densitya AZ-01 4 Yes Flush 22.00 2 40 High AZ-02 3 Yes Flush 23.00 2 45 Low AZ-03 3 No None 24.00 2 40 Low AZ-04 3 Yes Flush 17.00 1 25 Low AZ-05 3 No None 24.00 2 40 Medium AZ-06 3 No None 20.00 1 30 High AZ-07 4 No None 22.00 1 25 High AZ-08 3 Yes Flush 19.00 1 35 High AZ-09 4 Yes Flush 25.00 2 40 Low AZ-10 4 No None 25.00 1 25 Medium AZ-11 3 Yes Flush 22.00 1 35 Medium AZ-12 3 Yes Flush 22.00 2 40 High AZ-14 3 Yes Flush 22.00 2 50 Low AZ-15 3 Yes Flush 24.00 2 55 Low NY-01 3 No None 21.00 2 30 Medium NY-02 3 No Raised 20.50 2 30 High NY-03 4 No None 19.67 1 30 High NY-04 3 Yes Raised 27.00 2 40 High TX-01 3 Yes Flush 11.00 1 45 Low TX-02 4 No None 21.00 1 65 Low TX-03 3 No None 22.00 2 30 Medium TX-04 3 No None 23.50 2 35 Medium TX-05 3 Yes Raised 24.00 2 45 Low TX-06 3 No Flush 23.00 2 45 Medium TX-07 3 No None 22.33 1 60 Low TX-08 4 Yes Flush 12.00 1 40 Medium TX-09 4 Yes Raised 24.00 2 40 Low TX-10 4 Yes Flush 23.00 2 40 Medium TX-11 3 Yes Raised 26.00 2 55 High a Signal density: • High = more than 2 signals/mile • Medium = between 1 and 2 signals/mile • Low = less than 1 signal/mile

64 (a) Elevated video cameras (b) Ground-level video cameras Figure 13. Examples of equipment used for data collection. RESULTS To apply Harmelink’s procedure and determine left-turn lane warrants, the following variables are needed: • Time required for a left-turning vehicle to clear the advancing stream, • Time to complete a left turn, and • Critical gap. Average Time-to-Clear or Time-to-Turn Values A total of 3570 vehicles were observed in the field studies. Heavy trucks only represented a small portion of the data collected (39 vehicles), and since their operations are known to be slower than passenger cars, they were excluded from the evaluations. Of the remaining vehicles, 2945 vehicles started from a stopped position. A vehicle was included as starting from a stopped position if the vehicle spent at least 0.25 sec between arriving at the front of the queue and starting the left-turn maneuver. Table 39 lists the time-to-clear values for passenger cars for each site. In addition to calculating the average value, the average plus one standard deviation was also calculated, which allows the left-turn lane warrants to be designed for a greater portion of drivers, as opposed to only half of the drivers. The Harmelink procedure used average time to clear, or turning times.

