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Table 15. Summary statistics for headway and time gap data for I-80 at S. Expressway WB — Table 15 Summary statistics for headway and time gap data for I-80 at S. Expressway WB

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Table 1. Measures of effectiveness related to sensitivity analysis Importance of Standstill Distance and Headway

Figure 1. Wavetronix SmartSensor HD

Figure 2. Example of Wavetronix detector and camera setup

Figure 5. Wavetronix setup north of I-235 at 73rd St. (Lane 1 is a weaving lane)

Figure 11. Wavetronix setup at I-74 at Middle Rd. (Lane 1 is an exit, Lane 6 is an entrance)

Figure 12. Wavetronix setup at I-74 at Spruce Hills Dr. (Lane 5 is an entrance)

Figure 14. Wavetronix setup at I-80 at S. Expressway (Lane 1 is an entrance, Lane 7 is an exit)

Figure 15. Example of an image processed for standstill distance measurements Finally, the vanishing point filter option in Photoshop CC 2014 was used to find the actual bumper-to-bumper standstill distance measurements. The vanishing point filter allows the user to create a flat plane on which measurements are to be made. If there is an object or a mark of known length in the established plane, that reference point can be used to create a baseline measurement that Photoshop uses to measure anything else in that plane. In the case of this research, the painted lane lines were used as the baseline measurement. The standard for painted lane lines on freeways is that they be 10 feet in length, and they are painted using an automated system. Google Earth was used to measure these lines and confirm that they meet the 10 foot standard. An example of one fully processed image is shown in Figure 15.

Table 2. Des Moines Wavetronix detector accuracy summary (first collection period)

Overall, the total Wavetronix detector counts were within | to 9 percent of the manual video counts, with the exception of the detectors on I-235, which counted half as much traffic as was actually present. These differences could have been due to an issue with how the detectors were set up at those locations; whatever the cause, the I-235 locations were excluded from the analysis. The lane assignments and vehicle class assignments were also generally within | to 4 percent of reality, and often less than | percent off. Where temporary setups were used, nearby Iowa DOT sensors were also used to further validate the temporary setup counts. Examples of visual comparisons including all three data sources are shown in Figure 16 through Figure 18.

Figure 16. Example of visual comparison of lane proportions (NB I-35/80 at Hickman, September 18, 5:00 to 5:30 p.m.)

Figure 17. Example of visual comparison of five-minute counts (NB I-35/80 at Hickman, September 18, 5:00 to 5:30 p.m.)

Figure 18. Example of visual comparison of lane proportions (NB I-35/80 at Hickman, September 18, 5:00 to 5:30 p.m.)

Table 4. I-74 at Spruce Hills Drive Wavetronix detector accuracy

Figure 19. Histogram comparing individual vehicle headways from manual count and Wavetronix detectors

Table 6. Rural I-80 west of Quad Cities Wavetronix detector accuracy

Figure 20. Example of Photoshop accuracy test image using 2 in. x 2 in. squares in a grid pattern

Figure 21. Example of a histogram of vehicle length (taken from I-80/35 NB at Hickman) While the Wavetronix detector assigns each vehicle to one of seven vehicle classes based on its length, this research was focused only on comparing passenger cars with trucks. It was therefore necessary to define a threshold length to distinguish between cars and trucks. With any chosen length, there is always some overlap in the types of vehicles and the capabilities included in each eroup. In particular, small trucks can sometimes behave as cars and other times as larger trucks. So, with that in mind, 35 feet was the length cutoff selected because the Iowa DOT uses four classes for its permanent sensors (O—10 feet, 10-19 feet, 19-35 feet, and 35—256 feet). Additionally, the distribution of vehicle lengths was observed through histograms. These revealed two distinct peaks, one for cars (which small trucks spill into) and a much smaller one for large trucks (see an example in Figure 21).

FHWA Office of Operations. 2013. Traffic Control Systems Handbook: Chapter 3. Control Concepts - Urban an Suburban Streets. ops.fhwa.dot.gov/publications/fhwahop06006/chapter_3p1.htm The headway analysis itself consisted in part of calculating the headway and time gap for each vehicle pair, defining cars versus trucks, defining a maximum headway threshold for car following, filtering the data to congested conditions and following vehicles only, fitting statistical distributions to the data, finding summary statistics for the headway for each following combination for each site, and comparing all the results. It should be noted that headway and time gap are two different variables. Headway is the time between successive vehicles measured from the same point on each vehicle (the front bumper in the case of the Wavetronix data). Time gap is the time from the back bumper of the leading vehicle to the front bumper of the following vehicle, as shown in Figure 22. Thus, a car can be following another car with the same headway as a car following a truck, but due to the length of the truck, the car following the truck will have the shorter time gap.

