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52 increase in speed; however, the average compliance rates are not the 0.10 level) in predicting treatment compliance when statistically different. In other words, the performance at these accounting for interaction between other model variables. two devices is independent of the posted speed limit. The per- formance of the overhead flashing beacons (passive activation) Gap Acceptance shows a statistically different compliance rate between the device on the 30-mph (48-km/h) roadway and the device on the This section summarizes the findings on characteristics of 35-mph (55-km/h) roadway, with the device on the higher- gap acceptance behavior as observed at the field study sites. speed roadway having a higher compliance rate. Reviewing the Appendix N contains more discussion and findings. specific sites showed that the 30-mph (48-km/h) site was in a The analysis of gap acceptance data had two components: commercial area while the 35-mph (55-km/h) site was in a res- behavioral analysis and statistical analysis. The former was idential area. Given that other devices show a decrease in com- concerned with identifying actions and patterns that pedes- pliance with an increase in speed limit, the findings for overhead trians commonly use in crossing events. The latter was flashing beacons (pushbutton activation) may be an anomaly. intended to provide a mathematical model to determine gap The median refuge island and high-visibility marking sites size for a proportion of the crossing population. all had decreases in compliance rates with increases in speed limit. The F-statistical tests revealed that the compliance rates Behavioral Analysis were statistically different, which indicates that the speed limit affects the performance of the device. Flags, refuge Specific behavioral patterns affect how data are presented. islands, and high-visibility markings all perform better on the One particular pattern is the concept of the "rolling gap." Dur- lower-speed roadways. ing data reduction, gap lengths were measured based on the Figure 26 shows a clear break between two groups of treat- times when vehicles entered the crosswalk. At certain sites, ments at the 35-mph (55-km/h) speed limit. The most effec- particularly sites with high volumes of traffic, pedestrians did tive treatments are all red signal or beacon devices. On a not wait to cross the street when all lanes were completely 35-mph (55-km/h) roadway, the best compliance rate clear. Rather, they anticipated that the lanes would clear as they observed for a treatment not showing a red indication to the crossed and used a "rolling gap" to cross the street; essentially, motorist is about 63 percent. Compliance rates go as low as 8 there was a separate gap for each lane of traffic that occurred percent for the 35-mph (55-km/h) speed limit group. For the to coincide with the pedestrian's path across the street. 25-mph (40-km/h) speed limit roadways, all the devices have For example, consider the conditions presented in Figure 27. a high compliance (greater than 60 percent). There is not a sufficient gap for the pedestrian to cross the The statistical analysis of covariance also indicated that the entire two-lane segment from the curb to the median between posted speed limit was a statistically significant variable (at approaching vehicles because the traffic volumes are too high B C Acceptable A Opening Figure 27. Pedestrian waiting to cross at crosswalk with high traffic volumes.
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53 and are distributed between both lanes. In the "rolling gap"sce- Each roadway approach was considered individually in the nario, the pedestrian would begin the crossing maneuver when analysis; that is, each site was analyzed separately, and if the the acceptable opening between vehicles A and C occurred in roadway was divided at that site, each side of the roadway the near (curb) lane, even though a second vehicle (vehicle B) had a unique analysis. As a result, 47 distinct analyses were might be approaching in the adjacent lane. However, by the performed, in addition to an overall analysis of all gaps for time the pedestrian reaches the adjacent lane, vehicle B has reference. already passed through the crosswalk, leaving an open lane to From these analyses, graphs were generated showing the complete the crossing. After this, another approaching vehicle cumulative distribution of pedestrians accepting gaps of in the curb lane (vehicle C) might enter the crosswalk, giving various lengths. Figure 28 shows an example of this type of the appearance that the actual gap was very small; but if the graph. The data from some sites did not meet the conver- pedestrian properly timed the crossing, the gap is acceptable to gence criterion. For the logistic model to run successfully, the pedestrian at a comfortable walking speed. the values of accepted and rejected gaps must overlap, that CA-LA-2 is a four-lane divided roadway with a configura- is, there should be a gap length (or small range of gap tion similar to that shown in Figure 27. Under these condi- lengths) that was both accepted and rejected. At sites with tions, there is essentially a separate available gap for each lane no overlap in values, the maximum likelihood estimate did that the pedestrian decides to accept or reject. Those gaps may not converge, but SAS continued with the analysis and or may not begin or end at the same time, but they occur in matched a function. Under these conditions, the function such a way that, when taken together, they create a combined does not have the smooth S-curve as shown in Figure 28 but gap sufficient for the pedestrian to cross the entire segment. rather resembles a step function, with a straight (and very Of the 66 accepted gaps at the CA-LA-2 study site, 60 percent steep) line between the values of the longest gap rejected and (39 accepted gaps) were "rolling gaps." the shortest gap accepted. The results obtained from these functions have a lower level of confidence than the functions where the maximum likelihood estimate existed. This con- Statistical Analysis dition is explained in further detail in Appendix N. The The Statistical Analysis Software (SAS) computer pro- complete set of results from the SAS logistical analysis is gram was used to conduct a logit transformation analysis. shown in Table 23. 100% 90% 80% 70% Percentage Accepting Gap 60% 50% 40% 30% 20% 10% 0% 0 2 4 6 8 10 12 14 16 Gap (s) Figure 28. Sample cumulative distribution of gap acceptance.