65 Table 39. Time-to-clear and time-to-turn values for passenger cars starting from a stopped position at each site. Site Number of Vehicles Average (sec) Average + Standard Deviation (sec) Clear Approach Lane Clear Opposing Lane Time to Turn Time to Clear Approach1 Time to Clear Opposing2 Time to Turn AZ-01 100 1.01 2.38 3.38 1.39 3.00 4.35 AZ-02 77 0.79 2.14 2.93 1.12 2.70 3.79 AZ-03 69 0.91 2.47 3.38 1.21 2.95 4.11 AZ-04 155 1.34 3.08 4.42 1.74 3.74 5.37 AZ-05 85 1.24 3.15 4.40 1.68 3.90 5.52 AZ-06 15 1.30 3.42 4.72 1.94 4.43 6.08 AZ-07 65 0.83 2.88 3.71 1.26 3.55 4.68 AZ-08 92 0.94 2.06 3.00 1.39 2.81 4.12 AZ-09 96 0.89 2.37 3.27 1.24 2.90 4.10 AZ-10 40 2.21 4.45 6.66 3.06 5.61 8.62 AZ-11 80 1.42 3.26 4.68 1.88 4.00 5.82 AZ-12 100 1.19 2.90 4.09 1.67 3.60 5.21 AZ-13 40 1.32 2.92 4.24 2.06 4.01 6.05 AZ-14 30 1.68 3.40 5.08 2.42 4.22 6.55 AZ-15 286 0.95 2.78 3.74 1.34 3.48 4.76 NY-01 100 0.80 2.12 2.93 1.14 2.68 3.76 NY-02 89 0.86 2.23 3.09 1.34 3.00 4.29 NY-03 85 1.01 2.53 3.53 1.36 3.20 4.52 NY-04 95 0.95 2.75 3.70 1.34 3.37 4.65 TX-01 219 0.99 2.01 3.00 1.31 2.51 3.79 TX-02 340 0.98 2.14 3.11 1.39 2.77 4.11 TX-03 113 0.80 2.28 3.08 1.10 2.78 3.79 TX-04 89 1.02 2.46 3.47 1.48 3.19 4.61 TX-05 120 1.24 2.56 3.80 1.67 3.07 4.72 TX-06 100 0.78 2.43 3.21 1.11 2.99 4.06 TX-07 32 1.17 2.20 3.36 1.65 2.81 4.41 TX-08 58 1.57 2.46 4.03 2.05 2.97 5.01 TX-09 42 2.05 3.49 5.54 2.96 4.50 7.45 TX-10 47 1.74 3.14 4.88 2.23 3.73 5.95 TX-11 86 1.99 3.79 5.78 2.67 4.75 7.39 1 Time to clear approach = elapsed time from the start of the turning maneuver to the time when no part of the turning vehicle remains in the approach lane (e.g., rear bumper has crossed the centerline) 2 Time to clear opposing = elapsed time from the start of the turning maneuver to the time when no part of the turning vehicle remains in the opposing lane (e.g., rear bumper has crossed the curb line extended)

66 Figure 14 shows each site’s average turning time by crossing distance, subdivided by the number of lanes and the presence of a left-turn lane (LTL). The plot shows a general trend of longer turning times for wider crossing distances, although it also shows small turning times for some of the wider crossing distances. The effects of crossing width may not be obvious in this plot because the effects of other variables, such as posted speed limit, may be influencing the values. Harmelink provided values for a two-lane highway and a four-lane highway (see Table 40). Table 40 compares the findings from this study with findings from previous studies. The average turning time for the sites included in this study was determined by the number of lanes and by generally assumed crossing widths for crossing one lane (12 ft or less) and crossing two lanes (22 ft or more). When subdividing by the number of lanes being crossed (see the second-from- bottom row in Table 40), the average turning time for these 30 study sites were similar—about 3.6 sec. As can be seen in Figure 14, at some sites, some vehicles crossing one lane traveled similar distances as when crossing two lanes. When only including those sites with more typical crossing widths, the average turning times are similar to the values assumed by Harmelink. For example, crossing 11 or 12 ft took an average of 3.2 sec, while Harmelink assumed 3.0 sec. Harmelink assumed a four-lane highway would have a 4.0-sec crossing time, while the sites in this study with a width greater than 22 ft took 3.7 sec. This comparison demonstrates that only including “typical” crossing widths of 12 ft for one lane and 22 ft or greater for two lanes removes several sites. Stated in another manner, several sites do not fit the “typical” lane width mode. The evaluation procedure may be better if it considers the crossing distance rather than just the number of lanes. This permits consideration of shoulders, bike lanes, and other conditions that increase the crossing distance. Figure 14. Plot of average turning time by crossing distance. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 10 12 14 16 18 20 22 24 26 28 A ve ra ge T ur ni ng T im e (s ec ) Crossing Distance (ft) 2 Lanes, without LTL 1 Lane, without LTL 2 Lanes, with LTL 1 Lane, with LTL