One important note about the raw data is that not all vehicles are assigned a speed by the detecto due to an internal quality control mechanism. Because the speed of the leading vehicle is required to calculate the time gap, only vehicle pairs in which the leading vehicle had an assigned speed were used in the analysis. The analysis of these data was broken up into four main parts: headway and time gap calculation, vehicle class threshold determination, vehicle following determination/filtering, and headway and time gap distribution analysis. The overall process from data collection to analysis is shown in the flowchart in Figure 24. Headway and Time Gap Calculation

Figure 25. Correlation of leading and following vehicle speeds versus headway (from I-80 at S. Expressway) It can be seen from the graph that leading and following vehicle speeds are highly correlated at small values of headway, and that as the headway increases, the correlation decreases. This

Table 8. Summary of detectors used in the analysis Due to the data validation process as well as the filtering process, the data from several detectors were excluded from the analysis. Regarding data validation, both Wavetronix detectors placed on I-235 in Des Moines counted around half as many vehicles as were counted manually, so the data obtained from these detectors were not used. Additionally, it was determined that in order to filter the data to mostly following vehicles, only through lane headways of four seconds or less and headways observed during a period of time when the 15 minute through vehicle flow rate exceeded 1,000 veh/hr/In would be used. This filtering completely eliminated the detector on I- 74 at the Spruce Hills Drive exit in the Quad Cities because it was not operating for long and the flow rate never exceeded 1,000 veh/hr/In. Limited high-traffic intervals also significantly reduced the sample size of the other two locations in the Quad Cities area (I-74 at the Middle Road exit and the rural location on I-80 west of the Quad Cities). Finally, for consistency’s sake, the same data set was used for analyzing the headways and time gaps for each detector; this required that both the leading and following vehicle had a speed measured by the detector. For most detectors, at least 60 to 70 percent of vehicles had speeds, but the detector on I-80/35 southbound at the Hickman Road entrance only had speeds for 17 percent of vehicles (and only 2 percent of through vehicles). The percentages of vehicles with speeds and the detectors that were excluded are summarized in Table 8.

Figure 26. Average headway versus flow rates for headways less than 4 seconds

Figure 27. Average time gap versus flow rates for headways less than 4 seconds

Table 9. Headway and time gap summary statistics for I-80/35 SB at University Table 10. Headway and time gap summary statistics for I-80/35 NB at University

Table 11. Headway and time gap summary statistics for I-80/35 NB at Hickman

When comparing the means, t-tests were not used because the large sample sizes led to a situation where differences in headways that are within the error of the detector were rejected by the t-test as being significantly different. For example, the mean difference of headways from car following car (CC) between I-80/35 southbound at University Avenue (in Table 9) and I-80/35 northbound at University Avenue (in Table 11) is only 3 hundredths of a second, but the sample size leads the t-test to conclude that they are different, with a p-value of 2.586x10°. This is not always the case; because observations involving trucks are less frequent, this phenomena of “false rejections” is less common outside the CC observations. For the sake of consistency, however, all comparisons were made assuming that a practical difference of headway or time gap is one tenth (0.1) of a second. The selection of the 0.1 second value was based on the measurement error of the Wavetronix detector. While it was not possible to validate the accuracy of the time stamp for individual vehicles, the average of individual headways was found to differ by 0.03 seconds from a manual measurement for a 10 minute peak period at the I-80/35 northbound location at Hickman Road. Because this was a relatively short period, the true error

The maximum difference between any two values was only 0.17 seconds. The closeness of these summary statistics indicates that there are not practical differences in headway and time gap values at these sites with the same driver populations. This means that the preferred headway and time gap should be fairly consistent throughout Des Moines, unless there are significantly different roadway geometries or other factors. The summary statistics of the three Des Moines locations combined are presented in Table 13. In all, 9 out of 48 comparisons fell outside 0.1 seconds of each other, and most of those were nc far out of that range, which is summarized in Table 12.