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54 Table 23. Result of SAS logistic analysis for approaches with more than 20 pedestrians. Maximum 50th 85th Likelihood Percentile Percentile Number of Estimate Site Approach '(x) Gap (s) Gap (s) Pedestrians Converges? CA-LA-2 NB 1/SB 2 5.0462-0.8193x 6.2 8.3 34 Y CA-LA-2 NB 2/SB 1 7.9928-1.5001x 5.3 6.5 32 Y CA-SM-2 NB 1/SB 2 12.6355-2.4996x 5.1 5.8 40 Y CA-SM-2 NB 2/SB 1 37.0931-7.2800x 5.1 5.3 30 N CA-SM-3 NB 1/SB 2 6.9634-1.1879x 5.9 7.3 31 Y CA-SM-3 NB 2/SB 1 11.8970-2.0942x 5.7 6.5 29 Y MD-P1 NB 2/SB 1 65.1435-10.6485x 6.2 6.3 21 N MD-TO-1 NB 6.7212-0.9039x 7.4 9.4 22 Y MD-TO-1 SB 14.4907-1.7604x 8.2 9.2 34 Y UT-SL-2 NB 6.2673-1.2341x 5.1 6.5 22 Y WA-KI-3 WB 42.176-8.7008x 4.8 5.0 22 N ALL Sites and Approaches 6.2064-0.9420x 6.6 8.4 512 Y Findings section above. If there is separation of data, the maximum likelihood estimate does not converge; however, SAS will still Several elements can affect the size of the 85th percentile provide an output, which will often have a very large standard accepted gap. First, the amount of data can have a significant error. An example is the NB2/SB1 approach of CA-SM-2, effect, especially when only a few pedestrians were faced with which had 125 observed gaps. An examination of the data making a gap acceptance decision. To minimize the potential reveals that almost all gaps between 1 and 5 seconds were effect that only a few pedestrians could have on the results, rejected (one 5-second gap was accepted), and all the gaps only those approaches with more than 20 pedestrians on the approach were considered in this evaluation. above 5 seconds were accepted. The logit model tries to match Second, the distribution of the data can affect the analysis these data with an equation, but because of the complete sep- of a large number of data points. At the NB2/SB1 approach of aration for the accepted and rejected gaps, the equation CA-LA-2, there were 241 observed gaps but only 32 pedestri- almost forms a straight vertical line between 5 and 6 seconds ans. Out of these 241 gaps, 196 required the pedestrian to where no data exist. make a gap acceptance decision on a gap of 3 seconds or less Table 24 lists those approaches whose distribution has sep- while only 10 were gaps of longer than 10 seconds. With such aration of data. This table shows the values of the longest gaps dense traffic, the gap acceptance was skewed lower. The gap rejected by at least 85 percent of pedestrians and of the short- acceptance results would be stronger if based only on free- est gaps accepted by at least 85 percent of pedestrians. flow vehicles; however, using only free-flow vehicles does not Results from the logit model indicate a trend in the 85th capture the conditions faced by the pedestrian. When the percentile accepted gaps, in that the accepted gap increased as location is within a coordinated corridor, the pedestrian may crossing distance increased. The trend for the 85th percentile ignore the gaps within the platoons of vehicles and wait for accepted gap is compared with the critical gap for a walking the larger gap present between the platoons. speed of 3.5 ft/s (1.1 m/s) in Figure 23. Inspection of Figure Third, the lack of some overlap in the accepted and rejected 29 reveals that the observed gaps were less than the calculated gaps is an important factor, as mentioned in the analysis critical gap for a walking speed of 3.5 ft/s (1.1 m/s). Thus, the Table 24. Summary of gap distribution for approaches with separation of data. Value of Longest Rejected Value of Shortest Accepted Site Approach Gap (s) Gap (s) CA-SM-2 NB 1/SB 2 4.0 6.0 CA-SM-2 NB 2/SB 1 5.0 6.0 CA-SM-3 NB 2/SB 1 4.0 7.0 MD-P1 NB 2/SB 1 6.0 7.0 MD-TO-1 SB 7.0 10.0 WA-KI-3 WB 4.0 6.0