67 Table 40. Comparisons of turning times for passenger cars. Study Average Clear Approach Lane (sec) Average (85th Percentile for Previous Studies or Average + Standard Deviation for Current Study) Turning Time (sec) Two-Lane Highway Four-Lane Highway Harmelink (1) 1.9 sec (based on 150 vehicles) 3.0 sec 4.0 sec 1994 Green Book (7), Figure IX-33 Not calculated 4.3 sec (passenger car, based on 47-ft path) Miscky and Mason (71), 2 Pennsylvania Intersections Not provided 4.0 (4.6) sec 4.3 (5.1) sec Not studied Fitzpatrick and Wolff (13), 1 Texas Intersection Not provided 3.4 (4.1) sec (based on 71 vehicles) Not studied Current Study (Subdivided by Number of Lanes) 1.1 sec (based on 2945 vehicles) 3.6 (4.7) sec (based on 1181 vehicles) 3.7 (5.1) sec (based on 1764 vehicles) Current Study (Grouped by Typical Crossing Width) 1.1 sec (based on 2945 vehicles) 3.2 (4.1) sec (based on 277 vehicles, crossing width of 11 or 12 ft) 3.9 (5.4) sec (based on 1264 vehicles, crossing widths of 22 to 27 ft) 3.6 (4.8) sec (based on 1404 vehicles, crossing width of 12.5 to 21.5 ft) Creating Prediction Equations Several variables were available for investigating the influence on time-to-clear values, including variables specific to the vehicle/driver and variables associated with the intersections. Time-to-clear values are: • Clear approach lane (sec); • Clear opposing lane(s) (sec); and • Turning time, which was a sum of clear approach lane and clear opposing lane values (sec). Vehicle/driver variables are: • Accepted lag or gap time (sec), • Time in the queue (sec), and • Time at the head of the queue (sec). Intersection variables are: • Number of legs (four or three legs), • Presence of a left-turn lane (yes or no), • Median type (flush, none, or raised),

68 • Crossing width (ft), • Number of lanes (crossing either one or two lanes), • Posted speed limit (mph), and • Signal density (high is more than two signals per mile, medium is between one and two signals per mile, and low is less than one signal per mile). Over 3500 driver maneuvers were available for the investigation. The following discussion focuses on the turning time evaluation. Analysis of the time-to-clear values began with considering which variables to include in the models. Initially, the number of lanes was believed to be correlated with crossing width, and therefore both variables would not be included in the same model. Additional investigations revealed that when the left-turning vehicle is crossing one lane, it is crossing between 11 and 25 ft of pavement. When the vehicle is crossing two lanes, it is crossing between 20.5 and 27 ft of pavement. Therefore, there is some overlap in crossing distance values. Several of the sites with one lane had a parking lane or bike lane, which can reinforce the impression that the site is a lower-speed facility. Therefore, both variables were considered in the models. Because both random effects from drivers and fixed effects from the intersection characteristics are present, a linear mixed-effects model was used. Several combinations of variables were considered. A log transformation was used with the accepted gap/lag time, the head of the queue time, and the time in the queue. Posted speed limit was tried as both a continuous variable and as a discrete variable. The presence of a left-turn lane, signal density group (low, medium, or high), and number of lanes were all discrete variables. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used to select the better models. Table 41 shows the model selected for turning time. To provide an appreciation for the impacts the variables have on predicting turning time, a reasonable range for each variable was selected. This range was used in the equations to illustrate each variable’s contribution to the total turning time. Figure 15 lists the range selected for low, middle, and high and shows the plots of the results. The x-axis uses 1 to represent low, 3 to represent middle, and 5 to represent high values. Those variables that plot close to 0 (y-axis) have minimum influence on predicting time to turn and include lag/gap time, time at the head of the queue, time in the queue, and the number of lanes. Crossing width (shown with a triangle) followed by posted speed limit (shown with open squares) showed the greatest influences. The continuous lines without markers show the intercept or the predicted time to turn using the assumed values listed in the figure. Figure 16 shows the results by crossing width when using a middle value for gap (7.5 sec), time at the head of the queue (7.0 sec), time in the queue (30.0 sec), and 45-mph posted speed limit. When the crossing width is 26 ft, Figure 16 shows that it takes 4.8 sec to cross a two-lane roadway or 5.3 sec to cross a four-lane roadway. Figure 17 shows the results by posted speed limit when assuming two lanes. If the crossing width is 17 ft, then the predicted turning time is 1.9 sec for 65 mph, 2.3 sec for 55 mph, 2.8 sec for 45 mph, 3.2 sec for 35 mph, and 3.7 sec for 25 mph.