Table 13. Summary statistics for headway and time gap data for Des Moines overall

Table 14. Summary statistics for headway and time gap data for I-80 at S. Expressway EB

Because the westbound traffic had so many more observations meeting the filtering criteria, the overall statistics are essentially the same as the westbound statistics. These values are similar to the values found in Des Moines, though a few measurement differences were outside of 0.1 seconds. For CT, the mean headway difference was 0.12 seconds, the median headway difference was ().12 seconds, the mean time gap difference was 0.13 seconds, and the median time gap difference was 0.11 seconds. For TT, the mean headway difference was 0.17 seconds, the median headway difference was 0.13 seconds, and the median time gap difference was 0.11 seconds. While it seems like a lot of measurements are off, they are not substantially more than the threshold for the most part, and the biggest difference is still only 0.17 seconds. Despite this difference in traffic operation and sample size, the summary statistics are quite similar between the two directions. The differences in measurements were less than 0.1 seconds for the mean and median headway and time gap values for CC, TC, and TT. For CT, the mean headway was off by 0.14, the median headway was off by 0.38, the mean time gap was off by 0.16, and the median time gap was off by 0.38. It is interesting that the means are not much different than the 0.1 second threshold while the medians are both off by 0.38 seconds (lower for the westbound traffic). Overall, it appears that there is enough evidence to support the finding in Des Moines that headway and time gap values do not vary much when considering the same driver population faced with different geometries. This is especially true if the focus is narrowed to only mean values, because the median values have been shown to be more volatile when comparing sites.

Table 17. Summary statistics for headway and time gap data for I-74 at Middle Road It should be noted that only 10 instances of TT pairs meeting the filtering criteria were observed by this detector, which is not a large enough sample size to judge its similarity to the other locations. However, it is still included in the table for the sake of consistency and completeness. The numbers of CT and TC pairs observed were also fairly low but were still substantial enough to get an idea of the true measurements. In order to be 95% confident that the true mean is within +0.2 seconds of the estimated mean, at least 78 observations are necessary, according to the sample size formula based on the normal distribution and using a standard deviation of 0.9, which was observed at this site and others.

Figure 28. Truck length histograms for the three urban areas This consistent difference in time gaps but not headways could be due to various reasons. First, it could just be a result of the small sample size. However, none of the other measurements differec much from the other two locations, and they were consistently off by about the same amount, so this does not appear to be the most likely explanation. The most likely explanation is that there is a higher percentage of small trucks on I-74 compared to the locations in Des Moines and Council Bluffs. Cars may interact with these smaller trucks differently than they interact with 18 wheelers. If cars do interact differently with smaller trucks and these vehicles are present in different proportions, this could affect the overall average, because both smaller and larger trucks are considered trucks by this analysis. It appears that this could be the case, as evidenced by the histograms of vehicle length, in which the Quad Cities location clearly has more small trucks than the other locations (see Figure 28).

Figure 30. Histogram of unfiltered standstill distances

Figure 31. Flowchart for standstill distance analysis

Table 18. Summary of standstill distance by city It is interesting that the means are generally around 10 to 12.5 feet, except for those in Des Moines and Iowa City, but Iowa City only has 11 observations. However, the data from Ames, Cedar Rapids, and Council Bluffs were also limited. Therefore, the statistical analysis focused on only the top three cities: Des Moines, the Quad Cities, and Sioux City. The histograms for these three cities are presented in Figure 32.

* for 95% confidence, ** for 99%, *** for 99.9% Table 19. P-values for t-tests for mean standstill distance comparisons by city

Figure 33. Square root of standstill distance histograms by city The t-test comparisons resulted in the p-values reported in Table 19.

Table 20. Number of incidents resulting from different causes by city

Table 21. Summary of standstill distances for Des Moines by cause of incident

* for 95% confidence, ** for 99%, *** for 99.9% Table 22. P-values for t-tests for mean standstill distance comparisons by incident cause for Des Moines

Table 24. P-values for t-tests for mean standstill distance comparisons by incident cause for the Quad Cities

* for 95% confidence, ** for 99%, *** for 99.9% In Des Moines, the only statistically significant result is the extremely marginally significant comparison (p-value of 0.0499) between slow traffic and unknown cause, which does not have a strong interpretation. The Quad Cities data, however, show a highly significant difference between construction and slow traffic and between construction and stalled vehicle.