69 Table 41. Regression model for turning time. Linear mixed-effects model fit by maximum likelihood AIC 10220 BIC 10337 logLik −5091 Random effects: Formula: ~log(LGT) + log(TAH) + log(TIQ) | Site (14) Structure: General positive-definite, Log-Cholesky parametrization StdDev Corr Intercept Log(LGT) Log(TAH) Log(TIQ) Residual 0.6946100 0.1229598 0.1756780 0.1039284 0.9942578 (Intr) 0.330 0.403 0.839 (LGT) −0.557 −0.067 (TAH) 0.440 Fixed effects: TT ~ log(LGT) + log(TAH) + log(TIQ) + CW + CW_SQ + PSL + NOL (15) Value Std. Error DF t-value p-value Intercept Log(LGT) Log(TAH) Log(TIQ) CW CW_SQ PSL NOL2 8.500324 0.079616 0.376136 0.115794 −0.511235 0.017133 −0.045157 −0.525688 2.0449751 0.0312464 0.0353656 0.0255075 0.2145448 0.0057080 0.0097226 0.2570695 3498 3498 3498 3498 25 25 25 25 4.156688 2.547988 10.635661 4.539611 −2.382880 3.001602 −4.644551 −2.044925 0.0000 0.0109 0.0000 0.0000 0.0251 0.0060 0.0001 0.0515 Where: • TT = turning time (sec), • LGT = accepted lag or gap time (sec), • TAH = time at the head of the queue (sec), • TIQ = time in the queue (sec), • CW = crossing width (ft), • CW_SQ = square of crossing width (ft), • PSL = posted speed limit (mph), and • NOL2 = inclusion of the indicator variable when the number of lanes is 2. Equation: TT = 8.500324 + 0.017133 × CW2 – 0.511235 × CW + 0.079616 × log(LGT) + 0.376136 × log(TAH) + 0.115794 × log(TIQ) – 0.045157 × PSL – 0.525688 × NOL2 (16)

70 Variables Low Value Middle Value High Value Accepted Lag/Gap Time (sec) Time @ Head of Queue (sec) Time in Queue (sec) Crossing Width* (ft) Posted Speed Limit (mph) Number of Lanes Crossed Is 2 3.0 sec 0.5 sec 1.0 sec 12 ft 25 mph Yes 7.5 sec 7.0 sec 30.0 sec 21 ft 45 mph Yes 20.0 sec 15.0 sec 60.0 sec 30 ft 65 mph Yes *considers both crossing width squared and crossing width: CW^2-CS Figure 15. Variable’s contribution to predicting turning time using low, middle, and high values. -6 -4 -2 0 2 4 6 8 10 1 2 3 4 5 V ar ia bl e' s C on tr ib ui on t o Ti m e- to -T ur n V al ue fo r R an ge of V ar ia bl e V al ue s (s ec ) 1=Represents low value for variable, 5=high value for variable Lag/Gap Time Time @ Head Time in Queue CW^2-CW Posted Speed L imit Num Lanes=2 Intercept SUM, 2 Lanes SUM, 4 Lanes

71 (a) Contribution of Variable to Turning Time (b) By Number of Lanes Variables Assumed Value Accepted Log/Gap Time (sec) Time @ Head of Queue (sec) Time in Queue (sec) Crossing Width (ft) Posted Speed Limit (mph) 7.5 sec 7.0 sec 30.0 sec 12 to 30 ft 45 mph Figure 16. Variables’ contribution to predicting turning time by crossing width. -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 12 14 16 18 20 22 24 26 28 30 Tu rn in g Ti m e by V ar ia bl e (s ec ) Crossing Width (ft) Lag/Gap Time Time @ Head Time in Queue CW^2-CW Posted Speed L imit Num Lanes=2 Intercept 2.0 4.0 6.0 8.0 12 14 16 18 20 22 24 26 28 30 Tu rn in g Ti m e (s ec ) Crossing Width (ft) 2 lanes 4 lanes

72 Variables Assumed Value Accepted Log/Gap Time (sec) Time @ Head of Queue (sec) Time in Queue (sec) Crossing Width (ft) Number of Lanes Crossed Is 2 7.5 sec 7.0 sec 30.0 sec 12 to 30 ft Yes Figure 17. Turning time by posted speed limit (assumed two-lane highway). The most influential variables are crossing width and posted speed limit. A change from a crossing width of 11 ft to 27 ft results in an additional 2.24 sec in total turning time when other variables are set to the middle values listed in Figure 15. The posted speed limit variable is associated with a decrease in turning time for the higher speeds. For turning time, an additional 1.81 sec is subtracted when the roadway has a 65-mph posted speed as compared to a 25-mph posted speed limit. The posted speed limit range represented in the dataset is 25 to 65 mph. The amount of time spent at the head of the queue had a statistically significant impact on turning time. Initial expectation was that as drivers have to wait for an acceptable gap, they drive faster to clear the roadway. However, the relationship was in the opposite direction. As the amount of time at the head of the queue increases, the clearance times also increase, but only by a small amount. A representative range observed for the 30 sites was between 1 sec and 15 sec at the head of the queue. A change from a 1-sec to 15-sec time at the head of the queue value results in an additional 0.44 sec in total turning time when other variables are set to the middle values listed in Figure 15. 0.0 2.0 4.0 6.0 8.0 12 14 16 18 20 22 24 26 28 30 Tu rn in g Ti m e (s ec ) Crossing Width (ft) 25 35 45 55 65

73 A similar condition existed for time in the queue. Expectations were that drivers would drive faster after waiting in a queue. The findings were that drivers took a slightly greater amount of time after waiting in a long queue; however, the increase was very small. A representative range observed for the 30 sites was between 1 and 60 sec at the head of the queue. A change from 1 sec to 60 sec in the time at the head of the queue value results in an additional 0.21 sec in total turning time when other variables are set to the middle values listed in Figure 15. The relationship between clearance time and the accepted lag or gap time was in the direction expected although it did not have as large an influence as initially thought. The preliminary thought was that drivers notably drive faster (i.e., lower turning time) when accepting a small gap. The evaluation only found a small increase in clearance time for larger gaps. For a 20-sec gap as compared to a 5-sec gap, the increase in turning time was about 0.05 sec. The difference in clearance time for the number of lanes was also small. Initially it was believed that the number of lanes variable should not be included due to anticipated correlation with crossing width. When verified that it could be included, the expectation was that longer crossing times would be associated with the higher number of lanes. The finding, however, is that the time is decreased by a constant when two lanes are being crossed. For turning time, the amount is about 0.43 sec. In most situations, clearing two lanes was also accompanied by a wider crossing width. The larger time calculated due to the wider crossing width offsets some of the negative time that is added when crossing two lanes. The number of lane variable may be a surrogate for other characteristics of a multilane facility that were not captured in the other variables. The results from the regression models can be used to calculate the turning time for use in Harmelink or other models. The suggested equation is listed in Table 41. Critical Gap Critical gap is defined as the time interval between two opposing vehicles that is necessary for a left-turning vehicle to safely complete a left-turn maneuver. Two methods were used to determine critical gap: logistic regression and Raff/Hart. Logistic regression is appropriate when the dependent variable is binary or dichotomous (e.g., either the acceptance or rejection of a gap). The mean response is a probability when the dependent variable is a 0 or 1 (accept or reject) indicator variable. The shape of the response function is curvilinear and can be approximated using a logistic function. A property of a logistic function is that it can be easily converted into a linear form. The transformation is called the logistic, or logit, transformation. The simple, dichotomous choice logistic function is: ܲሺݔሻ ൌ ଵଵାୣ୶୮ ሾିሺఉబାఉభ௫ሻሿ (17) Where: P(x) = probability of accepting a gap at x; x = value related to the gap acceptance decision, gap length; and