Table 25. Summary of standstill distance by vehicle pair type An initial look at the summary statistics seems to indicate that vehicle pairs involving a truck tend to have larger standstill distances. To evaluate this impression statistically, t-tests were used. Though the smaller datasets for CT, TC, and TT make it difficult to assess the normality of their distributions, it can be seen in the overall distribution that the data are skewed and can be made more symmetric by taking the square root of the distances. Applying this procedure to the The summary statistics for standstill distance for each vehicle pair type are presented in Table 25.

* for 95% confidence, ** for 99%, *** for 99.9%

Table 27. Number of observations of each pair type in each city Every city contributes something to each pair type, and Des Moines contributes fairly evenly across the different pair types. About 58 percent of CC observations are from Des Moines, and about 33 percent of CT and TC observations are from Des Moines. While these numbers are somewhat unbalanced, they are much more balanced than most of the incident-based variables described subsequently. These results were not likely to be overly influenced by the Des Moines data, as some of the other incident-based variables, because the data were fairly well spread out throughout the different cities, as seen in Table 27.

Table 28. Summary of standstill distance by lighting conditions The summary statistics for standstill distance for each lighting condition (day or night) are shown in Table 28.

Table 29. Summary of standstill distance by weather conditions The weather conditions were observed from the video of each incident. Due to the small samp. size and the lack of a theoretical basis for a difference in standstill distance between clear and cloudy conditions, the data for these conditions were combined and compared to the rainy condition data using a t-test. Again, this t-test was conducted on the square roots of the measurements. This test resulted in a p-value of 0.0884, which means that there is not a statistically significant difference with a minimum confidence level of 95%. Even if the distan had been found to be significantly significant, it would have to be taken with a grain of salt, again because of the sample size and coverage. All three incidents involving rain occurred in L Moines.

Table 30. Summary of standstill distance by curve presence

Table 31. Summary of standstill distance by cause

for 95% confidence, ** for 99%, *** for 99.9% However, caution should be used when interpreting these results due to the unbalanced nature of the data. Because Des Moines yielded so many more observations than the other cities and appears to have consistently lower standstill distances than other cities, the influence on the means of other variables can be large.

Table 34. Summary of standstill distances for incidents caused by construction for each city

Table 36. Summary of standstill distances for incidents caused by a stalled vehicle for each city

Figure 34. Average speed on weekdays The weaving segment located in the southbound direction of I-80/35 between Hickman Road and University Avenue was modeled as a case study. As is common in modeling practice to achieve realistic outputs, the network model was extended to one mile north and one mile south of the study segment. The layout of the study area as it was modeled is shown in Figure 35. This location is part of the greater Des Moines metropolitan area and experiences considerable traffic congestion during peak hours due to a large amount of commuters using I-80/35 and the adjacent roads. Figure 34 plots the speeds measured by the Wavetronix detectors on different work days. Recurrent congestion is observed between 5:15 p.m. and 5:30 p.m., when speeds drop to almost half of the speed limit. The geometric characteristics of the network, including the number of lanes, lane widths, link lengths, and levels were coded in VISSIM version 7 using the Microsoft Bing Maps live map feature. In addition, lane width and length were verified with Google Earth Pro because previous studies indicated that Google Earth positional images were accurate for assessing horizontal positions (Potere 2008).

Figure 35. Case study network coded in VISSIM

Figure 36. Cumulative distribution of free flow speed

Figure 38. Screenshot of video monitoring for vehicle count and vehicle composition

Figure 39. Screenshot of video monitoring for weaving percentage

Figure 40. Speed comparison between simulator outputs and field data

Figure 41. Flow density comparison

Figure 42. Difference between CC1 and headway

Figure 43. Flow density plot by varying standstill distance As shown in Figure 43 through Figure 51, changing all driver behavior parameters except for the headway does not have a significant effect on the dispersion of the data.

Figure 44. Flow density plot by varying headway

Figure 45. Flow density plot by varying following variation

Figure 47. Flow density plot by varying following thresholds

Figure 48. Flow density plot by varying speed dependency oscillation

Figure 49. Flow density plot by varying oscillation acceleration

Figure 50. Flow density plot by varying standstill acceleration

Figure 51. Flow density plot by varying acceleration with 50 mph

Figure 52. Speed comparison between the observed data, calibrated simulation data, and default simulation data

Figure 54. Flow density plot comparison between the observed data, calibrated simulation data, and default simulation data

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