74 βo, β1 = regression coefficients. The logistic function can be converted to a linear form with the following transformation: ݃ ሺݔሻ ൌ ݈݋݃௘ ௉ሺ௫ሻଵି௉ሺ௫ሻ ൌ ሺߚ଴ ൅ ߚଵݔሻ (18) Where: g (x) = logit, transformation of probability P(x). The logistic regression coefficients for each site were determined using the method of maximum likelihood implemented in JMP (SAS product). The maximum likelihood estimates for the coefficients are listed in Table 42. Sample logistic curves for Sites AZ-01, NY-03, and TX-03 are shown in Figure 18. The time gap for a 50 percent probability can be determined by substituting 0.5 for P in the above equation and the regression coefficients for βo and β1. For example, 50 percent of the drivers at TX-03 accepted a 5.02-sec gap, while drivers at AZ-01 accepted a 4.18-sec gap. The following illustrates the calculation of the 50th percentile value for TX-03: ݃ ሺݔሻ ൌ ݈݋݃௘ ଴.ହଵି଴.ହ ൌ ሺെ4.22079 ൅ 0.840289ݔሻ (19) 0 ൌ ሺെ4.22079 ൅ 0.840289ݔሻ x = 5.02 sec Raff and Hart (72) defined the critical lag, L, as the size lag for which the number of accepted lags shorter than L is the same as the number of rejected lags longer than L. Raff and Hart did not include gaps in the study, arguing that one driver will only accept a gap of a particular size, but another driver may reject several gaps of the same size. More recent studies indicate that the acceptance of lags is not significantly different from the acceptance of gaps and that the lag and gap data can be combined (73, 74). Therefore, the lag and gap data for each vehicle maneuver were merged in this study. Raff and Hart used the number of accepted gaps and the number of rejected gaps. The same approach could be used with cumulative percent. Both approaches were used with this dataset with similar results. An example of the Raff/Hart graphical method is illustrated in Figure 19.

75 Table 42. Logistic regression coefficients for field sites. Site βo β1 Calculated Gaps (sec) Using Regression Coefficients 50th Percentile 85th Percentile AZ-01 −7.08753 1.696152 4.18 5.20 AZ-02 −1.77842 0.851137 2.09 4.13 AZ-03 −2.69889 0.81338 3.32 5.45 AZ-04 −10.3758 1.654808 6.27 7.32 AZ-05 −1.81918 0.494428 3.68 7.19 AZ-06 Model Unstable AZ-07 −6.94864 1.285945 5.40 6.75 AZ-08 −3.91809 0.873803 4.48 6.47 AZ-09 −3.70749 0.763491 4.86 7.13 AZ-10 −1.37498 0.533511 2.58 5.83 AZ-11 −3.12467 0.602826 5.18 8.06 AZ-12 −4.21706 0.768667 5.49 7.74 AZ-13 −2.29175 0.347882 6.59 11.57 AZ-14 −29.3524 6.040599 4.86 5.15 AZ-15 −4.12241 0.826803 4.99 7.08 NY-01 −3.83717 1.049497 3.66 5.31 NY-02 −5.57702 1.405221 3.97 5.20 NY-03 −4.42662 1.090183 4.06 5.65 NY-04 −4.11451 0.770901 5.34 7.59 TX-01 −5.59645 1.183262 4.73 6.20 TX-02 −4.88761 0.981591 4.98 6.75 TX-03 −4.22079 0.840289 5.02 7.09 TX-04 −4.07481 1.157537 3.52 5.02 TX-05 −3.54230 0.681631 5.20 7.74 TX-06 −4.07647 0.810744 5.03 7.17 TX-07 −5.54214 0.98852 5.61 7.36 TX-08 −4.00150 0.904033 4.43 6.35 TX-09 −4.91986 0.910026 5.41 7.31 TX-10 −2.09213 0.585126 3.58 6.54 TX-11 −2.32148 0.483307 4.80 8.39

76 Figure 18. Plot of logit model for three field sites. (a) Frequency (b) Percent Figure 19. Illustration of Raff/Hart graphical method for identifying critical gap. The findings from the Raff/Hart method and the logistic regression method are listed in Table 43. The sites were also grouped by crossing distance and posted speed limit to seek trends in gap acceptance values. Previous research in simulators has found that drivers accept smaller gaps at higher speeds. Alexander et al. (75) used a simulator to evaluate turning left from the major road onto the minor road. The velocity of the oncoming traffic was the variable that had the greatest effect on the median accepted gap size. Yan et al. (76) also studied drivers’ gap acceptance decision in a simulator focusing on major traffic speed, driver age, and driver gender. They found that traffic speed had a significant effect on the gap acceptance maneuver. The mean value gap found within the speed, gender, and age groups used by Yan et al. is shown in Table 44. 0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 12 14 P ro ba bi lit y of A cc ep ti ng a G ap Gap (sec) AZ-01 NY-03 TX-03 0 20 40 60 80 100 120 0 5 10 15 20 C um ul at iv e G ap Gap/Lag Length (sec) TX-11 accept reject 0% 20% 40% 60% 80% 100% 0 5 10 15 20C um ul at iv e % o f G ap Gap/Lag Length (sec) TX-11 accept reject

77 Table 43. Results for gap acceptance methods. Site Left- Turn Lane? Posted Speed Limit (mph) Lanes Crossing Width (ft) Raff/Hart Gap Value Logit 50th Percentile Logit 85th Percentile Number of Cars TX-01 Yes 45 1 11 4.82 4.73 6.20 219 TX-08 Yes 40 1 12 5.50 4.43 6.35 170 Weighted average: 5.12 4.60 6.26 195 AZ-04 Yes 25 1 17 6.90 6.27 7.32 151 AZ-08 Yes 35 1 19 4.72 4.48 6.47 104 NY-03 No 30 1 19.67 4.33 4.06 5.65 94 AZ-06 No 30 1 20 3.70 Model unstable 25 Weighted average: 5.43 5.14 6.62 94 NY-02 No 30 2 20.5 4.37 3.97 5.20 94 NY-01 No 30 2 21 4.31 3.66 5.31 79 TX-02 No 65 1 21 6.31 4.98 6.75 268 AZ-01 Yes 40 2 22 4.07 4.18 5.20 99 AZ-07 No 25 1 22 6.51 5.40 6.75 87 AZ-11 Yes 35 1 22 5.72 5.18 8.06 100 AZ-12 Yes 40 2 22 5.25 5.49 7.74 99 AZ-13 Yes 55 2 22 9.03 6.59 11.57 74 AZ-14 Yes 50 2 22 4.77 4.86 5.15 34 TX-03 No 30 2 22 5.19 5.02 7.09 108 TX-07 No 60 1 22.33 7.19 5.61 7.36 33 AZ-02 Yes 45 2 23 3.44 2.09 4.13 97 TX-06 No 45 2 23 6.12 5.03 7.17 100 TX-10 Yes 40 2 23 4.68 3.58 6.54 100 TX-04 No 35 2 23.5 4.27 3.52 5.02 94 AZ-10 No 25 1 25 4.85 2.58 5.83 202 Weighted average: 5.35 4.34 6.51 104 AZ-03 No 40 2 24 4.07 3.32 5.45 69 AZ-05 No 40 2 24 5.67 3.68 7.19 90 AZ-15 Yes 55 2 24 5.77 4.99 7.08 277 TX-05 Yes 45 2 24 6.33 5.20 7.74 114 TX-09 Yes 40 2 24 5.81 5.41 7.31 63 AZ-09 Yes 40 2 25 5.76 4.86 7.13 98 TX-11 Yes 55 2 26 5.69 4.80 8.39 96 NY-04 Yes 40 2 27 5.85 5.34 7.59 92 Weighted average: 5.70 4.79 7.26 112

78 Table 44. Mean values of gap (sec). Speed Yan et al. Simulator Study (76) This Study Female Male Number Vehicles Raff/ Hart Logit 50th Percentile Young Middle Old Young Middle Old 25 mph 7.56 6.97 10.99 6.35 6.60 8.76 440 5.88 4.40 55 mph 6.00 5.63 7.11 5.26 5.61 6.23 447 6.29 5.21 This field study included three sites with a 25-mph speed limit and three sites with a 55-mph speed limit. The weighted average gap accepted using the Raff/Hart method and the logit 50th percentile was calculated and is also listed in Table 44. These findings are also illustrated in Figure 20. The relationship between posted speed limits from the field studies is similar to the finding from the simulator study—smaller gaps are accepted at the higher posted speed sites. The difference is on the order of 1.0 to 1.5 sec. The average gaps accepted from the field studies were smaller than the simulator study, which could be a reflection of the more ideal situation for drivers in a simulator (e.g., lack of pressure to make a gap decision from other drivers, no need to rush to a destination for an appointment, etc.). Gap acceptance at the field study sites was also examined by crossing distance. Logically, a driver would want a longer gap to cross additional pavement. Figure 21 shows the gap acceptance for each site by crossing distance. An apparent trend of larger gaps for greater distances or even the inverse is not evident in Figure 21. Weighted averages were calculated for four groups: • One lane (11 to 12 ft), • Wide one lane (17 to 20 ft), • Narrow two lanes or very wide one lane (20.5 to 23.5 ft), and • Two lanes or very wide one lane (24 to 27 ft). The weighted averages are illustrated in Figure 22. The results using the Raff/Hart method or the logit 85th percentile were as expected. Gap acceptance values increase as the crossing width increases, although only by a small amount (less than 1 sec between the one-lane group and the two-lane or very-wide-one-lane group). The logit 50th percentile group showed a contrary relationship with smaller gaps for wider crossing distances.

79 Figure 20. Plot of median gap acceptance for 25-mph and 55-mph sites from this field study and Yan et al. (76). Figure 21. Gap acceptance result by crossing distance for field study sites. 4 5 6 7 8 9 10 11 12 25 mph, female, simulator 25 mph, male, simulator 25 mph, 440 veh, 3 field sites 55 mph, female, simulator 55 mph, male, simulator 55 mph, 447 veh, 3 field sites G ap (s ec ) Groups Young (Yan et al.) Middle (Yan et al.) Old (Yan et al.) Raff/Hart (this study) Logit 50th Percentile (this study) 0 2 4 6 8 10 12 14 10 12 14 16 18 20 22 24 26 28 G ap (s ec ) Crossing Distance (ft) Raff/Hart Logit 50th Percentile Logit 85th Percentile

80 Figure 22. Gap acceptance result by crossing distance group for field study sites. 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 1 lane (11 to 12 ft) Wide 1 lane (17 to 20 ft) Narrow 2 lanes or very wide 1 lane (20.5 to 25 ft) 2 lanes (24 to 27 ft) W ei gh te d A ve ra ge G ap ( se c) Raff/Hart Gap Value Logit 50th Percentile Logit 85th Percentile